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A note on the evaluation of complex integrals using filtering interpretations

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2 Author(s)
Dugre, J. ; University of Rhode Island, Kingston, RI ; Jury, E.I.

The evaluation of complex integrals of the form r_{k} = {1 \over 2{\pi}j} \oint H(z) H(z^{-1}) z^{k} {dz \over z} for all k is 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 function H(z) to ensure that \{ r_{k}\} {-\infty \atop +\infty} 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 of H(z) . The filtering interpretations proposed in [1] are extended to the evaluation of more general complex integrals with integrands of the form H(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.

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Acoustics, Speech and Signal Processing, IEEE Transactions on  (Volume:30 ,  Issue: 5 )