Generalized Walsh Bases and Applications

TL;DR

This paper explores the convergence of generalized Walsh series for $L^1$ signals and demonstrates their potential in signal encoding and encryption using $N\times N$ unitary matrices.

Contribution

It introduces a new framework for generalized Walsh bases based on unitary matrices and applies it to signal encoding and encryption.

Findings

Convergence properties of generalized Walsh series are established.

Generalized Walsh bases depend on $N\times N$ unitary matrices.

Applications in signal encoding and encryption are demonstrated.

Abstract

We investigate convergence properties of generalized Walsh series associated with signals $f\in L^1[0,1]$. We also show how the dependence of the generalized Walsh bases on $N\times N$ unitary matrices allows for applications in signal encoding and encryption, provided the signals are piece-wise constant on $N$-adic subintervals of $[0,1]$.