Digital Instrumentation for Walsh-Fourier Spectrum Measurement

Abstract

<p>A review of Walsh Spectral Analysers (WSA) using direct and fast transform methods is presented. A serial processor is developed that uses long shift registers to perform a Hadamard transform. This is extended by adding additional hardware to yield coefficients in dyadic and sequency order. Incoming data is thereby stored in a permuted manner, followed by sequential retrieval and transfer to a Hadamard transform processor. This scheme is faster than an earlier processor described by Geadah and Corinthios. Also a new pipeline structure with identical stages is evolved.</p> <p>The design of a Microprocessor-based Walsh-Fourier Spectral Analyser is given in detail. It uses an off-the-shelf single board microcomputer System 80/10 in conjunction with a special purpose board. The latter includes A/D conversion circuitry, a direct memory access controller, and a frequency multiplication module (FMM). The purpose of FMM is to generate 2ᵐ sampling pulses (64 in the system built) within one cycle of the input signal; this feature is required to compute the Fourier/Walsh coefficients of a periodic signal without leakage error. The new FMM circuit is a substantial improvement over earlier designs and permits a higher frequency of operation at a low clock frequency.</p> <p>Two methods (one by Siemens and Kitai and the other by Tadokoro and Higuchi) of Walsh to Fourier conversion are reviewed. The conversion process is compared with the Cooley-Tukey FFT methods with respect to the number of multiplications, memory requirements, and effects of finite word length in computation.</p> <p>The Walsh to Fourier conversion process is implemented through software to obtain 64 sine and cosine components. The instrument is interfaced to a HP 2647A intelligent graphic terminal for the display of Walsh and Fourier coefficients.</p>