Hi Marc, synchrosqueezing and the closely related continuous wavelet transform do not provide perfect reconstruction of the input signal in general like the DWT does.
You may want to look at MODWPT and/or MODWT.
The MODWT will give you an octave band decomposition of the input signal (into progressively finer octave bands) with energy conservation and perfect reconstruction without loss of time resolution.
For example
load wecg;
wt = modwt(wecg);
Now if you look at the energies of the wt matrix by row and sum those you will get back the energy of the original signal
sum(var(wt,1,2))
% compare to
var(wecg)
Now if you want to progressively build up your signal from "details" at different levels, use MODWTMRA
mra = modwtmra(wt);
If you sum this mra long the columns you will eventually build back up the original signal.
max(abs(wecg-sum(mra)'))
You can view what the contributions look like at different levels:
subplot(6,1,1);
plot(wecg);
for kk = 2:6
subplot(6,1,kk);
plot(mra(kk-1,:));
end
For a more finely tuned time-frequency analysis see MODWPT and MODWPTDETAILS.
