Help for package Rwave

Version:

2.6-5

Date:

2022-10-18

Title:

Time-Frequency Analysis of 1-D Signals

Author:

Rene Carmona [aut], Bruno Torresani [aut], Brandon Whitcher [ctb], Andrea Wang [ctb], Wen-Liang Hwang [ctb], Robert Alberts [ctb], Jonathan M. Lees [ctb, cre]

Maintainer:

Jonathan M. Lees <jonathan.lees@unc.edu>

Depends:

R (≥ 2.14)

Description:

A set of R functions which provide an environment for the Time-Frequency analysis of 1-D signals (and especially for the wavelet and Gabor transforms of noisy signals). It was originally written for Splus by Rene Carmona, Bruno Torresani, and Wen L. Hwang, first at the University of California at Irvine and then at Princeton University. Credit should also be given to Andrea Wang whose functions on the dyadic wavelet transform are included. Rwave is based on the book: "Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S", by Rene Carmona, Wen L. Hwang and Bruno Torresani (1998, eBook ISBN:978008053942), Academic Press.

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

University of California

URL:

https://carmona.princeton.edu/TFbook/tfbook.html, https://r-forge.r-project.org/projects/rwave/

Packaged:

2022-10-20 16:53:19 UTC; lees

Repository:

CRAN

Date/Publication:

2022-10-21 23:17:49 UTC

NeedsCompilation:

yes

Transient Signal

Description

Transient signal.

Usage

data(A0)

Format

A vector containing 1024 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(A0)
plot.ts(A0)

Transient Signal

Description

Transient signal.

Usage

data(A4)

Format

A vector containing 1024 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(A4)
plot.ts(A4)

Transient Signal

Description

Transient signal.

Usage

data(B0)

Format

A vector containing 1024 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(B0)
plot.ts(B0)

Transient Signal

Description

Transient signal.

Usage

data(B4)

Format

A vector containing 1024 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(B4)
plot.ts(B4)

Transient Signal

Description

Transient signal.

Usage

data(C0)

Format

A vector containing 1024 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(C0)
plot.ts(C0)

Transient Signal

Description

Transient signal.

Usage

data(C4)

Format

A vector containing 1024 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(C4)
plot.ts(C4)

Transient Signal

Description

Transient signal.

Usage

data(D0)

Format

A vector containing 1024 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(D0)
plot.ts(D0)

Transient Signal

Description

Transient signal.

Usage

data(D4)

Format

A vector containing 1024 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(D4)
plot.ts(D4)

Continuous Wavelet Transform with derivative of Gaussian

Description

Computes the continuous wavelet transform with for (complex-valued) derivative of Gaussian wavelets.

Usage

DOG(input, noctave, nvoice=1, moments, twoD=TRUE, plot=TRUE)

Arguments

input

input signal (possibly complex-valued).

noctave

number of powers of 2 for the scale variable.

moments

number of vanishing moments of the wavelet (order of the derivative).

nvoice

number of scales in each octave (i.e. between two consecutive powers of 2)

twoD

logical variable set to T to organize the output as a 2D array (signal_size x nb_scales), otherwise, the output is a 3D array (signal_size x noctave x nvoice)

plot

if set to T, display the modulus of the continuous wavelet transform on the graphic device

Details

The output contains the (complex) values of the wavelet transform of the input signal. The format of the output can be

2D array (signal_size x nb_scales)

3D array (signal_size x noctave x nvoice)

Value

continuous (complex) wavelet transform

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Examples

 x <- 1:512
    chirp <- sin(2*pi * (x + 0.002 * (x-256)^2 ) / 16)
  
 DOG(chirp, noctave=5, nvoice=12, 3, twoD=TRUE, plot=TRUE)

Heart Rate Data

Description

Successive beat-to-beat intervals for a normal patient.

Usage

data(Ekg)

Format

A vector containing 16,042 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples

data(Ekg)
plot.ts(Ekg)

How Are You?

Description

Example of speech signal.

Usage

data(HOWAREYOU)

Format

A vector containing 5151 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(HOWAREYOU)
plot.ts(HOWAREYOU)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(HeartRate)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942), eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(HeartRate)
plot.ts(HeartRate)

Sampling Gabor Ridge

Description

Given a ridge phi (for the Gabor transform), returns a (regularly) subsampled version of length nbnodes.

Usage

RidgeSampling(phi, nbnodes)

Arguments

phi

ridge (1D array).

nbnodes

number of samples.

Details

Gabor ridges are sampled uniformly.

Value

Returns a list containing the discrete values of the ridge.

node

time coordinates of the ridge samples.

phinode

frequency coordinates of the ridge samples.

References

See discussions in the text of "Time-Frequency Analysis”.

Singular Value Decomposition

Description

Computes singular value decomposition of a matrix.

Usage

SVD(a)

Arguments

a

input matrix.

Details

R interface for Numerical Recipes singular value decomposition routine.

Value

a structure containing the 3 matrices of the singular value decomposition of the input.

References

See discussions in the text of “Time-Frequency Analysis”.

Examples

   hilbert <- function(n) { i <- 1:n; 1 / outer(i - 1, i, "+") }
     X <- hilbert(6)
     z  = SVD(X)
     z

Undocumented Functions in Rwave

Description

Numerous functions were not documented in the original Swave help files.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Wigner-Ville function

Description

Compute the Wigner-Ville transform, without any smoothing.

Usage

WV(input, nvoice, freqstep = (1/nvoice), plot = TRUE)

Arguments

input

input signal (possibly complex-valued)

nvoice

number of frequency bands

freqstep

sampling rate for the frequency axis

plot

if set to TRUE, displays the modulus of CWT on the graphic device.

Value

(complex) Wigner-Ville transform.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(W_tilda.1)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Examples


data(W_tilda.1)
plot.ts(W_tilda.1)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(W_tilda.2)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Examples


data(W_tilda.2)
plot.ts(W_tilda.2)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(W_tilda.3)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Examples


data(W_tilda.3)
plot.ts(W_tilda.3)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(W_tilda.4)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Examples


data(W_tilda.4)
plot.ts(W_tilda.4)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(W_tilda.5)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Examples


data(W_tilda.5)
plot.ts(W_tilda.5)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(W_tilda.6)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Examples


data(W_tilda.6)
plot.ts(W_tilda.6)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(W_tilda.7)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Examples


data(W_tilda.7)
plot.ts(W_tilda.7)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(W_tilda.8)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Examples


data(W_tilda.8)
plot.ts(W_tilda.8)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(W_tilda.9)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Examples


data(W_tilda.9)
plot.ts(W_tilda.9)

Logarithms of the Prices of Japanese Yen

Description

Logarithms of the prices of a contract of Japanese yen.

Usage

data(YN)

Format

A vector containing 500 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(YN)
plot.ts(YN)

Daily differences of Japanese Yen

Description

Daily differences of YN.

Usage

data(YNdiff)

Format

A vector containing 499 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(YNdiff)
plot.ts(YNdiff)

Zero Padding

Description

Add zeros to the end of the data if necessary so that its length is a power of 2. It returns the data with zeros added if nessary and the length of the adjusted data.

Usage

adjust.length(inputdata)

Arguments

inputdata

either a text file or an S object containing data.

Value

Zero-padded 1D array.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(amber7)

Format

A vector containing 7000 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(amber7)
plot.ts(amber7)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(amber8)

Format

A vector containing 7000 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(amber8)
plot.ts(amber8)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(amber9)

Format

A vector containing 7000 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(amber9)
plot.ts(amber9)

Acoustic Returns

Description

Acoustic returns from natural underwater clutter.

Usage

data(back1.000)

Format

A vector containing 7936 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(back1.000)
plot.ts(back1.000)

Acoustic Returns

Description

Acoustic returns from ...

Usage

data(back1.180)

Format

A vector containing 7936 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(back1.180)
plot.ts(back1.180)

Acoustic Returns

Description

Acoustic returns from an underwater metallic object.

Usage

data(back1.220)

Format

A vector containing 7936 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(back1.220)
plot.ts(back1.220)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(backscatter.1.000)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(backscatter.1.000)
plot.ts(backscatter.1.000)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(backscatter.1.180)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(backscatter.1.180)
plot.ts(backscatter.1.180)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(backscatter.1.220)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(backscatter.1.220)
plot.ts(backscatter.1.220)

Ridge Chaining Procedure

Description

Chains the ridge estimates produced by the function crc.

