A Note on Delta-PCM for Signals with Bounded Derivative.

In this memorandum we study a delta-PCM quantizing scheme for real-valued signals with bonded derivative. Our performance criterion is the maximum instantaneous difference between the signal and its representation. We look at the trade-off between the sampling interval and the number of quantization levels used to represent each sample, subject to a constraint that the number of bits per second used to represent the signal be held constant. Our conclusion is that best performance is obtained when the number the quantization levels per sample is 2-i.e. delta-modulation.