MATLAB: Inverse continuous wavelet transform and [Parm] in cwtft

cmorwaveletWavelet Toolbox

what is parm means when you set the name of wavelet function in cwtft.wave = {wname,[7.6]}. also can I change Fb and Fc when I use 'morl' function in cwtft transform? and If not, then how can I reconstruct my signal with cwt transform? cause cwt let me to select optional value for fb and fc (cmorfb-fc).

N = 1024;
t = linspace(0,1,N);
y = sin(2*pi*8*t).*(t<=0.5)+sin(2*pi*16*t).*(t>0.5);
dt = 0.05;s0 = 2*dt;ds = 0.4875;NbSc = 20;
wname = 'morl';sig = {y,dt};sca = {s0,ds,NbSc};
*wave = {wname,[7.6]}*;
cwtsig = cwtft(sig,'scales',sca,'wavelet',wave);
sigrec = icwtft(cwtsig,'signal',sig,'plot');

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thought someone need the answer. cwtft and icwtft use Fourier transform of wavelet function to reconstruct the signal. The ‘morl’ in wname is analytic morlet function. So it’s exactly complex morlet and will give you phase and magnitude information about signal. The ‘parm’ in wave={‘morl’,[parm]} is wo or 2*pi*fc. So it’s corresponded to center frequency. Default value of ‘parm’ is 6 so fc=6/2*pi.molet wavelet function is psi(t,fc)=exp(j*2*pi*fc*t)*exp(-t^2/2) and its Fourier transform is psi^(k)=sqrt(2*pi)exp(-0.5(2*pi*k-ko)^2). ko= parm = 2*pi*fc. so you can config fc of morlet wavelet with changing parm. dunno how to make formulation nice. someone edit it plz.

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MATLAB: Inverse CWT using coif4

Hi Zozo, I'll give you a couple examples where you reconstruct an approximation to a time-localized 100 Hz component.

But first, I should say the following. Your time- and scale-localized reconstruction of a signal will be better if you use cwtft.m and icwtft.m with logarithmically-spaced scales. The reason for that is that you have to keep in mind the inverse CWT is a single integral approximation to a double integral problem. It turns out that the stability of the reconstruction is better when we use certain scales and for certain wavelets where the Fourier transform has a nice expression. For the coif4 wavelet, that is not the case.

   dt = 0.001;
   t = linspace(0,1,1000);
   x = cos(2*pi*100*t).*(t<0.5)+sin(2*pi*300*t).*(t>=0.75)+0.2*randn(size(t));
   scales = 1:30;
   cwtcoefs = cwt(x,scales,'coif4');
   cwtstruct = struct('wav','coif4','cfs',cwtcoefs,'scales',scales,'meanSIG',mean(x),'dt',dt);
   xrec = icwtlin(cwtstruct,'IdxSc',6:8);
   plot(t,x,'r-.'); 
   hold on;
   plot(t,xrec,'k'); 
   legend('Original Signal','Reconstruction with coif4 wavelet');
%Now using cwtft.m and icwtft.m
s0 = 2*dt;
ds = 0.4875;
NbSc = 20;
wname = 'morl';
sig = {x,dt};
sca = {s0,ds,NbSc};
wave = {wname,[]};
cwtsig = cwtft(sig,'scales',sca,'wavelet',wave);
newcfs = zeros(size(cwtsig.cfs));
indices = 4:6;
newcfs(indices,:) = cwtsig.cfs(indices,:);
cwtsig.cfs = newcfs;
xrec1 = icwtft(cwtsig);
figure;
plot(t,x,'r-.'); 
hold on;
plot(t,xrec1,'k');
legend('Original Signal','Reconstruction with Morlet Wavelet');

If you compare the two, you'll see that both techniques essentially isolate the 100-Hz component, but that the Morlet wavelet with logarithmically-spaced scales does a better job at the getting the amplitude right.

If you just want to find the localization of the signal feature at certain scales, then the coif4 wavelet works. If you are concerned about an accurate amplitude scaling, then cwtft and icwtft work better than cwt.m paired with icwtlin.m

Hope that helps, Wayne

MATLAB: Undecimated wavelet transform

Hi Kalai, you can use either swt() or ndwt() (for a 1-D signal) to do the nondecimated wavelet transform.

Wayne

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