# Extract a Maximum Energy / Minimum Curvature Curves This function consecutively extracts maximum energy / minimum curvature curves from a synchrosqueezing representation. This code is translated from MATLAB Synchrosqueezing Toolbox, version 1.1 developed by Eugene Brevdo (http://www.math.princeton.edu/~ebrevdo/). ```r curve_ext_multi(Tx, fs, nc, lambda = 1e3, clwin = 4) ``` ## Arguments - `Tx`: same as input to `curve_ext`. synchrosqueezed output of `x` (columns associated with time `t`) - `fs`: same as input to `curve_ext`. frequencies associated with rows of `Tx` - `nc`: Number of curves to extract - `lambda`: same as input to `curve_ext`. lambda default = 1e3. - `clwin`: frequency clearing window; after curve extraction, a window of frequencies (`Cs[,i]-clwin) : (Cs[,i]+clwin)` is removed from the original representation. (default = 2) ## Details This function consecutively extracts maximum energy / minimum curvature curves from a synchrosqueezing representation. As curves are extracted, their associated energies are zeroed out in the synsq representation. Curve extraction is then again performed on the remaining representaton. For more details, see help `curve_ext` and Sec. IIID of [1]. ## Returns - **Cs**: `[N x nc]` matrix of curve indices (`N=ncol(Tx)`) - **Es**: `[nc x 1]` vector of associated (logarithmic) energies ## References [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. ## See Also `synsq_cwt_fw`, `curve_ext`, `curve_ext_recon`. ## Examples ```r set.seed(7) 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 # Denoised signal opt$gamma <- thresh fr <- cwt_iw(cwtfit$Wx, opt$type, opt) # Synchrosqueezed wavelet transform using denoised signal sstfit2 <- synsq_cwt_fw(tt, fr, nv, opt) # Ridge extraction lambda <- 1e+04 nw <- 16 imtfit <- curve_ext_multi(sstfit2$Tx, log2(sstfit2$fs), 1, lambda, nw) # Reconstruction curvefit <- curve_ext_recon(sstfit2$Tx, sstfit2$fs, imtfit$Cs, opt, nw) par(mfrow=c(2,1)) image.plot(list(x=tt, y=sstfit2$fs, z=t(abs(sstfit2$Tx))), log="y", xlab="Time", ylab="Frequency", main="Time-Frequency Representation by SST", col=designer.colors(64, c("azure", "cyan", "blue", "darkblue")), ylim=c(0.5, 25)) lines(tt, sstfit2$fs[imtfit$Cs[,1]], col="red", lty=3, lwd=2) plot(tt, f0, type="l") lines(tt, curvefit, lty=2) ```

curve_ext_multi function