A Weighted Z Spectrum, Parallel Algorithm, and Processors for Mathematical Model Estimation

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 successive 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.

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