# Filtering of the Synchrosqueezing Representation This function filters the Synchrosqueezing representation `Tx`, having associated frequencies fs (see `synsq_cwt_fw`). This band-pass filter keeps frequencies in the range `[fm, fM]`. This code is translated from MATLAB Synchrosqueezing Toolbox, version 1.1 developed by Eugene Brevdo (http://www.math.princeton.edu/~ebrevdo/). ```r synsq_filter_pass(Tx, fs, fm, fM) ``` ## Arguments - `Tx`: synchrosqueezed output of `x` (columns associated with time `t`). output of `synsq_cwt_fw` - `fs`: frequencies associated with rows of `Tx` - `fm`: Minimum band pass values. scalars, or vectors with each value associated with a time index (`length(fm)=ncol(Tx)`) - `fM`: Maximum band pass values. scalars, or vectors with each value associated with a time index (`length(fM)=ncol(Tx)`) ## Details This function filters the Synchrosqueezing representation `Tx`, having associated frequencies `fs` (see `synsq_cwt_fw`). This band-pass filter keeps frequencies in the range `[fm, fM]`. ## Returns - **Txf**: Filtered version of `Tx` (same size), with zeros outside the pass band rows. - **fmi**: time-length vector of min-frequency row indices - **fMi**: time-length vector of max-frequency row indices ## See Also `synsq_cwt_fw`, `synsq_cwt_fw`. ## Examples ```r 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(2,2)) #image.plot(list(x=tu, y=sstfit$asc, z=t(abs(sstfit$Wx))), log="y", # xlab="Time", ylab="Scale", main="Time-Scale Representation by CWT", # col=designer.colors(64, c("azure", "cyan", "blue", "darkblue")), ylim=c(1, 0.0625)) # Extracting the second component by filtering of continuous wavelet transform am <- 0.2 * rep(1, length(tu)) aM <- 0.3 * rep(1, length(tu)) #lines(tu, am, col="red", lty=3, lwd=2) #lines(tu, aM, col="red", lty=3, lwd=2) tmp <- synsq_filter_pass(sstfit$Wx, sstfit$asc, am, aM); furcwt <- cwt_iw(tmp$Txf, opt$type, opt); #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") #plot(tu, furcwt, type="l", main="CWT", xlab="time", ylab="f", col="red", # xlim=c(1.5,8.5), ylim=c(-1,1)) #lines(tu, feq2(tu), col="blue") # Remove all energy for normalized frequencies above 1. # synsq_filter_pass(Tx, fs, -Inf, 1) ```

synsq_filter_pass function