Usage

cfamily(ccridge, bstep=1, nbchain=100, ptile=0.05)

Arguments

ccridge

unchained ridge set as the output of the function crc

bstep

maximal length for a gap in a ridge.

nbchain

maximal number of chains produced by the function.

ptile

relative threshold for the ridges.

Details

crc returns a measure in time-frequency (or time-scale) space. cfamily turns it into a series of one-dimensional objects (ridges). The measure is first thresholded, with a relative threshold value set to the input parameter ptile. During the chaining procedure, gaps within a given ridge are allowed and filled in. The maximal length of such gaps is the input parameter bstep.

Value

Returns the results of the chaining algorithm

ordered map

image containing the ridges (displayed with different colors)

chain

2D array containing the chained ridges, according to the chain data structure
chain[,1]: first point of the ridge
chain[,2]: length of the chain
chain[,3:(chain[,2]+2)]: values of the ridge

nbchain

number of chains produced by the algorithm

References

See discussion in text of “Practical Time-Frequency Analysis”.

Examples


## Not run: 
   data(HOWAREYOU)
 plot.ts(HOWAREYOU)
 
cgtHOWAREYOU <- cgt(HOWAREYOU,70,0.01,100)

clHOWAREYOU <- crc(Mod(cgtHOWAREYOU),nbclimb=1000)

cfHOWAREYOU <- cfamily(clHOWAREYOU,ptile=0.001)
image(cfHOWAREYOU$ordered > 0)

## End(Not run)

Continuous Gabor Transform

Description

Computes the continuous Gabor transform with Gaussian window.

Usage

cgt(input, nvoice, freqstep=(1/nvoice), scale=1, plot=TRUE)

Arguments

input

input signal (possibly complex-valued).

nvoice

number of frequencies for which gabor transform is to be computed.

freqstep

Sampling rate for the frequency axis.

scale

Size parameter for the window.

plot

logical variable set to TRUE to display the modulus of the continuous gabor transform on the graphic device.

Details

The output contains the (complex) values of the gabor transform of the input signal. The format of the output is a 2D array (signal_size x nb_scales).

Value

continuous (complex) gabor transform (2D array).

Warning

freqstep must be less than 1/nvoice to avoid aliasing. freqstep=1/nvoice corresponds to the Nyquist limit.

References

See discussion in text of “Practical Time-Frequency Analysis”.

Examples

data(HOWAREYOU)
   plot.ts(HOWAREYOU)
 
cgtHOWAREYOU <- cgt(HOWAREYOU,70,0.01,100)

Chen's Chirp

Description

Chen's chirp.

Usage

data(ch)

Format

A vector containing 15,000 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(ch)
plot.ts(ch)

Verify Maximum Resolution

Description

Stop when 2^{maxresoln} is larger than the signal size.

Usage

check.maxresoln(maxresoln, np)

Arguments

maxresoln

number of decomposition scales.

np

signal size.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(chirpm5db.dat)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples

## Not run: 
data(chirpm5db.dat)


## End(Not run)

Threshold Phase based on Modulus

Description

Sets to zero the phase of time-frequency transform when modulus is below a certain value.

Usage

cleanph(tfrep, thresh=0.01, plot=TRUE)

Arguments

tfrep

continuous time-frequency transform (2D array)

thresh

(relative) threshold.

plot

if set to TRUE, displays the maxima of cwt on the graphic device.

Value

thresholded phase (2D array)

References

See discussion in text of “Practical Time-Frequency Analysis”.

Dolphin Click Data

Description

Dolphin click data.

Usage

data(click)

Format

A vector containing 2499 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(click)
plot.ts(click)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(click.asc)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(click.asc)
plot.ts(click.asc)

Ridge Estimation by Corona Method

Description

Estimate a (single) ridge from a time-frequency representation, using the corona method.

Usage

corona(tfrep, guess, tfspec=numeric(dim(tfrep)[2]), subrate=1,
temprate=3, mu=1, lambda=2 * mu, iteration=1000000, seed=-7,
stagnant=20000, costsub=1, plot=TRUE)

Arguments

tfrep

Time-Frequency representation (real valued).

guess

Initial guess for the algorithm.

tfspec

Estimate for the contribution of the noise to modulus.

subrate

Subsampling rate for ridge estimation.

temprate

Initial value of temperature parameter.

mu

Coefficient of the ridge's second derivative in cost function.

lambda

Coefficient of the ridge's derivative in cost function.

iteration

Maximal number of moves.

seed

Initialization of random number generator.

stagnant

Maximum number of stationary iterations before stopping.

costsub

Subsampling of cost function in output.

plot

When set(default), some results will be shown on the display.

Details

To accelerate convergence, it is useful to preprocess modulus before running annealing method. Such a preprocessing (smoothing and subsampling of modulus) is implemented in corona. The parameter subrate specifies the subsampling rate.

Value

Returns the estimated ridge and the cost function.

ridge

1D array (of same length as the signal) containing the ridge.

cost

1D array containing the cost function.

Warning

The returned cost may be a large array, which is time consuming. The argument costsub allows subsampling the cost function.

References

See discussion in text of “Practical Time-Frequency Analysis”.

Ridge Estimation by Modified Corona Method

Description

Estimate a ridge using the modified corona method (modified cost function).

Usage

coronoid(tfrep, guess, tfspec=numeric(dim(tfrep)[2]), subrate=1,
temprate=3, mu=1, lambda=2 * mu, iteration=1000000, seed=-7,
stagnant=20000, costsub=1, plot=TRUE)

Arguments

tfrep

Estimate for the contribution of the noise to modulus.

guess

Initial guess for the algorithm.

tfspec

Estimate for the contribution of the noise to modulus.

subrate

Subsampling rate for ridge estimation.

temprate

Initial value of temperature parameter.

mu

Coefficient of the ridge's derivative in cost function.

lambda

Coefficient of the ridge's second derivative in cost function.

iteration

Maximal number of moves.

seed

Initialization of random number generator.

stagnant

Maximum number of stationary iterations before stopping.

costsub

Subsampling of cost function in output.

plot

When set(default), some results will be shown on the display.

Details

To accelerate convergence, it is useful to preprocess modulus before running annealing method. Such a preprocessing (smoothing and subsampling of modulus) is implemented in coronoid. The parameter subrate specifies the subsampling rate.

Value

Returns the estimated ridge and the cost function.

ridge

1D array (of same length as the signal) containing the ridge.

cost

1D array containing the cost function.

Warning

The returned cost may be a large array. The argument costsub allows subsampling the cost function.

References

See discussion in text of “Practical Time-Frequency Analysis”.

Ridge Extraction by Crazy Climbers

Description

Uses the "crazy climber algorithm" to detect ridges in the modulus of a continuous wavelet or a Gabor transform.

Usage

crc(tfrep, tfspec=numeric(dim(tfrep)[2]), bstep=3, iteration=10000,
rate=0.001, seed=-7, nbclimb=10, flag.int=TRUE, chain=TRUE,
flag.temp=FALSE)

Arguments

tfrep

modulus of the (wavelet or Gabor) transform.

tfspec

numeric vector which gives, for each value of the scale or frequency the expected size of the noise contribution.

bstep

stepsize for random walk of the climbers.

iteration

number of iterations.

rate

initial value of the temperature.

seed

initial value of the random number generator.

nbclimb

number of crazy climbers.

flag.int

if set to TRUE, the weighted occupation measure is computed.

chain

if set to TRUE, chaining of the ridges is done.

flag.temp

if set to TRUE: constant temperature.

Value

Returns a 2D array called beemap containing the (weighted or unweighted) occupation measure (integrated with respect to time)

References

See discussion in text of “Practical Time-Frequency Analysis”.

Examples

   data(HOWAREYOU)
 plot.ts(HOWAREYOU)
 
cgtHOWAREYOU <- cgt(HOWAREYOU,70,0.01,100)

clHOWAREYOU <- crc(Mod(cgtHOWAREYOU),nbclimb=1000)

Crazy Climbers Reconstruction by Penalization

Description

Reconstructs a real valued signal from the output of crc (wavelet case) by minimizing an appropriate quadratic form.

