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Session 1320

POLES AND ZEROS, AND MATLAB®, OH MY!

Thad B. Welch†, Cameron H.G. Wright‡, and Michael G. Morrow† † Department of Electrical Engineering U.S. Naval Academy, MD ‡ Department of Electrical Engineering U.S. Air Force Academy, CO

1. Introduction

Digital signal processing (DSP) using MATLAB® is being taught at the undergraduate level all around the world1-8. Even with the tremendous computational capabilities of MATLAB®, the significance of the pole/zero plot remains a mystery to many of our students. The ability to predict the effect of pole/zero location on either the magnitude or phase plot can be significantly enhanced using computer software. Software programs already exist that allow a student to calculate the magnitude and phase response associated with the arbitrary placement or movement of real and complex poles/zeros upon the complex plane. Unfortunately, these programs all have significant limitations.

2. Discussion

Our program adds several features that are either totally unavailable, or only partially available from these other programs. Specifically, we use the familiar MATLAB® environment to add a graphical user interface (GUI), see Fig. 1, that allows for easy interactive pole/zero placement, relocation, and/or deletion. This GUI includes both real and complex conjugate pairs of both poles and zeros. After a satisfactory pole/zero plot is constructed (e.g., the notched filter shown in Fig. 2), clicking on the Plot mag/phase button causes the magnitude and phase plots to be calculated and displayed in a separate figure (e.g., Fig. 3). The transfer function

0 5 B00zz55 H z = A

is also calculated and returned to the MATLAB® workspace using the familiar numerator coefficient variable B and the denominator coefficient variable, A. Rapid updates are possible and there is no need for a command line interface. Additionally, clicking the Load/run DSK button with the mouse downloads the calculated filter coefficients to an attached TMS320C31 DSK and executes this filter. Since the order of a filter designed using this technique is not expected to be large, implementation using only direct form II (DF-II) is provided.

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Wright, C., & Morrow, M., & Welch, T. (1999, June), Poles, Zeros, And Matlab®, Oh My! Paper presented at 1999 Annual Conference, Charlotte, North Carolina. 10.18260/1-2--7889