Pair of Dual Wavelet Frames on Local Fields

TL;DR

This paper introduces an algorithm for constructing orthogonal wavelet frames on local fields of positive characteristic, providing a general form and analyzing their properties via Fourier transform.

Contribution

It presents a new algorithm based on polyphase matrices for constructing orthogonal wavelet frames on local fields, and describes their general form and properties.

Findings

Algorithm for wavelet frame construction on local fields

General form of orthogonal tight wavelet frames

Analysis of wavelet properties using Fourier transform

Abstract

In this paper, an algorithm based on polyphase matrix for constructing a pair of orthogonal wavelet frames is suggested, and a general form for all orthogonal tight wavelet frames on local fields of positive characteristic is described. Moreover, we investigate their properties by means of the Fourier transform.