Walsh functions in secure coding, signal processing and cellular radio communication: Historical development during the years 1960– 1990

Abstract

Walsh functions have been introduced in mathematics in 1923 by Joseph L. Walsh. They constitute a complete set of orthogonal functions which assume only the values +1 and -1. By this property and by their algebraic properties as character functions of the dyadic group of binary numbers they became by the development of digital technology important mathematical means for the design and analysis in telecommunication systems. The paper gives an overview on important historical steps in Walsh functions applications in (1) in cryptography to arrange secure encoding of fast digital data streams ( work of Jim Massey and others), (2) (2) to the development of the Fast Walsh Fourier Transform algorithm (FWFT) which compares in its use to the classical FFT algorithm as used in 1D and 2D signal processing ( contribution of J.E.Welchel in 1968) and (3) (3) the use of Walsh functions in long distance space communication and for carrier multiplexing of digital channels in cellular radio telecommunication ( work Golomb, Viterbi, Harmuth and others).