Usage

crcrec(siginput, inputwt, beemap, noct, nvoice, compr, minnbnodes=2,
w0=2 * pi, bstep=5, ptile=0.01, epsilon=0, fast=FALSE, para=5, real=FALSE,
plot=2)

Arguments

siginput

original signal.

inputwt

wavelet transform.

beemap

occupation measure, output of crc.

noct

number of octaves.

nvoice

number of voices per octave.

compr

compression rate for sampling the ridges.

minnbnodes

minimal number of points per ridge.

w0

center frequency of the wavelet.

bstep

size (in the time direction) of the steps for chaining.

ptile

relative threshold of occupation measure.

epsilon

constant in front of the smoothness term in penalty function.

fast

if set to TRUE, uses trapezoidal rule to evaluate $Q_2$.

para

scale parameter for extrapolating the ridges.

real

if set to TRUE, uses only real constraints.

plot

1: displays signal,components,and reconstruction one after another. 2: displays signal, components and reconstruction.

Details

When ptile is high, boundary effects may appeare. para controls extrapolation of the ridge.

Value

Returns a structure containing the following elements:

rec

reconstructed signal.

ordered

image of the ridges (with different colors).

comp

2D array containing the signals reconstructed from ridges.

Display chained ridges

Description

displays a family of chained ridges, output of cfamily.

Usage

crfview(beemap, twod=TRUE)

Arguments

beemap

Family of chained ridges, output of cfamily.

twod

If set to T, displays the ridges as an image. If set to F, displays as a series of curves.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Continuous Wavelet Transform

Description

Computes the continuous wavelet transform with for the (complex-valued) Morlet wavelet.

Usage

cwt(input, noctave, nvoice=1, w0=2 * pi, twoD=TRUE, plot=TRUE)

Arguments

input

input signal (possibly complex-valued)

noctave

number of powers of 2 for the scale variable

nvoice

number of scales in each octave (i.e. between two consecutive powers of 2).

w0

central frequency of the wavelet.

twoD

logical variable set to T to organize the output as a 2D array (signal_size x nb_scales), otherwise, the output is a 3D array (signal_size x noctave x nvoice).

plot

if set to T, display the modulus of the continuous wavelet transform on the graphic device.

Details

The time series is padded with zeroes to avoid problems with circular versus linear convolution. This does not affect usage, as the matrix returned has the added columns removed. (JML Sep 29, 2021).

The output contains the (complex) values of the wavelet transform of the input signal. The format of the output can be

2D array (signal_size x nb_scales)

3D array (signal_size x noctave x nvoice)

Since Morlet's wavelet is not strictly speaking a wavelet (it is not of vanishing integral), artifacts may occur for certain signals.

Value

continuous (complex) wavelet transform

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Examples

    x <- 1:512
    chirp <- sin(2*pi * (x + 0.002 * (x-256)^2 ) / 16)
    retChirp <- cwt(chirp, noctave=5, nvoice=12)

Cauchy's wavelet transform

Description

Compute the continuous wavelet transform with (complex-valued) Cauchy's wavelet.

Usage

cwtTh(input, noctave, nvoice=1, moments, twoD=TRUE, plot=TRUE)

Arguments

input

input signal (possibly complex-valued).

noctave

number of powers of 2 for the scale variable.

nvoice

number of scales in each octave (i.e. between two consecutive powers of 2).

moments

number of vanishing moments.

twoD

logical variable set to T to organize the output as a 2D array (signal size x nb scales), otherwise, the output is a 3D array (signal size x noctave x nvoice).

plot

if set to T, display the modulus of the continuous wavelet transform on the graphic device.

Details

The output contains the (complex) values of the wavelet transform of the input signal. The format of the output can be

2D array (signal size \times nb scales)

3D array (signal size \times noctave \times nvoice)

Value

tmp

continuous (complex) wavelet transform.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Examples

    x <- 1:512
    chirp <- sin(2*pi * (x + 0.002 * (x-256)^2 ) / 16)
    retChirp <- cwtTh(chirp, noctave=5, nvoice=12, moments=20)

Continuous Wavelet Transform Display

Description

Converts the output (modulus or argument) of cwtpolar to a 2D array and displays on the graphic device.

Usage

cwtimage(input)

Arguments

input

3D array containing a continuous wavelet transform

Details

The output contains the (complex) values of the wavelet transform of the input signal. The format of the output can be

2D array (signal_size x nb_scales)

3D array (signal_size x noctave x nvoice)

Value

2D array continuous (complex) wavelet transform

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Examples

    x <- 1:512
    chirp <- sin(2*pi * (x + 0.002 * (x-256)^2 ) / 16)
    retChirp <- cwt(chirp, noctave=5, nvoice=12, twoD=FALSE, plot=FALSE)
    retPolar <- cwtpolar(retChirp)
    retImageMod <- cwtimage(retPolar$modulus)
    retImageArg <- cwtimage(retPolar$argument)

Continuous Wavelet Transform with Phase Derivative

Description

Computes the continuous wavelet transform with (complex-valued) Morlet wavelet and its phase derivative.

Usage

cwtp(input, noctave, nvoice=1, w0=2 * pi, twoD=TRUE, plot=TRUE)

Arguments

input

input signal (possibly complex-valued)

noctave

number of powers of 2 for the scale variable

nvoice

number of scales in each octave (i.e., between two consecutive powers of 2).

w0

central frequency of the wavelet.

twoD

logical variable set to T to organize the output as a 2D array (signal size \times nb scales), otherwise, the output is a 3D array (signal size \times noctave \times nvoice).

plot

if set to TRUE, display the modulus of the continuous wavelet transform on the graphic device.

Value

list containing the continuous (complex) wavelet transform and the phase derivative

wt

array of complex numbers for the values of the continuous wavelet transform.

f

array of the same dimensions containing the values of the derivative of the phase of the continuous wavelet transform.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Examples

    ## discards imaginary part with error,
    ## c code does not account for Im(input)
    x <- 1:512
    chirp <- sin(2*pi * (x + 0.002 * (x-256)^2 ) / 16)
    chirp <- chirp + 1i * sin(2*pi * (x + 0.004 * (x-256)^2 ) / 16)
    retChirp <- cwtp(chirp, noctave=5, nvoice=12)

Conversion to Polar Coordinates

Description

Converts one of the possible outputs of the function cwt to modulus and phase.

Usage

cwtpolar(cwt, threshold=0)

Arguments

cwt

3D array containing the values of a continuous wavelet transform in the format (signal size \times noctave \times nvoice) as in the output of the function cwt with the logical flag twodimension set to FALSE.

threshold

value of a level for the absolute value of the modulus below which the value of the argument of the output is set to -\pi.

Details

The output contains the (complex) values of the wavelet transform of the input signal. The format of the output can be

2D array (signal size \times nb_scales)

3D array (signal size \times noctave \times nvoice)

Value

Modulus and Argument of the values of the continuous wavelet transform

output1

3D array giving the values (in the same format as the input) of the modulus of the input.

output2

3D array giving the values of the argument of the input.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Examples

    x <- 1:512
    chirp <- sin(2*pi * (x + 0.002 * (x-256)^2 ) / 16)
    retChirp <- cwt(chirp, noctave=5, nvoice=12, twoD=FALSE, plot=FALSE)
    retPolar <- cwtpolar(retChirp)

Squeezed Continuous Wavelet Transform

Description

Computes the synchrosqueezed continuous wavelet transform with the (complex-valued) Morlet wavelet.

Usage

cwtsquiz(input, noctave, nvoice=1, w0=2 * pi, twoD=TRUE, plot=TRUE)

Arguments

input

input signal (possibly complex-valued)

noctave

number of powers of 2 for the scale variable

nvoice

number of scales in each octave (i.e. between two consecutive powers of 2).

w0

central frequency of the wavelet.

twoD

logical variable set to T to organize the output as a 2D array (signal size \times nb scales), otherwise, the output is a 3D array (signal size \times noctave \times nvoice).

plot

logical variable set to T to T to display the modulus of the squeezed wavelet transform on the graphic device.

Details

The output contains the (complex) values of the squeezed wavelet transform of the input signal. The format of the output can be

2D array (signal size \times nb scales),

3D array (signal size \times noctave \times nvoice).

Value

synchrosqueezed continuous (complex) wavelet transform

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Inverse Dyadic Wavelet Transform

Description

Invert the dyadic wavelet transform.

