Cascading tricks for designing composite filters with sharp transition bands

This article presents novel tricks regarding cascading two digital filters to produce composite filters with very sharp transition bands for high-performance applications. The key point of the proposed tricks is to shape the magnitude frequency response of a prototype infinite impulse response (IIR) filter by a two-tap finite impulse response (FIR) filter using its nulls. In particular, we choose either a comb filter or a complementary comb filter of coefficients +1/-1, also called a shaping filter, to sharpen the transition bands of a prototype filter. The magnitude frequency response of the shaping filter compensates the Gibbs phenomenon commonly appearing in the passband edge and produces sharp transition bands for the cascaded filter. As compared to an equivalent IIR filter, the price paid is an additional comb/complementary comb filter of low complexity.