Estimation of the Signal-to-Noise Ratio in High Information and Constant Factor Delta Modulation Systems

A "statistical average step size," γav, which is a function of the rms power of a band-limited white Gaussian input signal, is defined for high information and first order constant factor delta modulation systems. The signal-to-noise ratios (SNR) are then calculated for these instantaneously adaptive delta modulation systems by substituting γavfor the fixed step size in the formulas for quantization (i.e., granular) and slope-overload noise applicable to linear (single integration) delta modulation systems. The calculated SNRs are in close agreement to those obtained by computer simulations. As γavis difficult to calculate exactly, an empirical expression is found which is applicable to different encoding conditions. This empirically formulated γavcan be used to estimate SNR to an acceptable accuracy for most practical situations. A noise component not present in linear delta modulation is identified and called "overshoot noise" and the cross-correlation ρxebetween input and error signals is studied. The SNR and ρxefor linear delta modulation are presented as reference bases.