Masters Theses

Date of Award

3-1987

Degree Type

Thesis

Degree Name

Master of Science

Major

Electrical Engineering

Major Professor

Bruce W. Bomar

Committee Members

Roy Joseph, Ronald Belz

Abstract

Computation of the discrete Fourier transform (DFT) with a general purpose microprocessor offers the usual advantages of these chips. They are programmable, small, inexpensive, and use little power. However, DFT computation speed is not as great as could be obtained with an architecture more tailored to the application. The recent introduction of microprocessors with architectures designed specifically for digital signal processing (DSP) should offer much faster computation, but the question remains as to how well the DSP chips actually perform in DFT applications. In this study, one of the popular chips, the Texas Instruments TMS32020, is evaluated for DFT use.

Fourier transform theory is discussed and the general structures of DFT programs are introduced by computer programs written in BASIC. Direct calculation of the DFT and calculation via a Fast Fourier Transform (FFT) algorithm are considered. The architecture of the TMS32020 is examined and assembler programs for the direct DFT and FFT calculation of the DFT are presented. Signals of known amplitude, frequency, phase, and data sample size are used to verify the program performance. Execution speed as a function of DFT size is then determined.

The results show that the architecture and instruction set of the TMS32020 allow fast, compact code to be developed for the DFT. The memory space is large enough for a 32K point single butterfly radix-2 FFT computation. The direct DFT program performs a 64 point complex DFT in 7.16 milliseconds. The FFT speed is excellent, although not comparable to modern digital spectrum analyzers. The single butterfly radix-2 FFT program computes a 1024 point FFT in 85 milliseconds. The execution speed of the FFT program is faster than that of the direct DFT program for any data sample size. However, neither program is optimized for speed.

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