Spectral analysis of -ary digital signals encoded by -ary convolutional codes (Corresp.)

A method for spectral calculation of -ary digital signals encoded by -ary convolutional codes is developed. We have assumed a parallel encoding process such that for a code with rate and constraint length , the encoder can be modeled as a Mealy machine of inputs, outputs, and -ary memory cells. From this model and from the generator matrix of the code, the characterizing matrices of the Mealy machine are found in a straightforward way. Two assumptions are made on the statistics of the input signal. 1) The input sequence is a wide-sense stationary vector process of dimension . 2) The input vectors are statistically independent. With these assumptions and from the characterizing matrices of the Mealy machine, the method developed by Cariolaro and Tronca can be readily used. The continuous and discrete components of the spectrum of the coded signal are expressed in matrix form, which is particularly appropriate for computer programming.