# inverse continuous wavelet transform and [Parm] in cwtft

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');

• I have encountered the same problem! Have you figured out the way to deal with this? Thank you! – user5371 Sep 4 '13 at 3:28

Why won't cmorwavf work?

http://www.mathworks.co.uk/help/wavelet/ref/cmorwavf.html

Could you then construct a matrix of (complex) Morlet wavelet co-efficients (suitably dilated and translated) and simply invert it for the inverse wavelet transform?

• I can transform my signal with complex morlet continuous wavelet transform and obtain the coefficients in matlab. it has a easy code.But Matlab Wavelet Toolbox does not support the inverse CWT for a general CWT.this question appeared for me when I was trying to find an answer on this post: dsp.stackexchange.com/questions/10583/… I thought its easy to reconstruct a signal when you have its coefficients but it seems its not easy. Thanks for reply – SAH Sep 4 '13 at 13:26
• You could apply the wavelet transform to all colums of eye(N) to obtain an N dimensional wavelet trasform, I think – Tom Kealy Sep 4 '13 at 13:37
• Can I get Inverse Continues wavelet transform this way? Would you explain more? what is N by the way? – SAH Sep 4 '13 at 13:40
• As long as your matrix is square, the inverse transform should be as simple as inverting the matrix. This Haar matrix implementation may be helpful mathworks.co.uk/matlabcentral/fileexchange/…. – Tom Kealy Sep 4 '13 at 13:41
• I have looked at the codes. but didn't understand it well. I will try to understand it. but would you explain what he has done in the link you introduced? – SAH Sep 4 '13 at 13:50

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.

• this is the answer of question. thought you may need it. Also I don't know how to write formulation nice. anyone edit it please. – SAH Sep 7 '13 at 16:52