On the Design and Analysis of a Class of PCM Systems

This paper considers the problem of transmitting bandlimited signals using binary signaling over a noise-free channel. A functional block diagram of the type of PCM system under consideration is shown in Fig. 1.* The two major differences between the problem considered here and previous work arc the measure of system performance and signal classes considered. The measure of system performance usually considered is related to the integral mean-squared error. 1-3 This type of performance measure lends itself to a frequency-domain analysis. While this criterion is widely used, it doesn't provide direct information regarding the size of the error as a function of time. To investigate this time behavior, we use a time-domain approach and use the maximum error over time as a measure of system performance. Because of the desire to consider input signals that engineers would normally call bandlimited [i.e., trigonometric polynomials, sinusoids as well as functions in £ 2 (-- 00 > 0 0 ) w ^ h finite bandwidth] we treat a * For special classes of signals, other types of P C M systems such as D P C M and Delta Modulation are sometimes used. These systems will not be considered here. 917