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On the Power Spectral Density of Constrained Sequences

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2 Author(s)
Pimentel, C. ; Dept. of Electron. & Syst., Univ. Fed. de Pernambuco, Recife ; da Rocha, V.C.

This paper derives a simple closed-form expression for computing the power spectral density (PSD) of constrained sequences whose constraints are characterized by a function of an ergodic Markov process specified in terms of a Mealy machine. A suitable matrix description of the stochastic behavior of the constrained sequence is used to express its autocorrelation sequence in a compact matrix form that simplifies the calculation of the PSD. Examples of the application of this technique in cases of practical interest are provided, including differentially encoded binary sequences, source-driven binary Huffman codes, maximum entropy (d,k) codes, and convolutional- or block-encoded sequences. A unified treatment to several widely used constrained sequences is provided

Published in:

Communications, IEEE Transactions on  (Volume:55 ,  Issue: 3 )