Usage

dwinverse(wt, filtername="Gaussian1")

Arguments

wt

dyadic wavelet transform

filtername

filters used. ("Gaussian1" stands for the filters corresponds to those of Mallat and Zhong's wavlet. And "Haar" stands for the filters of Haar basis.

Value

Reconstructed signal

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Plot Dyadic Wavelet Transform Extrema

Description

Plot dyadic wavelet transform extrema (output of ext).

Usage

epl(dwext)

Arguments

dwext

dyadic wavelet transform (output of ext).

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Extrema of Dyadic Wavelet Transform

Description

Compute the local extrema of the dyadic wavelet transform modulus.

Usage

ext(wt, scale=FALSE, plot=TRUE)

Arguments

wt

dyadic wavelet transform.

scale

flag indicating if the extrema at each resolution will be plotted at the same scale.

plot

if set to TRUE, displays the transform on the graphics device.

Value

Structure containing:

original

original signal.

extrema

extrema representation.

Sf

coarse resolution of signal.

maxresoln

number of decomposition scales.

np

size of signal.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Kernel for Reconstruction from Gabor Ridges

Description

Computes the cost from the sample of points on the estimated ridge and the matrix used in the reconstruction of the original signal, using simple trapezoidal rule for integrals.

Usage

fastgkernel(node, phinode, freqstep, scale, x.inc=1, x.min=node[1],
x.max=node[length(node)], plot=FALSE)

Arguments

node

values of the variable b for the nodes of the ridge

phinode

values of the frequency variable \omega for the nodes of the ridge

freqstep

sampling rate for the frequency axis

scale

size of the window

x.inc

step unit for the computation of the kernel.

x.min

minimal value of x for the computation of G_2.

x.max

maximal value of x for the computation of G_2.

plot

if set to TRUE, displays the modulus of the matrix of G_2.

Details

Uses trapezoidal rule (instead of Romberg's method) to evaluate the kernel.

Value

matrix of the G_2 kernel.

References

See discussions in the text of “Time-Frequency Analysis”.

Kernel for Reconstruction from Wavelet Ridges

Description

Computes the cost from the sample of points on the estimated ridge and the matrix used in the reconstruction of the original signal, using simple trapezoidal rule for integrals.

Usage

fastkernel(node, phinode, nvoice, x.inc=1, x.min=node[1],
x.max=node[length(node)], w0=2 * pi, plot=FALSE)

Arguments

node

values of the variable b for the nodes of the ridge.

phinode

values of the scale variable a for the nodes of the ridge.

nvoice

number of scales within 1 octave.

x.inc

step unit for the computation of the kernel

x.min

minimal value of x for the computation of Q_2.

x.max

maximal value of x for the computation of Q_2.

w0

central frequency of the wavelet

plot

if set to TRUE, displays the modulus of the matrix of Q_2.

Details

Uses trapezoidal rule (instead of Romberg's method) to evaluate the kernel.

Value

matrix of the Q_2 kernel.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Generate Gabor function

Description

Generates a Gabor for given location and frequency.

Usage

gabor(sigsize, location, frequency, scale)

Arguments

sigsize

length of the Gabor function.

location

position of the Gabor function.

frequency

frequency of the Gabor function.

scale

size parameter for the Gabor function. See details.

Details

The size parameter here corresponds to the standard deviation for a gaussian. In the Carmona (1998, eBook ISBN:978008053942) book, equation 3.23 has a different scale factor.

Value

complex 1D array of size sigsize.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Examples


m1 = gabor(1024, 512,  2 * pi, 20 )

plot.ts(Re(m1) )

Crazy Climbers Reconstruction by Penalization

Description

Reconstructs a real-valued signal from ridges found by crazy climbers on a Gabor transform.

Usage

gcrcrec(siginput, inputgt, beemap, nvoice, freqstep, scale, compr,
        bstep=5, ptile=0.01, epsilon=0, fast=TRUE, para=5, minnbnodes=3,
        hflag=FALSE, real=FALSE, plot=2)

Arguments

siginput

original signal.

inputgt

Gabor transform.

beemap

occupation measure, output of crc.

nvoice

number of frequencies.

freqstep

sampling step for frequency axis.

scale

size of windows.

compr

compression rate to be applied to the ridges.

bstep

size (in the time direction) of the steps for chaining.

ptile

threshold of ridge

epsilon

constant in front of the smoothness term in penalty function.

fast

if set to TRUE, uses trapezoidal rule to evaluate Q_2.

para

scale parameter for extrapolating the ridges.

minnbnodes

minimal number of points per ridge.

hflag

if set to FALSE, uses the identity as first term in the kernel. If not, uses Q_1 instead.

real

if set to TRUE, uses only real constraints.

plot

1: displays signal,components, and reconstruction one after another.
2: displays signal, components and reconstruction.

Details

When ptile is high, boundary effects may appear. para controls extrapolation of the ridge.

Value

Returns a structure containing the following elements:

rec

reconstructed signal.

ordered

image of the ridges (with different colors).

comp

2D array containing the signals reconstructed from ridges.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Kernel for Reconstruction from Gabor Ridges

Description

Computes the cost from the sample of points on the estimated ridge and the matrix used in the reconstruction of the original signal.

Usage

gkernel(node, phinode, freqstep, scale, x.inc=1, x.min=node[1],
x.max=node[length(node)], plot=FALSE)

Arguments

node

values of the variable b for the nodes of the ridge.

phinode

values of the scale variable a for the nodes of the ridge.

freqstep

sampling rate for the frequency axis.

scale

size of the window.

x.inc

step unit for the computation of the kernel.

x.min

minimal value of x for the computation of Q_2.

x.max

maximal value of x for the computation of Q_2.

plot

if set to TRUE, displays the modulus of the matrix of Q_2.

Value

matrix of the Q_2 kernel

References

See discussions in the text of “Time-Frequency Analysis”.

Reconstruction from a Ridge

Description

Reconstructs signal from a “regularly sampled” ridge, in the Gabor case.

Usage

gregrec(siginput, gtinput, phi, nbnodes, nvoice, freqstep, scale,
epsilon=0, fast=FALSE, plot=FALSE, para=0, hflag=FALSE, real=FALSE,
check=FALSE)

Arguments

siginput

input signal.

gtinput

Gabor transform, output of cgt.

phi

unsampled ridge.

nbnodes

number of nodes used for the reconstruction.

nvoice

number of different scales per octave

freqstep

sampling rate for the frequency axis

scale

size parameter for the Gabor function.

epsilon

coefficient of the Q_2 term in reconstruction kernel

fast

if set to T, the kernel is computed using trapezoidal rule.

plot

if set to TRUE, displays original and reconstructed signals

para

scale parameter for extrapolating the ridges.

hflag

if set to TRUE, uses Q_1 as first term in the kernel.

real

if set to TRUE, uses only real constraints on the transform.

check

if set to TRUE, computes cwt of reconstructed signal.

Value

Returns a list containing:

sol

reconstruction from a ridge.

A

<gaborlets,dualgaborlets> matrix.

lam

coefficients of dual wavelets in reconstructed signal.

dualwave

array containing the dual wavelets.

gaborets

array containing the wavelets on sampled ridge.

solskel

Gabor transform of sol, restricted to the ridge.

inputskel

Gabor transform of signal, restricted to the ridge.

Q2

second part of the reconstruction kernel.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Reconstruction from a Ridge

Description

Reconstructs signal from sample of a ridge, in the Gabor case.

Usage

gridrec(gtinput, node, phinode, nvoice, freqstep, scale, Qinv,
epsilon, np, real=FALSE, check=FALSE)

Arguments

gtinput

Gabor transform, output of cgt.

node

time coordinates of the ridge samples.

phinode

frequency coordinates of the ridge samples.

nvoice

number of different frequencies.

freqstep

sampling rate for the frequency axis.

scale

scale of the window.

Qinv

inverse of the matrix Q of the quadratic form.

epsilon

coefficient of the Q_2 term in reconstruction kernel

np

number of samples of the reconstructed signal.

real

if set to TRUE, uses only constraints on the real part of the transform.

check

if set to TRUE, computes cgt of reconstructed signal.

Value

Returns a list containing the reconstructed signal and the chained ridges.

sol

reconstruction from a ridge.

A

<gaborlets,dualgaborlets> matrix.

lam

coefficients of dual gaborlets in reconstructed signal.

dualwave

array containing the dual gaborlets.

gaborets

array of gaborlets located on the ridge samples.

solskel

Gabor transform of sol, restricted to the ridge.

inputskel

Gabor transform of signal, restricted to the ridge.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Sampled Identity

Description

Generate a sampled identity matrix.

