CALCULATED QUANTIZING NOISE OF SINGLE-INTEGRATION DELTA-MODULATION CODERS

We calculate the granular quantizing noise for a delta modulator that has unequal positive and negative step sizes. The asymmetry leads to a highly colored noise spectrum. We perform this calculation by adding a ramp function of time to the input of a symmetrical coder. The resulting formulas can also be used for uniform DPCM and PCM coders. The idle‐channel spectrum consists of discrete lines which scatter somewhat irregularly in amplitude and frequency, they can be regarded as the result of sampling (aliasing) a sawtooth wave. These lines are phase‐modulated by a coder input. For a sinusoidal input, discrete side frequencies are produced which again have an irregular progression of amplitudes. Gaussian inputs lead, to gaussian line shapes; the lines broaden as input power is increased. A totally white spectrum (as is often assumed in connection with delta‐modulation‐system considerations) cannot be attained, however, before the onset of slope overload. We give a numerical example that uses a coder suitable for telephone applications. One can see that step asymmetry can be very advantageous in attaining low noise. © 1969 The Bell System Technical Journal