Filter Shape Factor And Selectivity

An Ideal Filter

The Ideal Filter would have unit gain (0dB) in its pass band and a gain of zero (-infinity dB) in its stop band. Between pass band and stop band there would be no indecision and would transition from 0dB to -infinity dB asymptotically. It would pass only the required frequencies without adding or subtracting anything from the signal and like a very discrete and fastidious butler we would not see it - just its perfect management of the frequencies in its care.

Sadly we cannot have perfect filters in the real word and so we compromise and accept some amount of non-unity gain in the pass band (insertion loss and pass band ripple) and non-zero gain in the stop band (finite stop band attenuation and stop band ripple). In addition, there is some transition from pass band to stop band that needs to be understood and managed. This Transition Band can be a defining characteristic in the usefulness of a filter for a given application, and is talked about using the terms Shape Factor and Selectivity.