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A Weighted Z Spectrum, Parallel Algorithm, and Processors for Mathematical Model Estimation
May 1996 (vol. 45 no. 5)
pp. 513-528

Abstract—A novel generalized spectral analysis approach which applies a weighting to z-transform spectra evaluated on contours in the z-transform plane is proposed. A parallel algorithm and 1D and 2D parallel processor architectures for the estimation of the pole-zero mathematical model of a system from a truncated version of its impulse response by succesive parallel evaluations of the proposed weighted z-transform spectra are subsequently presented. The algorithm is applicable to system identification and digital filter synthesis. The proposed weighted z-transform spectra and associated energy spectra make possible the evaluation of the poles and zeros of an infinite impulse response system of which the order is unknown from a truncated version of its impulse response with reasonable accuracy. A parallel dynamic weighting of z-transform spectra that is a function of |z| is shown to overcome the effect of exponential divergence of the z-transform of finite duration sequences as the z-plane center is approached. The resulting "bi-dimensional spectral decomposition," in terms of both hyperbolic and circular function content, is in contrast with that of Fourier and z-transforms which for finite duration sequences are shown to effect a decomposition in terms of only circular function content. Using parallel fast transform operations the proposed algorithm unmasks pole-zero peaks and through interpolation estimates the associated residues. The corresponding time-sequence component is deleted, the process repeated and the zeros determined using the evaluated residues. Optimal parallel and pipelined 1D- and 2D-type processor architectures are proposed, leading to the possibility of on line adaptive modeling of fast varying systems.

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Index Terms:
Complex exponential decomposition, complex frequency decomposition, digital filter synthesis, generalized spectral analysis, mathematical model estimation, parallel algorithms, parallel processing, pole-zero estimation, system identification, Z transform.
Michael J. Corinthios, "A Weighted Z Spectrum, Parallel Algorithm, and Processors for Mathematical Model Estimation," IEEE Transactions on Computers, vol. 45, no. 5, pp. 513-528, May 1996, doi:10.1109/12.509904
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