Instantaneous Companding of Quantized Signals

()55 Quantized pulse modulation has been the subject of considerable attention in the last decade.1"17 Proposals for practical application of such modulation usually provide for the transmission, by time division multiplex, of a class of signals covering an extensive power range. 1 · 6 Such proposals almost invariably assign a vital role to instantaneous compandors. The present discussion is devoted to the formulation of general quantitative criteria for the choice of a suitable companding characteristic. A. Fundamental Properties of Pulse Modulation* 1. Unquanlized Signals Unquantized pulse signals are produced when a band-limited signal (such as low-pass filtered speech) is sampled instantaneously at a rate greater than or equal to the minimum acceptable value of slightly more than twice the top signal frequency. The transmission of the continuous range of pulse amplitudes so produced is known as pulse amplitude modulation (PAM). Alternatively one may translate the sampled amplitudes into variations either in the width of periodic pulses of constant amplitude (pulse duration modulation or PDM), or in the spacing of pulses of uniform amplitude and width (pulse position modulation or PPM). Regardless of the mode of transmission, the unquantized signal pulses are sensitive to noise in the transmission medium. 2. Quantized Signals (PCM) Although sampling constitutes temporal quantization, it is convenient to adhere to conventional usage (as codified by Bennett 2 and Black1) in restricting the designation "quantized signals" to those which have been quantized in amplitude, as well as sampled in time, in order to permit encoded (i.e., essentially telegraphic) transmission.