Spectral Analysis of Digital Messages Through Finite-Memory Transformations

The spectral analysis is performed for the stochastic sequence{b_{n}} = {h(a_{n}, a_{n-1},cdots, a_{n-M+1})}, where{a_{n}}is an independent identically distributed digital sequence andhis an arbitrary complex function. The computation of the spectrum is based on a general matrix method for the spectral analysis of memoryless functions of Markov chains. The approach employs a recursive algorithm, whose computational time and storage requirements are sufficiently small for the algorithm to be implemented on a modern general purpose computer, even for moderately high values of both the size of the source alphabet and the parameterM. The method is also extended to the case in which the input sequence{a_{n}}is a stationary finite Markov chain.