Date of Award
Spring 2000
Document Type
Thesis - Restricted
Degree Name
Master of Science (MS)
Department
Electrical and Computer Engineering
First Advisor
Heinen, James A.
Second Advisor
Brown, Ronald H.
Third Advisor
Hock, Jeffery L.
Abstract
The Parks-McClellan algorithm is widely used in the digital signal processing (DSP) field. It is used to design weighted-Chebyshev finite-impulse-response (FIR) equiripple filters. The resulting filters are optimal, which means that with repeated use the algorithm produces linear-phase FIR filters with the minimum length possible given the filter specifications. This algorithm is implemented as the standard program remez in the MATLAB Signal Processing Toolbox. In this thesis, four new modifications of the Parks-McClellan algorithm are proposed in an attempt to improve this algorithm in various ways. MATLAB programs were developed to realize these new algorithms. The program remez_la is used to obtain the minimum filter order and design a minimum length filter for given filter specifications. Because of the initialization scheme used by the Remez exchange algorithm, it converges slowly, requiring a significant number of floating point operations (flops). The second program is called remez_lb. It introduces a new initialization scheme that uses the final extremal frequencies of the filter with order Nor N-1 as the initial frequencies of the filter with order N+1, thus reducing the number of iterations needed by the remez program, and therefore speeding up the design of a suitable filter. As shown in Chapter 5, the average savings of flops to design several sample filters is 18.80%. Program remez_2 is aimed at eliminating the filter transition region anomalies. It removes the magnitude response excursions in transition bands by introducing a pair of limits. Properly selecting transition band limits is more of an art than a science. The algorithm is flexible, but heavily relies on the designer's experience. II Program remez_3 is used to design filters with monotonic transition regions. The cost is that the filter orders are at least equal and sometimes higher than those produced by remez_2. For order-critical filter design applications, using program remez_2 is a better choice, while for transition-region-response-critical applications, the use of program remez_3 is indicated. Finally, a graphical user interface called "gui'' was developed. The purpose of this program is to help users conveniently design and compare filters. It combines four filter design programs (standard remez, remez_la, remez_2 and remez_3), enabling users to design an optimal Chebyshev filter with four different methods and compare the results easily and quickly.
Recommended Citation
Sun, Jian, "Improved Chebyshev Design of Linear-Phase Finite-Impulse-Response Digital Filters" (2000). Master's Theses (1922-2009) Access restricted to Marquette Campus. 4190.
https://epublications.marquette.edu/theses/4190