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arXiv · 1705.11127

Finite equal norm Parseval Wavelet Frames over Prime Fields

Asghar Rahimi·Niloufar Seddighi
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Abstract

In the framework of wave packet analysis, finite wavelet systems are particular classes of finite wave packet systems. In this paper, using a scaling matrix on a permuted version of the discrete Fourier transform (DFT) of system generator, we derive a locally-scaled version of the DFT of system genarator and obtain a finite equal-norm Parseval wavelet frame over prime fields. We also give a characterization of all multiplicative subgroups of the cyclic multiplicative group, for which the associated wavelet systems form frames. Finally, we present some concrete examples as applications of our results.

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Asghar Rahimi, Niloufar Seddighi. 2017-05-30. Finite equal norm Parseval Wavelet Frames over Prime Fields. https://doi.org/10.1142/s0219691317500400

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