synsq_filter_pass {SynchWave} | R Documentation |
Filtering of the Synchrosqueezing Representation
Description
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/).
Usage
synsq_filter_pass(Tx, fs, fm, fM)
Arguments
Tx |
synchrosqueezed output of |
fs |
frequencies associated with rows of |
fm |
Minimum band pass values. scalars, or vectors with each value associated
with a time index ( |
fM |
Maximum band pass values. scalars, or vectors with each value associated
with a time index ( |
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]
.
Value
Txf |
Filtered version of |
fmi |
time-length vector of min-frequency row indices |
fMi |
time-length vector of max-frequency row indices |
See Also
Examples
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)