Delta Modulation Granular Quantizing Noise

We present a statistical analysis of a single integration delta modulation system in which slope overload effects are negligible. In defining the delta modulation signal ensemble, we identify a binary phase parameter and show that when this parameter is random, the signal statistics are stationary, provided the input is stationary. Thus the delta modulation correlation functions depend on a single time variable and have Fourier transforms that are the power spectra of the delta modulation signals. After deriving the delta modulation correlation statistics and power density spectra, we use these functions to investigate the properties of the delta modulation granular quantizing noise. We demonstrate the ratio of input signal power to the quantizing noise power of three signals that approximate the system input. These signals are the integrated delta modulation signal, the signal at the output of the ideal low-pass interpolation filter usually considered in delta modulation studies, and the signal at the output of the optimum interpolation filter. We determine the properties of this filter by referring to the derived spectral density functions.