OVERVIEW

Throughout we have emphasized that the primary description of a filtering system is in the time domain, yet the majority of synthesis, analysis, and approximation procedures for linear time-invariant systems occur in the frequency domain. One reason for this is the historic development [28]. Network synthesis originated in the frequency domain and approximation developments remained there. In the earlier days of electronics, the magnitude response was considered to be the important network function; thus there was little reason to investigate the time-domain responses. Even the phase response received little attention, since it was well known that phase distortion did not affect speech transmission. It was not until the advent of television and other systems using pulses that it became apparent that the system impulse response was the more important system characterization.

Another reason is simply that many problems, such as synthesizing networks and approximating various frequency-domain functions, are more easily solved in the frequency domain than in the time domain. For example, no equivalent time-domain procedure is known to generate network element values given a specified impulse response. As a second example, if one wishes to obtain a maximally flat gain function, it is advantageous to remain in the frequency domain, where the error criterion is readily established. However, we must recognize that this frequency-domain requirement is specified to reduce the amplitude distortion encountered by time-domain signals whose frequency content lies within the constant magnitude region.

Time-domain approximations have not been totally neglected, but the desired time-domain responses are...