Frequency tracking using constrained adaptive notch filters synthesised from allpass sections

New constrained adaptive notch filter structures are proposed. These structures are synthesised from allpass filter sections, which are realised as structurally lossless bounded real functions with a minimum number of delay elements and multipliers. Both structures admit orthogonal tuning of their notch frequency and bandwidth. Frequency tracking is achieved simply by the evaluation of a function of a filter parameter. Connections are shown with the structures used by other workers. Signal enhancement outputs are obtained from both structures and their signal-to-noise improvement ratios are given. The mirror-image pair of polynomials present in a real allpass transfer function is shown to provide a significant simplification in the generation of the necessary gradient terms used in parameter adaptation. Simulations are included to verify the performance of these structures when they are used to track both single and multiple sinusoids in additive broadband noise