عنوان

A novel approach for generating two-variable very strict Hurwitz polynomials with applications in the design of stable two-dimensional recursive digital filters

TLpq303730426

انگلیسی

A novel approach for generating two-variable very strict Hurwitz polynomials with applications in the design of stable two-dimensional recursive digital filters

[Thesis]

M. A. Abiri

Concordia University (Canada)

1989

1

Ph.D.

Concordia University (Canada)

1989

A systematic procedure is proposed for the generation of two-variable Very Strict Hurwitz Polynomials (VSHPs). Methods and procedures for the design of stable two-dimensional (2-D) (1-D as special case) filters satisfying prescribed specifications are described next, and are then applied to the design of several filters such as lowpass, highpass, bandpass, fan, Laplacian, and homomorphic filters with low sensitivity. This thesis discusses the design of 2-D (1-D as special case) recursive digital filters, with guaranteed stability. Part of the work reported in this thesis is devoted to the study of different methods for generating stable two-variable Hurwitz polynomials. Then, a novel approach which uses the properties of positive definite matrices and their application in generating two-variable VSHPs is proposed. The method considers a passive usdnusd-port network usdNusd terminated in usdnusd-variable reactances as starting point. Based on realizability of this as an usdnusd-variable reactance network we were able to generate two-variable VSHPs. Also, for the same order of the VSHP, a greater number of variables is made available, which results in low sensitivities for the designed filters. The generated two-variable VSHP is then assigned to the denominator of a 2-D analog reference filter with a properly designated numerator polynomial. The resulting analog transfer function is discretized by the application of bilinear transformations. Non-linear programming techniques are employed to design recursive digital filters. Using this approach, several stable 2-D (1-D as special case) quarter plane recursive digital filters are designed. As the coefficient word-length has an effect on the cost as well as the speed of a filter, a practical algorithm based on an optimization procedure for the design of recursive digital filters with integer coefficients is described. The numerical performance of the algorithm has been illustrated by examples. Finally, a detailed sensitivity analysis is undertaken whereby the designed filters are compared with respect to different coefficient word-lengths. First, a sensitivity in terms of the structure of a filter is defined. Then, we concentrate on variations of the parameters pertaining to the 2-D recursive digital filter transfer functions derived previously. This can serve as a sensitivity measure of the digital filters. (Abstract shortened with permission of author.)

Applied sciences

Digital filters

Electrical engineering

Hurwitz polynomials

M. A. Abiri

p

[Thesis]

276903

a

Y