A note on the evaluation of complex integrals using filtering interpretations
J. Dugre, E.I. Jury · IEEE Transactions on Acoustics Speech and Signal Processing · 1982
The evaluation of complex integrals of the formr_{k} = \frac{1}{2\pij}\oint H(z) H(z^{-1}) z^{k}\frac{dz}{z}for allkis frequently required in control, communications, and digital filtering problems. The major drawback of all existing methods is that the evaluation of the integral has to be preceded or followed by a check of the stability of the transfer functionH(z)to ensure that{r_{k}}\min{-\infin}\max{+\infin}is a true correlation sequence. In this correspondence we modify the method proposed in [1] to yield a simple linear algorithm that does not require a separate cheek for the stability ofH(z). The filtering interpretations proposed in [1] are extended to the evaluation of more general complex integrals with integrands of the formH(z) G(z^{-1}). Finally, an algorithm using the Levinson recursions is presented as a fast method to generate correlation sequences in the ARMA case.