Digital Real-Time Spectral Analysis

Abstract

The fast Fourier transform algorithm, reported by Cooley and Tukey, results in substantial computational savings and permits a considerable amount of parallel computation. By making use of these features, estimates of the spectral components of a time function can be calculated by a special-purpose digital machine while the function is being sampled. In this paper, two digital machine organizations are suggested which use the algorithm for the case of N (the number of samples analyzed) being a power of 2 and the case of N being the product of two integers. The first machine consists of shift registers and arithmetic units organized in stages which perform calculations in parallel. It can be used when N is a power of 2 and can accept signals being sampled at a rate exceeding 500 000 samples per second. The second machine requires fewer shift registers and only one arithmetic unit but cannot operate in a continuous manner. This means that either a dead time between adjacent records of data must be allowed or a time compression unit must be used. In the first case the obtainable sampling rate depends upon the dead time which can be allowed between adjacent records of data. In the second case sampling rates up to 8000 samples per second are feasible. For this analyzer, N is required to be expressible as the product of two integers.