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
Definition of wavelet?
Started by ●September 30, 2003
Reply by ●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. > AlexHi, 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