How can I reconstruct the details and approximation after using 'swt' (stationary wavelet decomposition) of the wavelet toolbox?

Hi, I am currently using ‘swt’ of the wavelet toolbox to obtain a stationary wavelet decomposition of a signal. Is there a similar command to 'wrcoef' to reconstruct the details and approximation? Best. Marie

Answer 1

[Wayne King]

Hi Marie, Not directly for SWT, but there is a work around. Let me say however, that starting in R2015b there is MODWT-MODWTMRA that implements an undecimated discrete wavelet transform for arbitrary length time series and that does directly provide an equivalent for wrcoef.m

Here is the work around for SWT -- Let's assume you want D3

load wecg;
swc = swt(wecg,8,'sym4');
swctmp = zeros(size(swc));
swctmp(3,:) = swc(3,:);
D3 = iswt(swctmp,'sym4');

Now here is the MODWT-MODWTMRA way

wt = modwt(wecg); % 'sym4' is default wavelet
mra = modwtmra(wt);
d3 = mra(3,:);

Let's compare D3 and d3

I would recommend the MODWT-MODWTMRA way because that is more exactly what you want.