Krawtchouk transforms and convolutions

Abstract

We present an operator calculus based on Krawtchouk polynomials, including Krawtchouk transforms and corresponding convolution structure which provides an inherently discrete alternative to Fourier analysis. This approach is well suited for applications such as digital image processing. This paper includes the theoretical aspects and some basic examples.

Keywords

• krawtchouk polynomials
• orthogonal polynomials
• convolution
• probability theory
• fourier analysis