Usage

gsampleOne(node, scale, np)

Arguments

node

location of the reconstruction gabor functions.

scale

scale of the gabor functions.

np

size of the reconstructed signal.

Value

diagonal of the “sampled” Q_1 term (1D vector)

References

See discussions in the text of “Time-Frequency Analysis”.

Gabor Functions on a Ridge

Description

Generation of Gabor functions located on the ridge.

Usage

gwave(bridge, omegaridge, nvoice, freqstep, scale, np, N)

Arguments

bridge

time coordinates of the ridge samples

omegaridge

frequency coordinates of the ridge samples

nvoice

number of different scales per octave

freqstep

sampling rate for the frequency axis

scale

scale of the window

np

size of the reconstruction kernel

N

number of complex constraints

Value

Array of Gabor functions located on the ridge samples

References

See discussions in the text of "Time-Frequency Analysis”.

Real Gabor Functions on a Ridge

Description

Generation of the real parts of gabor functions located on a ridge. (modification of gwave.)

Usage

gwave2(bridge, omegaridge, nvoice, freqstep, scale, np, N)

Arguments

bridge

time coordinates of the ridge samples

omegaridge

frequency coordinates of the ridge samples

nvoice

number of different scales per octave

freqstep

sampling rate for the frequency axis

scale

scale of the window

np

size of the reconstruction kernel

N

number of complex constraints

Value

Array of real Gabor functions located on the ridge samples

References

See discussions in the text of “Time-Frequency Analysis”.

Estimate Hurst Exponent

Description

Estimates Hurst exponent from a wavelet transform.

Usage

hurst.est(wspec, range, nvoice, plot=TRUE)

Arguments

wspec

wavelet spectrum (output of tfmean)

range

range of scales from which estimate the exponent.

nvoice

number of scales per octave of the wavelet transform.

plot

if set to TRUE, displays regression line on current plot.

Value

complex 1D array of size sigsize.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Examples

# White Noise Hurst Exponent: The plots on the top row of Figure 6.8
# were produced by the folling S-commands. These make use of the two
# functions Hurst.est (estimation of Hurst exponent from CWT) and
# wspec.pl (display wavelet spectrum).

# Compare the periodogram and the wavelet spectral estimate.
wnoise <- rnorm(8192)
plot.ts(wnoise)
spwnoise <- fft(wnoise)
spwnoise <- Mod(spwnoise)
spwnoise <- spwnoise*spwnoise
plot(spwnoise[1:4096], log="xy", type="l")
lswnoise <- lsfit(log10(1:4096), log10(spwnoise[1:4096]))
abline(lswnoise$coef)
cwtwnoise <- DOG(wnoise, 10, 5, 1, plot=FALSE)
mcwtwnoise <- Mod(cwtwnoise)
mcwtwnoise <- mcwtwnoise*mcwtwnoise
wspwnoise <- tfmean(mcwtwnoise, plot=FALSE)
wspec.pl(wspwnoise, 5)
hurst.est(wspwnoise, 1:50, 5)

Ridge Estimation by ICM Method

Description

Estimate a (single) ridge from a time-frequency representation, using the ICM minimization method.

Usage

icm(modulus, guess, tfspec=numeric(dim(modulus)[2]), subrate=1,
mu=1, lambda=2 * mu, iteration=100)

Arguments

modulus

Time-Frequency representation (real valued).

guess

Initial guess for the algorithm.

tfspec

Estimate for the contribution of the noise to modulus.

subrate

Subsampling rate for ridge estimation.

mu

Coefficient of the ridge's second derivative in cost function.

lambda

Coefficient of the ridge's derivative in cost function.

iteration

Maximal number of moves.

Details

To accelerate convergence, it is useful to preprocess modulus before running annealing method. Such a preprocessing (smoothing and subsampling of modulus) is implemented in icm. The parameter subrate specifies the subsampling rate.

Value

Returns the estimated ridge and the cost function.

ridge

1D array (of same length as the signal) containing the ridge.

cost

1D array containing the cost function.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Trim Dyadic Wavelet Transform Extrema

Description

Trimming of dyadic wavelet transform local extrema, using bootstrapping.

Usage

mbtrim(extrema, scale=FALSE, prct=0.95)

Arguments

extrema

dyadic wavelet transform extrema (output of ext).

scale

when set, the wavelet transform at each scale will be plotted with the same scale.

prct

percentage critical value used for thresholding

Details

The distribution of extrema of dyadic wavelet transform at each scale is generated by bootstrap method, and the 95% critical value is used for thresholding the extrema of the signal.

Value

Structure containing

original

original signal.

extrema

trimmed extrema representation.

Sf

coarse resolution of signal.

maxresoln

number of decomposition scales.

np

size of signal.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Trim Dyadic Wavelet Transform Extrema

Description

Trimming of dyadic wavelet transform local extrema, assuming normal distribution.

Usage

mntrim(extrema, scale=FALSE, prct=0.95)

Arguments

extrema

dyadic wavelet transform extrema (output of ext).

scale

when set, the wavelet transform at each scale will be plotted with the same scale.

prct

percentage critical value used for thresholding

Details

The distribution of extrema of dyadic wavelet transform at each scale is generated by simulation, assuming a normal distribution, and the 95% critical value is used for thresholding the extrema of the signal.

Value

Structure containing

original

original signal.

extrema

trimmed extrema representation.

Sf

coarse resolution of signal.

maxresoln

number of decomposition scales.

np

size of signal.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Morlet Wavelets

Description

Computes a Morlet wavelet at the point of the time-scale plane given in the input

Usage

morlet(sigsize, location, scale, w0=2 * pi)

Arguments

sigsize

length of the output.

location

time location of the wavelet.

scale

scale of the wavelet.

w0

central frequency of the wavelet.

Details

The details of this construction (including the definition formulas) are given in the text.

Value

Returns the values of the complex Morlet wavelet at the point of the time-scale plane given in the input

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Examples


m1 = morlet(1024, 512, 20, w0=2 * pi)
plot.ts(Re(m1) )

Ridge Morvelets

Description

Generates the Morlet wavelets at the sample points of the ridge.

Usage

morwave(bridge, aridge, nvoice, np, N, w0=2 * pi)

Arguments

bridge

time coordinates of the ridge samples.

aridge

scale coordinates of the ridge samples.

nvoice

number of different scales per octave.

np

number of samples in the input signal.

N

size of reconstructed signal.

w0

central frequency of the wavelet.

Value

Returns the Morlet wavelets at the samples of the time-scale plane given in the input: complex array of Morlet wavelets located on the ridge samples

References

See discussions in the text of “Time-Frequency Analysis”.

Real Ridge Morvelets

Description

Generates the real parts of the Morlet wavelets at the sample points of a ridge

Usage

morwave2(bridge, aridge, nvoice, np, N, w0=2 * pi)

Arguments

bridge

time coordinates of the ridge samples.

aridge

scale coordinates of the ridge samples.

nvoice

number of different scales per octave.

np

number of samples in the input signal.

N

size of reconstructed signal.

w0

central frequency of the wavelet.

Value

Returns the real parts of the Morlet wavelets at the samples of the time-scale plane given in the input: array of Morlet wavelets located on the ridge samples

References

See discussions in the text of “Time-Frequency Analysis”.

Reconstruct from Dyadic Wavelet Transform Extrema

Description

Reconstruct from dyadic wavelet transform modulus extrema. The reconstructed signal preserves locations and values at extrema.

Usage

mrecons(extrema, filtername="Gaussian1", readflag=FALSE)

Arguments

extrema

the extrema representation.

filtername

filter used for dyadic wavelet transform.

readflag

if set to T, read reconstruction kernel from precomputed file.

Details

The reconstruction involves only the wavelet coefficients, without taking care of the coarse scale component. The latter may be added a posteriori.

Value

Structure containing

f

the reconstructed signal.

g

reconstructed signal plus mean of original signal.

h

reconstructed signal plus coarse scale component of original signal.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Dyadic Wavelet Transform

Description

Dyadic wavelet transform, with Mallat's wavelet. The reconstructed signal preserves locations and values at extrema.

