Adaptive notch filters from lossless bounded real all-pass functions for frequency tracking and line enhancing

The authors introduce constrained adaptive notch filters which are synthesized from a numerically robust all-pass filter section. This section is realized as a structurally lossless bounded real function which is canonic in both multipliers and delay elements. The notch filter structures admit orthogonal tuning of their notch frequency and bandwidth. For the two structures, frequency tracking and signal enhancement outputs are derived. The mirror image pair of polynomials present in a real all-pass transfer function is shown to yield significant simplification in the generation of the necessary gradient terms used in parameter adaptation. A cascade of such structures is shown to be suitable for tracking multiple sinusoids. Simulation results verify the utility of these structures for frequency tracking