wavelet decomposition of signal

I have signal with 1000 samples in it. When I apply DWT to it I get 502 coefficients. Further applying DWT gives 253 coefficients and again when i apply DWT i get 129 coefficients. Why I didn't get those coefficients as 500,250, 125. How does actually wavelet decomposition through DWT takes place in MATLAB??

Answer 1

[Wayne King]

Hi Smita, this is because of the setting of dwtmode. If you want to see the behavior you expect above, then do

dwtmode('per')

before computing the wavelet transform.

x = randn(1e3,1);
dwtmode('per');
[C,L] = wavedec(x,3,'sym4');

If you look at the L output, you will see the number of coefficients in the signal, L(end), and then 500 coefficients at level 1, 250 at level 2, etc.

Now return dwtmode to the default setting and repeat

   dwtmode('sym');
    [C,L] = wavedec(x,4,'sym4');
  L

Now you see the number as you report above.