# Wavelet decomposition

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]
[C,L]=wavedec(X,N,'db1');


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?

• For which $N$ did you observe this behavior? – Laurent Duval Oct 4 '15 at 12:31
• For N=3 and above. It keeps increasing irregularly with increasing N. – Manish Ramesh Oct 12 '15 at 10:29

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.