Spectral analysis of variable-length coded digital signals

A spectral analysis is conducted for a variable-length word sequence by an encoder driven by a stationary memoryless source. A finite-state sequential machine is considered as a model of the line encoder, and the spectral analysis of the encoded message is performed under the assumption that the sourceword sequence is composed of independent identically distributed words. Closed form expressions for both the continuous and discrete parts of the spectral density are derived in terms of the encoder law and sourceword statistics. The jump part exhibits jumps at multiple integers of per lambda(sub 0)T, where lambda(sub 0) is the greatest common divisor of the possible codeword lengths, and T is the symbol period. The derivation of the continuous part can be conveniently factorized, and the theory is applied to the spectral analysis of BnZS and HDBn codes.