Time-frequency localisation of Shannon wavelet packets

J. Yang, L. Shen

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)365-369
Number of pages5
JournalIEE Proceedings: Vision, Image and Signal Processing
Issue number6
StatePublished - Dec 2003
Externally publishedYes

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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