INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 655 



I. INTRODUCTION 



Quantized pulse modulation has been the subject of considerable 

 attention in the last decade.'" Proposals for practical application of 

 such modulation usually pro\'ide for the transmission, by time division 

 multiplex, of a class of signals covering an extensive power range.'' ^ 

 Such proposals almost in\'ariably 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 . Unquanfized 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 ampli- 

 tudes 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 sensiti^'e to noise in the transmission medium. 



3. Quantized Signals {PCM) 



Although sampling constitutes temporal quantization, it is convenient 

 to adhere to conventional usage (as codified b}^ Bennett- and Black') 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. Thus a finite range 

 of possible signal amplitudes, large enough to accommodate the strongest 

 signal to be encountered in a given appUcation, may be divided into N 

 equal parts or quantizing steps. Each instantaneous pulse amplitude of 

 a PAM signal is then compared with this ladder-like array; amplitude 

 Cfuantization is accomplished by replacing all amplitudes falling in any 

 portion of a quantizing step })y a single value uni(iuely characterizing 

 that interval. 



* This brief account is intended merely to specify the minimum amount of 

 background information required to avoid confusion in the present discussion. 

 Details may be found in the manj- excellent and readily accessible references al- 

 ready cited. 



