cwt_iw: Inverse Wavelet Transform

In SynchWave: Synchrosqueezed Wavelet Transform

Inverse Wavelet Transform

Description

This function performs the inverse wavelet transform of signal Wx.

This code is translated from MATLAB Synchrosqueezing Toolbox, version 1.1 developed by Eugene Brevdo (http://www.math.princeton.edu/~ebrevdo/).

Usage

cwt_iw(Wx, type, opt=NULL)

Arguments

Wx	wavelet transform of a signal, see cwt_fw.
type	wavelet used to take the wavelet transform, see cwt_fw and wfiltfn.
opt	options list used for forward wavelet transform.

Details

This function performs the inverse wavelet transform of signal Wx, and implements Eq. (4.67) of [1].

Value

x	the signal, as reconstructed from Wx.

References

[1] Mallat, S (2009) A Wavelet Tour of Signal Processing, New York: Academic Press.

See Also

cwt_fw, wfiltfn, est_riskshrink_thresh.

Examples

tt <- seq(0, 10, , 1024)
nv <- 32
f0 <- (1+0.6*cos(2*tt))*cos(4*pi*tt+1.2*tt^2)
sigma <- 0.5
f <- f0 + sigma*rnorm(length(tt))

# Continuous wavelet transform
opt <- list(type = "bump")
cwtfit <- cwt_fw(f, opt$type, nv, tt[2]-tt[1], opt)

# Hard thresholing
thresh <- est_riskshrink_thresh(cwtfit$Wx, nv)
cwtfit$Wx[which(abs(cwtfit$Wx) < thresh)] <- 0.0

# Reconstruction 
opt$gamma <- thresh
cwtrec <- cwt_iw(cwtfit$Wx, opt$type, opt)

par(mfrow=c(1,1))
plot(tt, f, type="p", lty=2, xlab="time", ylab="f", col="red", cex=0.1)
lines(tt, f0, col="blue")
lines(tt, cwtrec)

SynchWave documentation built on May 7, 2022, 5:05 p.m.