Improving FIR Filters by Using Cascade Techniques Tips & Tricks

Abstract

High-performance filtering is the holy grail for all digital signal processing (DSP) practitioners. However, highperformance filtering is almost synonymous with high implementation complexity and, thus, high cost. This article focuses on designing high-performance finite impulse response (FIR) filters with less complexity. We present novel methods for improving the frequency response of an FIR filter by cascading it with complementary comb filters (CCFs). In particular, we redesign a low-order FIR filter by intentionally inducing a ripple at the passband edge and using CCFs of various lengths to compensate for the ripple. We use the zeros of CCFs to reshape the frequency response of the low-order FIR filter, subsequently called the prototype filter. Thus, the composite filter approaches an ideal lowpass filter (LPF) more closely in both the transition band and stopband. Because a CCF contains only one adder and a few storage units, the cost is minimal. The composite filter also maintains a linear phase response because all CCFs have linear phase responses. Through shifting the LPF response to high-frequency bands, we obtain highpass filters and bandpass filters (BPFs) by using the same methodology.