How to reconstruct the original signal using the detail coefficients in the discrete wavelet transform?

I want to reconstruct the signal usign only the detail or either the approximation coefficents. is this possible?

Answer 1

[Jonas]

yes, it is possible to reconstruct using only approximation coefficients or detail coefficient. have a look into appcoeff() or detcoeff(), there are also examples in the documentation.

[Rasula Dias]

I am sorry but I can't seem to find how to instruction on how to reconstruct in either documentation. Would be very grateful if you could provide an example or a link of one.

[Jonas]

the example in appcoeff explains how to approximate your original data with approximation coefficients only. The data shape you can see there (subplot(2,1,2))is pretty similar to the original one but without high frequency parts. the link is https://de.mathworks.com/help/wavelet/ref/appcoef.html#mw_cf4c8214-04a7-4ad6-9646-fb9de3ed1386

if you are unhappy with the different scale feel free to rescale

if the question was if you can reconstruct the exact original data with details/approximation only, then the answer is no

[Nikolaos Sioulas]

@Jonas Hi I wanted to ask if you have any suggestion on how I coul reconstruct the approximations and details at all levels after using swt (undecimated discrete wavelet transform). Thanks!