Instantaneous companding of quantized signals

Instantaneous companding may be used to improve the quantized approximation of a signal by producing effectively nonuniform quantization. A revision, extension, and reinterpretation of the analysis of Panter and Dite permits the calculation of the quantizing error power as a function of the degree of companding, the number of quantizing steps, the signal volume, the size of the “equivalent dc component”' in the signal input to the compressor, and the statistical distribution of amplitudes in the signal. It appears, from Bennett's spectral analysis, that the total quantizing error power so calculated may properly be studied without attention to the detailed composition of the error spectrum, provided the signal is complex (such as speech or noise) and is sampled at the minimum information-theoretic rate. These calculations lead to the formulation of an effective process for choosing the proper combination of the number of digits per code group and companding characteristic for quantized speech communication systems. An illustrative application is made to the planning of a hypothetical PCM system, employing a common channel compandor on a time division multiplex basis. This reveals that the calculated companding improvement, for the weakest signals to be encountered in such a system, is equivalent to the addition of about 4 to 6 digits per code group, i.e., to an increase in the number of uniform quantizing steps by a factor between 2 4 = 16 and 2 6 = 64 Comparison with the results of related theoretical and experimental studies is also provided