Why does Wavelet GUI (e.g. Wavelet 1-D) reconstruct the signal from appr./detail coefficients, but not showing the coefficients straight away?

Hi All,

I always got a question about wavelet processing in Matlab.

In Matlab, when you use 'dwt' to decompose the signal and get the appr./detail coefficients, you can analyse what you want straight away with the output. However, in Wavelet GUI ('wavemenu' to invoke in command line), the default output of the dwt (say Wavelet 1-D) is the reconstructed signals.

To make it clear for the case of GUI, we take detail 1 coefficient (cD1) for example. By default, once the GUI computes cD1 with 'dwt', it uses 'upcoef' to construct the level 1 detail (D1) from cD1 coefficients, as following

------------------------------------------------------------------------

    load leleccum;
    [cA1,cD1] = dwt(s,'db1');
    s = leleccum(1:3920);
    l_s = length(s);
    D1 = upcoef('d',cD1,'db1',1,l_s);
    % D1 = idwt([],cD1,'db1',l_s);     %%or instead of upcoef, we can use idwt

------------------------------------------------------------------------

So far I get the idea of how upcoef works: it simply assume cA1 as a zero sequence and reconstruct the signal D1 using inverse DWT with cA1 and cD1.

My question is:

1. Why GUI does it? Does it mean people normally tend to be interested in the constructed detail signal (D1), rather than the detail coefficient (cD1)? But in most academic papers, researchers tend to analyse and utilise features from the coefficients, not from the constructed signal.
2. As far as I can understand, the reconstructed signal is to show people, how the signal would look like provided that only a particular coefficient sequence is preserved while other coefficient sequences are ignored. For example, in this case, cA1 is completely assigned as a zero sequence and only cD1 got reconstructed. Same ideas apply to situations where cD2 got reconstructed while cA1, cA2, cD1 would be assigned as zero. Does it convey more informative info than purely DWT coefficient sequences?

Thanks, Tidus