Optimal least squares time-domain synthesis of recursive digital filters

Abstract

61(e) = u3 I #(e, dB) I -3.01~ n 12 + L n u , ] 4 9 [P(e>lP(0)12npde (11) where the weighting function w3 dB can be adjusted to yield suitable results. The usefulness of this method is somewhat limited, however, in that the value for Onull[which must still be specified in (ll)] severely restricts the range over which 6 3 d B may be influenced.Finally, the beamwidth may be controlled by keeping the current amplitudes ni fixed a t some set of values determined in the optimization program, and then merely varying the spacing between rings. This causes expansion or contraction of the radiation pattern along the horizontal scale, thus altering the beamwidth.I t should be noted here that increasing the spacing k E may introduce large sidelobes in the B= 90° region (since optimization only took pjace over a certain "visible region" in real space). Therefore, it is recommended that this approach be used only for the case where wider beamwidths are desired (i.e., with decreased spacings).As a last point, it would be instructive to consider the Abstract-A method for finding the coefficients of an nth-order linear recursive digital filter, which gives the best least squares approximation to a desired pulse response over a finite interval, is presented. A relationship is derived between the approximating error corresponding to an optimal set of numerator coefficients and the error produced by an overdetermined set of linear equations, which is a function of the denominator coefficients only. This relation provides a computational algorithm for calcularing the optimal coefficients by iteratively solving weighted sets of linear equations in terms of the denominator coefficients only. Both theoretical and numerical results are presented. Also, bounds are found on the interval in which the norm of the optimum error must lie.

Cramer-Rao bounds for deterministic modal analysis

“…The literature begins in 1795 with the work of Prony [1] and proceeds to the reducedrank linear prediction techniques of Tufts and Kumaresan [2]- [4]; the least squares (or maximum likelihood) techniques of Evans and Fischl [5], Kumaresan, Scharf, and Manuscript received June 2, 1991; revised June 22, 1992. The associate editor coordinating the review of this paper and approving it for publication was Prof. Mysore Raghuveer.…”

Maximum likelihood estimation and MUSIC in array localization signal processing: A review

“…This general approach of using the linear prediction polynomial has been used by Kumaresan, Scharf and Shaw [1986] and Kumaresan and Shaw [1988] in spectral analysis and bY Evans and Fischl [1973] in filter design.…”

Investigation of Procedures for Automatic Resonance Extraction from Noisy Transient Electromagnetics Data. Volume I. Investigation of Resonance Extraction Procedures

“…To the authors' knowledge, only iterative procedures, such as that described by Evans and Fischl [19], (also described in Appendix G) can be used to choose both A' and z', simultaneously to minimize (5).…”