Reply by Martin Eisenberg●October 1, 20032003-10-01
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
Reply by Alexey Lukin●September 30, 20032003-09-30
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