The use of quantizing techniques in real time Fourier analysis

The purpose of the present paper is to present a general theory of the effect of quantizing upon digital computation of Fourier transforms. A similar theory applies in relation to correlation functions. The theory is relevant to spectral analysis and to a number of practical problems in signal detection schemes notably directional systems. Detection of a weak signal upon a noise background may be dependent upon the ability of a system to distinguish between the correlation functions of the signal and the noise background. The correlation functions are functions of both time and space. If a receiving array in space is steered by means of time delays between appropriate elements and if the response is processed by digital methods then the computation time determines the time for a complete sweep through the directions of interest. Such time may be reduced by very coarse quantizing before digital processing. A measure of the maximum errors arising from such quantization is provided by the theory.