For the following code,

X=[2 2 3 100 4 0 98 100 90 2 3 67 98 0 6 6 89 9 21 78]

where N is the level , I get n(approximation and detail coefficients)>n(X)

  1. What does this signify?

  2. Why does this increase happen?

  • $\begingroup$ For which $N$ did you observe this behavior? $\endgroup$ Oct 4 '15 at 12:31
  • $\begingroup$ For N=3 and above. It keeps increasing irregularly with increasing N. $\endgroup$ Oct 12 '15 at 10:29

This may be caused by "border effects" related to subsampling and signal length with perfect reconstruction filter banks.

For 2-band wavelets, there are standard non-expansive solutions (for instance with periodic border extension) when $2^N$ divides the length $L$ of your signal. In your case, one or two levels work without length increase, becauses $20=20/2+20/2 = (10/2+10/2)+10$. Then, starting at level $3$, you cannot divide $5$ into equal parts, since $2^3 = 8$ does not divide 20.


  1. It signifies that you have decomposed too deep to keep the number of samples constant.
  2. The increase happens because of your signal length, your decomposition level and your border extention.

For some applications (outside compression) this is not really an issue.


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