Krawtchouk transforms and Convolutions

TL;DR

This paper develops an efficient operator calculus using Krawtchouk polynomials, introducing transforms and convolutions as a discrete alternative to Fourier analysis, with theoretical insights and basic examples.

Contribution

It introduces a novel discrete operator calculus based on Krawtchouk polynomials, including transforms and convolutions, expanding the tools for discrete signal processing.

Findings

Krawtchouk transforms are effective for discrete data analysis

Convolution structure enables efficient computation

Provides theoretical foundation and initial examples

Abstract

We put together the ingredients for an efficient operator calculus based on Krawtchouk polynomials, including Krawtchouk transforms and corresponding convolution structure which provide an inherently discrete alternative to Fourier analysis. In this paper, we present the theoretical aspects and some basic examples.