RECURSIVE SYNTHESIS OF LINEAR TIME-VARIANT DIGITAL FILTER VIA CHEBYSHEV APPROXIMATION.

The present paper investigates the recursive realization of a rational generalized transfer function (GTF) as a linear time-variant (LTV) difference equation. We develop a relationship between a GTF and a time-variant difference equation. The unique realizability of a GTF as a LTV difference equation is discussed. Procedures for determining a timevariant difference equation from a given GTF having constant coefficients in its denominator are then developed. For a GTF having time-variant coefficients in its denominator, a "best" approximate realization is numerically determined based on the Chebyshev norm to minimize the residual vector.

[1]  J. Aggarwal,et al.  A simple form synthesis of linear time-variant digital filter via spectral decomposition of its impulse response , 1984 .

[2]  Y. D. Landau,et al.  Adaptive control: The model reference approach , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[3]  J. Aggarwal,et al.  Difference equation implementation of time-variant digital filters , 1983, The 22nd IEEE Conference on Decision and Control.

[4]  Yves Grenier,et al.  Time-dependent ARMA modeling of nonstationary signals , 1983 .

[5]  J. Aggarwal,et al.  One-dimensional linear shift- variant digital filtering using two-dimensional techniques , 1983 .

[6]  J. Aggarwal,et al.  Synthesis and implementation of recursive linear shift-variant digital filters , 1983 .

[7]  R.V. Monopoli,et al.  Adaptive control: The model reference approach , 1981, Proceedings of the IEEE.

[8]  Rashid Ansari,et al.  INTERPOLATORS AND DECIMATORS AS PERIODICALLY TIME-VARYING FILTERS. , 1981 .

[9]  Nian Chyi Huang,et al.  SYNTHESIS OF RECURSIVE LINEAR SHIFT-VARIANT DIGITAL FILTERS. , 1981 .

[10]  Jake K. Aggarwal,et al.  ON LINEAR SHIFT-VARIANT DIGITAL FILTERS. , 1979 .

[11]  Ronald W. Schafer,et al.  Digital Processing of Speech Signals , 1978 .

[12]  K. Pann,et al.  a Class of Convolutional Time-Varying Filters , 1976 .

[13]  A Descent Method for the Uniform Solution to Over-Determined Systems of Linear Equations , 1976 .

[14]  Z. Nikolic.  A RECURSIVE TIME‐VARYING BAND‐PASS FILTER , 1975 .

[15]  A. Sawchuk.  Space-variant image motion degradation and restoration , 1972 .

[16]  E. Cheney.  Introduction to approximation theory , 1966 .

[17]  Julius S. Bendat,et al.  Exact integral equation solutions and synthesis for a large class of optimum time variable linear filters , 1957, IRE Trans. Inf. Theory.

[18]  R. Booton.  An Optimization Theory for Time-Varying Linear Systems with Nonstationary Statistical Inputs , 1952, Proceedings of the IRE.