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Session 1220

The Design of Optimal Digital Filters Directly from Analog Prototypes

Aaron Robinson and Fred O. Simons, Jr. High-performance Computing and Simulation (HCS) Research Laboratory Department of Electrical Engineering Florida A&M University and Florida State University

Abstract - Generally analog prototype filters are not candidates for the design of optimum digital jilters because the processing requirements to convert from the analog protoppe jZter to the target digital filter are excessive, However, some optimized bilinear transform algorithms introduced by Simons and Harden to solve differential equation models were found to be adaptable to the problem of designing optimal digital filters without introducing excessive processing requirements. Based on these optimized bilinear transform algorithms, a procedure is derived whereby the coefficients of an analog proto~pe filter are adjusted in a parameter optimization process, The convergence of this process yields the digital filter that optimizes a cost function specifically formulated to realize desired digital filter goals and specljications. It is important to note that this new class of digital filters can be FIR or HR with the latter form also guaranteed to be stable,

Introduction The name optimal digital filter implies that filter design has been accomplished by specifying some criteria defined as optimal and the filter has been designed to meet that criteria. In many cases a prototype filter is chosen as a starting point and coefficient values are changed until satisfactory performance is reached. In such cases, digital tilters are normally chosen as a starting point because of the large number of calculations needed to transform analog prototypes to discrete domains. An alternate approach, with algorithms, which makes it feasible to design optimal digital filters based on analog filter prototypes is presented by the authors. Much of this alternate design process rest on powerful algorithms, developed by Simons and Harden to solve differential equations. [SIM088] These algorithms can be adapted to greatly reduce the number of computations required to derive a bilinear transformed digital H(z) model from a prototype H(s) analog model. This reduction in processing makes it feasible to base the optimal digital filter design on an analog prototype and arrive at solutions based on the changing coefficients of the analog filter. The end result is an optimally designed digital filter as well as an analog filter that could be claimed to be optimal in some sense.

In order to verify and converge on a proper filter design, the frequency response of the current filter in the design process must be continuously iterated until convergence to the optimal filter occurs. Frequency response calculations are also based on using new and efficient algorithms that are presented. These algorithms are based on real arithmetic operations, which account for their speed and efticiency[SIM087].

In addition to providing the algorithms used in the formulation of the filter design, a detailed outline of the process used to arrive at the new class of optimally designed digital filters is provided. Based on the presentations and evaluations of all algorithms and procedures, the authors present conclusions and ideas for future research.

Optimized Bilinear Transform Algorithms Calculation of the bilinear transform provides a method of transferring a polynomial in “s” to the “z” domain where digital processing techniques may be used. Since this transform accounts for a large percentage of the computations needed to complete the optimal design, more efficient means of calculating the transform becomes critical to an efficient optimization process.

Simons and Harden presented a treatise on “An Optimized Simulation of Dynamic Continuous Models” in which the authors derived algorithms that provided the basis for structuring an optimized PC program for simulating differential equation models of continuous dynamic subsystem components [SIM088]. These algorithms were adapted to reduce the number of computations needed to perform the bilinear transform.

$iiii% 1996 ASEE Annual Conference Proceedings } ‘..+,~yy’,:

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Simons, J. F. O., & Robinson, A. L. (1996, June), The Design Of Optimal Digital Filters Directly From Analog Prototypes Paper presented at 1996 Annual Conference, Washington, District of Columbia. 10.18260/1-2--5969