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The evaluation of complex integrals of the form for all 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 to ensure that is a true correlation sequence. In this correspondence we modify the method proposed in  to yield a simple linear algorithm that does not require a separate cheek for the stability of . The filtering interpretations proposed in  are extended to the evaluation of more general complex integrals with integrands of the form . Finally, an algorithm using the Levinson recursions is presented as a fast method to generate correlation sequences in the ARMA case.