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arXiv · 1511.04538

Orthonormal Wavelet System in $\ell^2 ({\mathbb{Z}}^2_N)$

Anupam Gumber·Niraj K. Shukla
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Abstract

Using the group theoretic approach based on the set of digits, we first investigate a finite collection of functions in $\ell^2 ({\mathbb{Z}}^2_N)$ 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 $\ell^2 ({\mathbb{Z}}^2_N)$. 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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BibTeXRIS

Anupam Gumber, Niraj K. Shukla. 2015-11-14. Orthonormal Wavelet System in $\ell^2 ({\mathbb{Z}}^2_N)$. https://arxiv.org/abs/1511.04538

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