A narrowband IIR digital filter with low sensitivity and roundoff noise

An efficient infinite-impulse response (IIR) structure is produced via spectral transformation of an appropriate finite-impulse response (FIR) prototype design. The filter specifications are prewarped to a halfband design by an allpass relationship to produce the efficient FIR prototype. The allpass coefficient is chosen to be exactly realizable with a small number of multiplier bits. Hence, the only coefficient quantization required is for the original FIR coefficients, which are relatively insensitive. The roundoff noise for fixed-point implementations is also quite low compared with conventional IIR designs. Scaling for overflow can be avoided completely, or, to save multipliers, a simple scale factor can be employed.