Tunable/adaptive second-order IIR notch filter

A modified second-order infinite impulse response (IIR) notch filter with constrained poles and zeros is presented to eliminate or retrieve sinusoids embedded in a broadband signal. Such a filter is ideally suited to either parallel or cascaded implementation. Two classes of problems are considered. The first is where the sinusoidal frequencies are known a priori. For this case a straightforward design procedure based on a set of design characteristic graphs is used to select tunable notch filter parameters. An interesting property of the notch filter model is that it can be converted to a line enhancer by interchanging the position of the poles and zeros. The second type of problem arises when the sinusoidal frequencies are unknown and possibly varying with time. This means that an adaptive solution is required and an important consideration is the parameter estimation accuracy. For this purpose, the paper derives the Cramer–Rao lower bound for the adaptive cascaded notch filter using a frequency-domain approach. Some simulation results are included to demonstrate the effectiveness of the proposed adaptive notch filter.