Orthonormal Wavelet System in ℓ² (Z²ₙ)
Gumber, Anupam · Shukla, Niraj K.
Original · EN
Using the group theoretic approach based on the set of digits, we first investigate a finite collection of functions in ℓ² (Z²ₙ) that satisfies some localization properties in a region of the time-frequency plane. The digits are associated with an invertible (expansive/non-expansive) matrix having integer entries. Next, we study and characterize an orthonormal wavelet system for ℓ² (Z²ₙ). In addition, some results connecting the uncertainty principle with functions that generate the orthonormal wavelet system having time-frequency localization properties are obtained.
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