inverse continuous wavelet transform and [Parm] in cwtft

Question

what is 'parm' means when you set the name of wavelet function in cwtft or icwtft. wave = {wname,[7.6]}. also can I change Fb and Fc when I use 'morl' function in cwtft or icwtft 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). Matlab doesn't have direct function for inverse wavelet transform.

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');

SAH SAH · Accepted Answer · 2013-09-07T17:05:43

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.

inverse continuous wavelet transform and [Parm] in cwtft

1 Answers