synsq_cwt_iw | R Documentation |
This function performs inverse synchrosqueezing transform.
This code is translated from MATLAB Synchrosqueezing Toolbox, version 1.1 developed by Eugene Brevdo (http://www.math.princeton.edu/~ebrevdo/).
synsq_cwt_iw(Tx, fs, opt=NULL)
Tx |
synchrosqueezed output of |
fs |
frequencies associated with rows of |
opt |
list of options. See |
This function performs
inverse synchrosqueezing transform of Tx
with associated
frequencies in fs
. This implements Eq. 5 of [1].
x |
reconstructed signal |
[1] Thakur, G., Brevdo, E., Fuckar, N. S. and Wu, H-T. (2013) The Synchrosqueezing algorithm for time-varying spectral analysis: Robustness properties and new paleoclimate applications. Signal Processing, 93, 1079–1094.
synsq_cwt_fw
, synsq_filter_pass
.
set.seed(7) n <- 2048 tu <- seq(0,10,, n) dt <- tu[2]-tu[1] feq1 <- function(t) (1+0.2*cos(t))*cos(2*pi*(2*t+0.3*cos(t))) feq2 <- function(t) (1+0.3*cos(2*t))*exp(-t/15)*cos(2*pi*(2.4*t+0.5*t^(1.2)+0.3*sin(t))) feq3 <- function(t) cos(2*pi*(5.3*t-0.2*t^(1.3))) feq <- function(t) feq1(t) + feq2(t) + feq3(t) s2 <- 2.4 noise <- sqrt(s2)*rnorm(length(tu)) fu0 <- feq(tu); fu <- fu0 + noise; fus <- cbind(feq1(tu), feq2(tu), feq3(tu)) # Continuous wavelet transform nv <- 32 opt <- list(type = "bump") cwtfit <- cwt_fw(fu, opt$type, nv, dt, opt) thresh <- est_riskshrink_thresh(cwtfit$Wx, nv) # Hard thresholding and Reconstruction cwtfit$Wx[which(abs(cwtfit$Wx) < thresh)] <- 0.0 fur <- cwt_iw(cwtfit$Wx, opt$type, opt) # Synchrosqueezed wavelet transform using denoised signal sstfit <- synsq_cwt_fw(tu, fur, nv, opt) #par(mfrow=c(1,2)) #image.plot(list(x=tu, y=sstfit$fs, z=t(abs(sstfit$Tx))), log="y", # xlab="Time", ylab="Frequency", main="Time-Frequency Representation by SST", # col=designer.colors(64, c("azure", "cyan", "blue", "darkblue")), ylim=c(1, 8)) # Extracting the second component by filtering of synchrosqueezed wavelet transform fm <- fM <- (2.4+0.5*1.2*tu^0.2+0.3*cos(tu)) #lines(tu, 0.88*fm, col="red", lty=3, lwd=2) #lines(tu, 1.22*fM, col="red", lty=3, lwd=2) tmp <- synsq_filter_pass(sstfit$Tx, sstfit$fs, 0.88*fm, 1.12*fM); fursst <- synsq_cwt_iw(tmp$Txf, w, opt); #plot(tu, fursst, type="l", main="SST", xlab="time", ylab="f", col="red", # xlim=c(1.5,8.5), ylim=c(-1,1)) #lines(tu, feq2(tu), col="blue") # Example: # tmp <- synsq_cwt_fw(t, x, 32) # Synchrosqueezing # Txf <- synsq_filter_pass(tmp$Tx, tmp$fs, -Inf, 1) # Pass band filter # xf <- synsq_cwt_iw(Txf, fs) # Filtered signal reconstruction
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.