Usage

mw(inputdata, maxresoln, filtername="Gaussian1", scale=FALSE, plot=TRUE)

Arguments

inputdata

either a text file or an R object containing data.

maxresoln

number of decomposition scales.

filtername

name of filter (either Gaussian1 for Mallat and Zhong's wavelet or Haar wavelet).

scale

when set, the wavelet transform at each scale is plotted with the same scale.

plot

indicate if the wavelet transform at each scale will be plotted.

Details

The decomposition goes from resolution 1 to the given maximum resolution.

Value

Structure containing

original

original signal.

Wf

dyadic wavelet transform of signal.

Sf

multiresolution of signal.

maxresoln

number of decomposition scales.

np

size of signal.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(noisy.dat)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(noisy.dat)
plot.ts(noisy.dat)

Noisy Gravitational Wave

Description

Noisy gravitational wave.

Usage

data(noisywave)

Format

A vector containing 8192 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(noisywave)
plot.ts(noisywave)

Prepare Graphics Environment

Description

Splits the graphics device into prescrivbed number of windows.

Usage

npl(nbrow)

Arguments

nbrow

number of plots.

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(pixel_8.7)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(pixel_8.7)
plot.ts(pixel_8.7)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(pixel_8.8)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(pixel_8.8)
plot.ts(pixel_8.8)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(pixel_8.9)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(pixel_8.9)
plot.ts(pixel_8.9)

Plot Dyadic Wavelet Transform Extrema

Description

Plot extrema of dyadic wavelet transform.

Usage

plotResult(result, original, maxresoln, scale=FALSE, yaxtype="s")

Arguments

result

result.

original

input signal.

maxresoln

number of decomposition scales.

scale

when set, the extrema at each scale is plotted withe the same scale.

yaxtype

y axis type (see R manual).

References

See discussions in the text of “Time-Frequency Analysis”.

Plot Dyadic Wavelet Transform

Description

Plot dyadic wavelet transform.

Usage

plotwt(original, psi, phi, maxresoln, scale=FALSE, yaxtype="s")

Arguments

original

input signal.

psi

dyadic wavelet transform.

phi

scaling function transform at last resolution.

maxresoln

number of decomposition scales.

scale

when set, the wavelet transform at each scale is plotted with the same scale.

yaxtype

axis type (see R manual).

References

See discussions in the text of “Time-Frequency Analysis”.

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(pure.dat)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(pure.dat)
plot.ts(pure.dat)

Pure Gravitational Wave

Description

Pure gravitational wave.

Usage

data(purwave)

Format

A vector containing 8192 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(purwave)
plot.ts(purwave)

Reconstruction from a Ridge

Description

Reconstructs signal from a “regularly sampled” ridge, in the wavelet case.

Usage

regrec(siginput, cwtinput, phi, compr, noct, nvoice, epsilon=0,
w0=2 * pi, fast=FALSE, plot=FALSE, para=0, hflag=FALSE,
check=FALSE, minnbnodes=2, real=FALSE)

Arguments

siginput

input signal.

cwtinput

wavelet transform, output of cwt.

phi

unsampled ridge.

compr

subsampling rate for the wavelet coefficients (at scale 1)

noct

number of octaves (powers of 2)

nvoice

number of different scales per octave

epsilon

coefficient of the Q_2 term in reconstruction kernel

w0

central frequency of Morlet wavelet

fast

if set to TRUE, the kernel is computed using trapezoidal rule.

plot

if set to TRUE, displays original and reconstructed signals

para

scale parameter for extrapolating the ridges.

hflag

if set to TRUE, uses Q_1 as first term in the kernel.

check

if set to TRUE, computes cwt of reconstructed signal.

minnbnodes

minimum number of nodes for the reconstruction.

real

if set to TRUE, uses only real constraints on the transform.

Value

Returns a list containing:

sol

reconstruction from a ridge.

A

<wavelets,dualwavelets> matrix.

lam

coefficients of dual wavelets in reconstructed signal.

dualwave

array containing the dual wavelets.

morvelets

array containing the wavelets on sampled ridge.

solskel

wavelet transform of sol, restricted to the ridge.

inputskel

wavelet transform of signal, restricted to the ridge.

Q2

second part of the reconstruction kernel.

nbnodes

number of nodes used for the reconstruction.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Reconstruction from a Ridge

Description

Reconstructs signal from a “regularly sampled” ridge, in the wavelet case, from a precomputed kernel.

Usage

regrec2(siginput, cwtinput, phi, nbnodes, noct, nvoice, Q2,
epsilon=0.5, w0=2 * pi, plot=FALSE)

Arguments

siginput

input signal.

cwtinput

wavelet transform, output of cwt.

phi

unsampled ridge.

nbnodes

number of samples on the ridge

noct

number of octaves (powers of 2)

nvoice

number of different scales per octave

Q2

second term of the reconstruction kernel

epsilon

coefficient of the Q_2 term in reconstruction kernel

w0

central frequency of Morlet wavelet

plot

if set to TRUE, displays original and reconstructed signals

Details

The computation of the kernel may be time consuming. This function avoids recomputing it if it was computed already.

Value

Returns a list containing:

sol

reconstruction from a ridge.

A

<wavelets,dualwavelets> matrix.

lam

coefficients of dual wavelets in reconstructed signal.

dualwave

array containing the dual wavelets.

morvelets

array containing the wavelets on sampled ridge.

solskel

wavelet transform of sol, restricted to the ridge.

inputskel

wavelet transform of signal, restricted to the ridge.

nbnodes

number of nodes used for the reconstruction.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Reconstruction from a Ridge

Description

Reconstructs signal from sample of a ridge, in the wavelet case.

Usage

ridrec(cwtinput, node, phinode, noct, nvoice, Qinv, epsilon, np,
w0=2 * pi, check=FALSE, real=FALSE)

Arguments

cwtinput

wavelet transform, output of cwt.

node

time coordinates of the ridge samples.

phinode

scale coordinates of the ridge samples.

noct

number of octaves (powers of 2).

nvoice

number of different scales per octave.

Qinv

inverse of the matrix Q of the quadratic form.

epsilon

coefficient of the Q_2 term in reconstruction kernel

np

number of samples of the reconstructed signal.

w0

central frequency of Morlet wavelet.

check

if set to TRUE, computes cwt of reconstructed signal.

real

if set to TRUE, uses only constraints on the real part of the transform.

Value

Returns a list containing the reconstructed signal and the chained ridges.

sol

reconstruction from a ridge

A

<wavelets,dualwavelets> matrix

lam

coefficients of dual wavelets in reconstructed signal.

dualwave

array containing the dual wavelets.

morvelets

array of morlet wavelets located on the ridge samples.

solskel

wavelet transform of sol, restricted to the ridge

inputskel

wavelet transform of signal, restricted to the ridge

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Kernel for Reconstruction from Wavelet Ridges

Description

Computes the cost from the sample of points on the estimated ridge and the matrix used in the reconstruction of the original signal, in the case of real constraints. Modification of the function kernel.

Usage

rkernel(node, phinode, nvoice, x.inc=1, x.min=node[1],
x.max=node[length(node)], w0=2 * pi, plot=FALSE)

Arguments

node

values of the variable b for the nodes of the ridge.

phinode

values of the scale variable a for the nodes of the ridge.

nvoice

number of scales within 1 octave.

x.inc

step unit for the computation of the kernel.

x.min

minimal value of x for the computation of Q_2.

x.max

maximal value of x for the computation of Q_2.

w0

central frequency of the wavelet.

plot

if set to TRUE, displays the modulus of the matrix of Q_2.

Details

Uses Romberg's method for computing the kernel.

Value

matrix of the Q_2 kernel

References

See discussions in the text of "Time-Frequency Analysis".

Kernel for Reconstruction from Wavelet Ridges

Description

Computes the cost from the sample of points on the estimated ridge and the matrix used in the reconstruction of the original signal

Usage

rwkernel(node, phinode, nvoice, x.inc=1, x.min=node[1],
x.max=node[length(node)], w0=2 * pi, plot=FALSE)

Arguments

node

values of the variable b for the nodes of the ridge.

phinode

values of the scale variable a for the nodes of the ridge.

nvoice

number of scales within 1 octave.

x.inc

step unit for the computation of the kernel.

x.min

minimal value of x for the computation of Q_2.

x.max

maximal value of x for the computation of Q_2.

w0

central frequency of the wavelet.

plot

if set to TRUE, displays the modulus of the matrix of Q_2.

