ABSTRACT
The approximation problem for filters is illustrated in Figure 2.1. A filter is often desired to produce a given slope of gain over one or more frequency intervals, to remain constant over other intervals, and to completely reject signals having frequencies contained in still other intervals. Thus, in the example shown in the figure, the desired gain is zero for very low and very high frequencies. The centerline, shown dashed, is the nominal behavior and the shaded band shows the permissible variation in the gain characteristic. Realizable circuits must always generate smooth curves and so cannot exactly meet the piecewise linear specification represented by the centerline. Thus, the realizable behavior is shown by the smooth, dark curve that lies entirely within the shaded tolerance band.
