OVERVIEW

The filtering system response plays a major role in determining the overall system response. For this reason familiarity with the fundamental aspects of filter responses is not only a must for the filter designer, but it is advantageous for the system designer and those who specify and use filters. Appreciation of the factors affecting the various responses results in more realistic system and filter requirements. Consequently design time, cost, and problems are reduced.

Accordingly we here consider ( a) restrictions in specifying arbitrary time- and frequency-domain responses, ( b) the expected tradeoffs as ideal responses are approximated in practice, ( c) three popular mathematical approximations and their application to filter responses, ( d) the characteristics of responses that have already been obtained and tabulated, and ( e) rise time and noise bandwidth, two important quantities in system design.

Before beginning these main topics, we introduce five basic filter types, each characterized by its attenuation response as a function of the radian frequency ?. These response characteristics are independent of the frequency range and apply equally well to light, X-rays, or the usual frequencies encountered in electronic engineering. The typical attenuation response in decibels is shown in terms of a passband, in which the attenuation is zero; a transition band; and a stop band that has a minimum attenuation there of A _min decibels.

1. Low pass (LP). The LP response (Fig. 3-1), has a passband between ? = 0 and ?