Details

The kernel is evaluated using Romberg's method.

Value

matrix of the Q_2 kernel

References

See discussions in the text of "Time-Frequency Analysis".

Simple Reconstruction from Crazy Climbers Ridges

Description

Reconstructs signal from ridges obtained by crc, using the restriction of the transform to the ridge.

Usage

scrcrec(siginput, tfinput, beemap, bstep=5, ptile=0.01, plot=2)

Arguments

siginput

input signal.

tfinput

time-frequency representation (output of cwt or cgt.

beemap

output of crazy climber algorithm

bstep

used for the chaining (see cfamily).

ptile

threshold on the measure beemap (see cfamily).

plot

1: displays signal,components, and reconstruction one after another.
2: displays signal, components and reconstruction.
Else, no plot.

Value

Returns a list containing the reconstructed signal and the chained ridges.

rec

reconstructed signal

ordered

image of the ridges (with different colors)

comp

2D array containing the signals reconstructed from ridges

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(sig_W_tilda.1)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(sig_W_tilda.1)
plot.ts(sig_W_tilda.1)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(sig_W_tilda.2)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(sig_W_tilda.2)
plot.ts(sig_W_tilda.2)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(sig_W_tilda.3)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(sig_W_tilda.3)
plot.ts(sig_W_tilda.3)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(sig_W_tilda.4)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(sig_W_tilda.4)
plot.ts(sig_W_tilda.4)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(sig_W_tilda.5)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Examples


data(sig_W_tilda.5)
plot.ts(sig_W_tilda.5)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(signal_W_tilda.1)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(signal_W_tilda.1)
plot.ts(signal_W_tilda.1)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(signal_W_tilda.2)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(signal_W_tilda.2)
plot.ts(signal_W_tilda.2)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(signal_W_tilda.3)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(signal_W_tilda.3)
plot.ts(signal_W_tilda.3)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(signal_W_tilda.4)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(signal_W_tilda.4)
plot.ts(signal_W_tilda.4)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(signal_W_tilda.5)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(signal_W_tilda.5)
plot.ts(signal_W_tilda.5)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(signal_W_tilda.6)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(signal_W_tilda.6)
plot.ts(signal_W_tilda.6)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(signal_W_tilda.7)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Examples


data(signal_W_tilda.7)
plot.ts(signal_W_tilda.7)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(signal_W_tilda.8)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Examples


data(signal_W_tilda.8)
plot.ts(signal_W_tilda.8)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(signal_W_tilda.9)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(signal_W_tilda.9)
plot.ts(signal_W_tilda.9)

Reconstruction from Dual Wavelets

Description

Computes the reconstructed signal from the ridge, given the inverse of the matrix Q.

Usage

skeleton(cwtinput, Qinv, morvelets, bridge, aridge, N)

Arguments

cwtinput

continuous wavelet transform (as the output of cwt)

Qinv

inverse of the reconstruction kernel (2D array)

morvelets

array of Morlet wavelets located at the ridge samples

bridge

time coordinates of the ridge samples

aridge

scale coordinates of the ridge samples

N

size of reconstructed signal

Value

Returns a list of the elements of the reconstruction of a signal from sample points of a ridge

sol

reconstruction from a ridge

A

matrix of the inner products

lam

coefficients of dual wavelets in reconstructed signal. They are the Lagrange multipliers \lambda's of the text.

dualwave

array containing the dual wavelets.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Reconstruction from Dual Wavelet

Description

Computes the reconstructed signal from the ridge in the case of real constraints.

Usage

skeleton2(cwtinput, Qinv, morvelets, bridge, aridge, N)

Arguments

cwtinput

continuous wavelet transform (as the output of cwt).

Qinv

inverse of the reconstruction kernel (2D array).

morvelets

array of Morlet wavelets located at the ridge samples.

bridge

time coordinates of the ridge samples.

aridge

scale coordinates of the ridge samples.

N

size of reconstructed signal.

Value

Returns a list of the elements of the reconstruction of a signal from sample points of a ridge

sol

reconstruction from a ridge.

A

matrix of the inner products.

lam

coefficients of dual wavelets in reconstructed signal. They are the Lagrange multipliers \lambda's of the text.

dualwave

array containing the dual wavelets.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Smoothing Time Series

Description

Smooth a time series by averaging window.

Usage

smoothts(ts, windowsize)

Arguments

ts

Time series.

windowsize

Length of smoothing window.

Value

Smoothed time series (1D array).

References

See discussions in the text of “Time-Frequency Analysis”.

Smoothing and Time Frequency Representation

Description

smooth the wavelet (or Gabor) transform in the time direction.

Usage

smoothwt(modulus, subrate, flag=FALSE)

Arguments

modulus

Time-Frequency representation (real valued).

subrate

Length of smoothing window.

flag

If set to TRUE, subsample the representation.

Value

2D array containing the smoothed transform.

References

See discussions in the text of “Time-Frequency Analysis”.

Ridge Estimation by Snake Method

Description

Estimate a ridge from a time-frequency representation, using the snake method.

Usage

snake(tfrep, guessA, guessB, snakesize=length(guessB),
tfspec=numeric(dim(modulus)[2]), subrate=1, temprate=3, muA=1,
muB=muA, lambdaB=2 * muB, lambdaA=2 * muA, iteration=1000000,
seed=-7, costsub=1, stagnant=20000, plot=TRUE)

Arguments

tfrep

Time-Frequency representation (real valued).

guessA

Initial guess for the algorithm (frequency variable).

guessB

Initial guess for the algorithm (time variable).

snakesize

the length of the initial guess of time variable.

tfspec

Estimate for the contribution of the noise to modulus.

subrate

Subsampling rate for ridge estimation.

temprate

Initial value of temperature parameter.

muA

Coefficient of the ridge's derivative in cost function (frequency component).

muB

Coefficient of the ridge's derivative in cost function (time component).

lambdaB

Coefficient of the ridge's second derivative in cost function (time component).

lambdaA

Coefficient of the ridge's second derivative in cost function (frequency component).

iteration

Maximal number of moves.

seed

Initialization of random number generator.

costsub

Subsampling of cost function in output.

stagnant

maximum number of steps without move (for the stopping criterion)

plot

when set (by default), certain results will be displayed

Value

Returns a structure containing:

ridge

1D array (of same length as the signal) containing the ridge.

cost

1D array containing the cost function.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Restriction to a Snake

Description

Restrict time-frequency transform to a snake.

Usage

snakeview(modulus, snake)

Arguments

modulus

Time-Frequency representation (real valued).

snake

Time and frequency components of a snake.

Details

Recall that a snake is a (two components) R structure.

Value

2D array containing the restriction of the transform modulus to the snake.

References

See discussions in the text of “Time-Frequency Analysis”.

Modified Snake Method

Description

Estimate a ridge from a time-frequency representation, using the modified snake method (modified cost function).

Usage

snakoid(modulus, guessA, guessB, snakesize=length(guessB),
tfspec=numeric(dim(modulus)[2]), subrate=1, temprate=3, muA=1,
muB=muA, lambdaB=2 * muB, lambdaA=2 * muA, iteration=1000000,
seed=-7, costsub=1, stagnant=20000, plot=TRUE)

Arguments

modulus

Time-Frequency representation (real valued).

guessA

Initial guess for the algorithm (frequency variable).

guessB

Initial guess for the algorithm (time variable).

snakesize

The length of the first guess of time variable.

tfspec

Estimate for the contribution of srthe noise to modulus.

subrate

Subsampling rate for ridge estimation.

temprate

Initial value of temperature parameter.

muA

Coefficient of the ridge's derivative in cost function (frequency component).

muB

Coefficient of the ridge's derivative in cost function (time component).

lambdaB

Coefficient of the ridge's second derivative in cost function (time component).

lambdaA

Coefficient of the ridge's second derivative in cost function (frequency component).

iteration

Maximal number of moves.

seed

Initialization of random number generator.

costsub

Subsampling of cost function in output.

stagnant

Maximum number of stationary iterations before stopping.

plot

when set(default), some results will be displayed

Value

Returns a structure containing:

ridge

1D array (of same length as the signal) containing the ridge.

cost

1D array containing the cost function.

plot

when set(default), some results will be displayed.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Simple Reconstruction from Ridge

Description

Simple reconstruction of a real valued signal from a ridge, by restriction of the transform to the ridge.

