ClimateUnboxed
ClimateUnboxed

Reputation: 8087

perfect reconstruction of wavelet transform using CWT

If I perform a standard wavelet transform and then perform the inverse, I was expecting to get the original signal back:

% dummy series:
Fs = 1e3;
t = 0:1/Fs:1;
x = exp(cos(2*pi*32*t).*(t>=0.1 & t<0.3) + sin(2*pi*64*t).*(t>0.7));

% perform default transform and inverse
wt=cwt(x)
rx=icwt(wt)

% plot
plot(t,x,t,rx)

Apart from the offset, the flat period signals are distorted.
original series and reconstruction from cwt and icwt It seems to be possible to perform a transform/inverse and have something close to the identity function, as here Wavelet reconstruction of time series , but reading the tutorials/help for cwt I do not see how to achieve this.

Upvotes: 1

Views: 1438

Answers (1)

alle_meije
alle_meije

Reputation: 2480

The matlab documentation explains that the CWT is not the best choice for perfect reconstruction. However if you want to compare different bands as signals with the same size as the original, you can use the MODWT (or the shift-invariant DWT by cycle-spinning, sometimes calles à trous).

Upvotes: 1

Related Questions