Definition of wavelet?

Started by September 30, 2003
```Hi comp.dsp,

One quick question: does the difinition of wavelet require at least
one vanishing moment, or not?

In other words, can the discrete filter {2, -1} be considered as
wavelet? (i believe it has the corresponding scaling function: {2, 1}
- and they form the orthogonal basis together)

Thanks.
Alex
```
```Alexey Lukin wrote:

> Hi comp.dsp,
>
> One quick question: does the difinition of wavelet require at
> least one vanishing moment, or not?
>
> In other words, can the discrete filter {2, -1} be considered as
> wavelet? (i believe it has the corresponding scaling function:
> {2, 1} - and they form the orthogonal basis together)
>
> Thanks.
> Alex

Hi,
from Percival & Walden, Wavelet Methods for Time Series Analysis:

"A wavelet filter must satisfy the following three basic properties:
sum(l=0..L-1, h[l]) = 0             (69a)
sum(l=0..L-1, h[l]^2) = 1           (69b)
and
sum(l=0..L-1, h[l]h[l+2n]) = 0      (69c)
for all nonzero integers n."

Martin
```