# Reconstruct Curves This function reconstructs the curves given by `curve_ext` or `curve_ext_multi`. This code is translated from MATLAB Synchrosqueezing Toolbox, version 1.1 developed by Eugene Brevdo (http://www.math.princeton.edu/~ebrevdo/). ```r curve_ext_recon(Tx, fs, Cs, opt=NULL, clwin=4) ``` ## Arguments - `Tx`: same as input to `curve_ext_multi`. synchrosqueezed output of `x` (columns associated with time `t`) - `fs`: same as input to `curve_ext_multi`. frequencies associated with rows of `Tx` - `opt`: same as input to `synsq_cwt_fw` and `synsq_cwt_iw` - `Cs`: same as output to `curve_ext_multi`. `[N x nc]` matrix of curve indices (`N=ncol(Tx)`) - `clwin`: same as input to `curve_ext_multi`. 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 reconstructs the curves given by `curve_ext` or `curve_ext_multi`. ## Returns - **xrs**: `[n x Nc]` matrix - the `Nc` reconstructed signals (each length `n`) ## 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_multi`, `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_recon function