Delta Modulation Quantizing Noise Analytical and Computer Simulation Results for Gaussian and Television Input Signals

Quantizing noise in delta modulation systems falls into two categories, granular noise and slope overload noise. Granular noise exists because the decoded output signal can assume only a specified number of levels in the range of interest. Slope overload noise occurs when the slope of the input signal is greater than the delta modulator is capable of reproducing. When the S/N ratio is not too small, the noise power from these two sources is additive. A formula for the slope overload noise power for Gaussian input signals is derived. This is used with an earlier result for the granular noise to give over-all signal-to-quantizing-noise ratios. It is shown by computer simulation that the assumptions employed in deriving these signal-to-quantizing-noise ratios are valid and that the analytical results provide good estimates of the true values of these ratios. Computer simulation of the Picturephone ∗ visual telephone, a low-bandwidth television system, illustrates that the formulas derived for Gaussian signals apply quite well to video signals. Estimates are given for the S/N ratios theoretically possible when a 4.5-mc monochrome television signal is transmitted by delta modulation. The characteristics of delta modulation quantizing noise may cause it to be subjectively less annoying than an equivalent amount of additive Gaussian noise.