Parks-Mc Clellan Filter Design Algorithm - History of The Parks-McClellan Algorithm

History of The Parks-McClellan Algorithm

In August 1970, James McClellan entered graduate school at Rice University with a concentration in mathematical models of analog filter design. James McClellan enrolled in a new course called "Digital Filters" due to his interest in filter design. The course was taught jointly by Thomas Parks and Sid Burrus. At that time, DSP was an emerging field and, as a result, lectures often involved recently published research papers. The following semester, the spring of 1971, Thomas Parks offered a course called "Signal Theory," which James McClellan took as well. During spring break of the semester, Thomas drove from Houston to Princeton in order to attend a conference. At the conference, he heard Ed Hofstetter's presentation about a new FIR filter design algorithm (Maximal Ripple algorithm). He brought the paper by Hofstetter, Oppenheim, and Siegel, back to Houston, thinking about the possibility of using the Chebyshev approximation theory to design FIR filters. He heard that the method implemented in Hofstetter's algorithm was similar to the Remez exchange algorithm and decided to pursue the path of using the Remez exchange algorithm. The students in the "Signal Theory" course were required to do a project and since Chebyshev approximation was a major topic in the course, the implementation of this new algorithm became James McClellan's course project. This ultimately led to the Parks-McClellan algorithm, which involved the theory of optimal Chebyshev approximation and an efficient implementation. By the end of the spring semester, James McClellan and Thomas Parks were attempting to write a variation of the Remez exchange algorithm for FIR filters. It took about six weeks to develop and by the end of May, some optimal filters had been designed successfully.