The design of cascaded FIR filters

Many filtering operations require the use of more than one filter connected in cascade. The stopband response of each of these filters must meet a given minimum attenuation requirement, whereas the overall passband peak ripple magnitude must be within a pre-specified tolerance limit. Generally, the design approaches require the passband ripple magnitude of each of the filters to be smaller than that of the overall filter. However, if the filters are jointly optimized so that the passband ripples of the filters are 180° out of phase, then the passband ripple magnitudes of the individual filters may be allowed to be very much larger than the maximum allowable overall ripple magnitude without violating the tolerance limit of the overall passband ripple magnitude. In this paper, we present a linear-programming technique for jointly optimizing the filters