Spectral Analysis of Digital Messages Through Finite-Memory Transformations

The spectral analysis is performed for the stochastic sequence , where is an independent identically distributed digital sequence and is 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 parameter . The method is also extended to the case in which the input sequence is a stationary finite Markov chain.