It is well known that the 2π minimally supported frequency scaling function φα(x) satisfying φ̂α(ω) = χ[-α,2π-α](ω), 0 < α < 2π, is not time localised. The Shannon wavelet packets φnα(x) are generated from φα(x) via an arbitrary pair of low-pass and high-pass filters (h,g), which is associated with an orthogonal multiresolution analysis. The authors prove that φnα(x) is time localised if α and n satisfy certain conditions. They also show that the decay properties of φnα(x) depend on the multiplicity of the zero ω = π of the symbol m0(ω) of the low-pass filter h.
|Original language||English (US)|
|Number of pages||5|
|Journal||IEE Proceedings: Vision, Image and Signal Processing|
|State||Published - Dec 2003|
ASJC Scopus subject areas
- Signal Processing
- Electrical and Electronic Engineering