Usage

sridrec(tfinput, ridge)

Arguments

tfinput

time-frequency representation.

ridge

ridge (1D array).

Value

(real) reconstructed signal (1D array)

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Time-Frequency Transform Global Maxima

Description

Computes the maxima (for each fixed value of the time variable) of the modulus of a continuous wavelet transform.

Usage

tfgmax(input, plot=TRUE)

Arguments

input

wavelet transform (as the output of the function cwt)

plot

if set to TRUE, displays the values of the energy as a function of the scale.

Value

output

values of the maxima (1D array)

pos

positions of the maxima (1D array)

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Time-Frequency Transform Local Maxima

Description

Computes the local maxima (for each fixed value of the time variable) of the modulus of a time-frequency transform.

Usage

tflmax(input, plot=TRUE)

Arguments

input

time-frequency transform (real 2D array).

plot

if set to T, displays the local maxima on the graphic device.

Value

values of the maxima (2D array).

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Average frequency by frequency

Description

Compute the mean of time-frequency representation frequency by frequency.

Usage

tfmean(input, plot=TRUE)

Arguments

input

time-frequency transform (output of cwt or cgt).

plot

if set to T, displays the values of the energy as a function of the scale (or frequency).

Value

1D array containing the noise estimate.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Percentile frequency by frequency

Description

Compute a percentile of time-frequency representation frequency by frequency.

Usage

tfpct(input, percent=0.8, plot=TRUE)

Arguments

input

time-frequency transform (output of cwt or cgt).

percent

percentile to be retained.

plot

if set to T, displays the values of the energy as a function of the scale (or frequency).

Value

1D array containing the noise estimate.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Variance frequency by frequency

Description

Compute the variance of time-frequency representation frequency by frequency.

Usage

tfvar(input, plot=TRUE)

Arguments

input

time-frequency transform (output of cwt or cgt).

plot

if set to T, displays the values of the energy as a function of the scale (or frequency).

Value

1D array containing the noise estimate.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

DOG Wavelet Transform on one Voice

Description

Compute DOG wavelet transform at one scale.

Usage

vDOG(input, scale, moments)

Arguments

input

Input signal (1D array).

scale

Scale at which the wavelet transform is to be computed.

moments

number of vanishing moments.

Value

1D (complex) array containing wavelet transform at one scale.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Gabor Functions on a Ridge

Description

Generate Gabor functions at specified positions on a ridge.

Usage

vecgabor(sigsize, nbnodes, location, frequency, scale)

Arguments

sigsize

Signal size.

nbnodes

Number of wavelets to be generated.

location

b coordinates of the ridge samples (1D array of length nbnodes).

frequency

frequency coordinates of the ridge samples (1D array of length nbnodes).

scale

size parameter for the Gabor functions.

Value

size parameter for the Gabor functions.

Morlet Wavelets on a Ridge

Description

Generate Morlet wavelets at specified positions on a ridge.

Usage

vecmorlet(sigsize, nbnodes, bridge, aridge, w0=2 * pi)

Arguments

sigsize

Signal size.

nbnodes

Number of wavelets to be generated.

bridge

b coordinates of the ridge samples (1D array of length nbnodes).

aridge

a coordinates of the ridge samples (1D array of length nbnodes).

w0

Center frequency of the wavelet.

Value

2D (complex) array containing wavelets located at the specific points.

Gabor Transform on one Voice

Description

Compute Gabor transform for fixed frequency.

Usage

vgt(input, frequency, scale, plot=FALSE)

Arguments

input

Input signal (1D array).

frequency

frequency at which the Gabor transform is to be computed.

scale

frequency at which the Gabor transform is to be computed.

plot

if set to TRUE, plots the real part of cgt on the graphic device.

Value

1D (complex) array containing Gabor transform at specified frequency.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Voice Wavelet Transform

Description

Compute Morlet's wavelet transform at one scale.

Usage

vwt(input, scale, w0=2 * pi)

Arguments

input

Input signal (1D array).

scale

Scale at which the wavelet transform is to be computed.

w0

Center frequency of the wavelet.

Value

1D (complex) array containing wavelet transform at one scale.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Sampling wavelet Ridge

Description

Given a ridge \phi (for the wavelet transform), returns a (appropriately) subsampled version with a given subsampling rate.

Usage

wRidgeSampling(phi, compr, nvoice)

Arguments

phi

ridge (1D array).

compr

subsampling rate for the ridge.

nvoice

number of voices per octave.

Details

To account for the variable sizes of wavelets, the sampling rate of a wavelet ridge is not uniform, and is proportional to the scale.

Value

Returns a list containing the discrete values of the ridge.

node

time coordinates of the ridge samples.

phinode

scale coordinates of the ridge samples.

nbnode

number of nodes of the ridge samples.

Plot Dyadic Wavelet Transform.

Description

Plot dyadic wavelet transform(output of mw).

Usage

wpl(dwtrans)

Arguments

dwtrans

dyadic wavelet transform (output of mw).

Log of Wavelet Spectrum Plot

Description

Displays normalized log of wavelet spectrum.

Usage

wspec.pl(wspec, nvoice)

Arguments

wspec

wavelet spectrum.

nvoice

number of voices.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(yen)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(yen)
plot.ts(yen)

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(yendiff)

Format

A vector containing observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998, eBook ISBN:978008053942) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Examples


data(yendiff)
plot.ts(yendiff)

Reconstruction from Wavelet Ridges

Description

Generate a zero kernel for reconstruction from ridges.

Usage

zerokernel(x.inc=1, x.min, x.max)

Arguments

x.min

minimal value of x for the computation of Q_2.

x.max

maximal value of x for the computation of Q_2.

x.inc

step unit for the computation of the kernel.

Value

matrix of the Q_2 kernel

Reconstruction from Dual Wavelets

Description

Computes the the reconstructed signal from the ridge when the epsilon parameter is set to zero

Usage

zeroskeleton(cwtinput, Qinv, morvelets, bridge, aridge, N)

Arguments

cwtinput

continuous wavelet transform (as the output of cwt).

Qinv

inverse of the reconstruction kernel (2D array).

morvelets

array of Morlet wavelets located at the ridge samples.

bridge

time coordinates of the ridge samples.

aridge

scale coordinates of the ridge samples.

N

size of reconstructed signal.

Details

The details of this reconstruction are the same as for the function skeleton. They can be found in the text

Value

Returns a list of the elements of the reconstruction of a signal from sample points of a ridge

sol

reconstruction from a ridge.

A

matrix of the inner products.

lam

coefficients of dual wavelets in reconstructed signal. They are the Lagrange multipliers \lambda's of the text.

dualwave

array containing the dual wavelets.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Reconstruction from Dual Wavelets

Description

Computes the the reconstructed signal from the ridge when the epsilon parameter is set to zero, in the case of real constraints.

Usage

zeroskeleton2(cwtinput, Qinv, morvelets, bridge, aridge, N)

Arguments

cwtinput

continuous wavelet transform (output of cwt).

Qinv

inverse of the reconstruction kernel (2D array).

morvelets

array of Morlet wavelets located at the ridge samples.

bridge

time coordinates of the ridge samples.

aridge

scale coordinates of the ridge samples.

N

size of reconstructed signal.

Details

The details of this reconstruction are the same as for the function skeleton. They can be found in the text

Value

Returns a list of the elements of the reconstruction of a signal from sample points of a ridge

sol

reconstruction from a ridge.

A

matrix of the inner products.

lam

coefficients of dual wavelets in reconstructed signal. They are the Lagrange multipliers \lambda's of the text.

dualwave

array containing the dual wavelets.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Transient Signal

Description

Usage

Format

Source

References

Examples

Transient Signal

Description

Usage

Format

Source

References

Examples

Transient Signal

Description

Usage

Format

Source

References

Examples

Transient Signal

Description

Usage

Format

Source

References

Examples

Transient Signal

Description

Usage

Format

Source

References

Examples

Transient Signal

Description

Usage

Format

Source

References

Examples

Transient Signal

Description

Usage

Format

Source

References

Examples

Transient Signal

Description

Usage

Format

Source

References

Examples

Continuous Wavelet Transform with derivative of Gaussian

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Heart Rate Data

Description

Usage

Format

Source

References

Examples

How Are You?

Description

Usage

Format

Source

References

Examples

Pixel from Amber Camara