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On the Computation of Correlation Sequences in 3-D Recursive Digital Filters

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Abstract

In this paper we are concerned with the computation of correlation sequences and complex integrals arising in Three-dimensional (3-D) recursive digital filtering applications. In particular, we focus on presenting a reliable and accurate method for evaluating triple complex integrals having a rational-form integrand. The basic idea is to reduce the triple complex integral into a double complex integral. The main computational tasks involved in the method includes the product-to-sum decomposition of the rational-form integrand, the integration of a definite integral, and the finding of inside-unit-circle (IUC) roots of 1-D polynomials. The proposed method of evaluating multiple complex integrals has its great applications in the design of optimal 3-D nonseparable-denominator recursive digital filters with minimum sensitivity and/or roundoff error. To demonstrate the effectiveness of the presented method, two numerical examples are given.

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Authors and Affiliations

  1. Department of Chemical Engineering, National Chung Cheng University, Chia-Yi, 621, Taiwan

    Chyi Hwang

  2. Department of Chemical Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung, 807, Taiwan

    Tong-Yi Guo

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  1. Chyi Hwang
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Hwang, C., Guo, TY. On the Computation of Correlation Sequences in 3-D Recursive Digital Filters. Multidimensional Systems and Signal Processing 13, 385–405 (2002). https://doi.org/10.1023/A:1019980430362

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