A general theory of amplitude quantization with applications to correlation determination

A general theory of amplitude quantization is presented and is used to investigate the effects of signal quantization on the determination of correlation functions. Theoretical expressions are obtained for the cross-correlation between signals and quantization noises and for the cross-correlation between quantization noises. From considerations of the theory of amplitude quantization, a general form for multiplier correlators is determined. The perfect analogue correlator, the digital computer applied to correlation determination, the relay correlator and the polarity-coincidence correlator are all shown to be special cases of this general form. In addition, a new correlation method termed Stieltjes correlation is deduced. This method, in which one of the inputs is coarsely quantized and the other is not, is described in detail and is shown to possess many advantages over the correlators mentioned above.