Adaptive IIR Notch Filters for tracking of quasi-harmonic signals

In this paper, a new procedure for the design of a cascade of IIR Adaptive Notch Filters (ANFs) is presented. The cascade is composed by second-order sections of modified Nehorai Constrained ANFs, with coefficients modeled by a single polynomial of arbitrary order. This approach allows for a design with less parameters to control notch positions than the number of cascaded sections. The resulting structure is particularly suitable for tracking components of quasi-harmonic signals. An example shows that the coefficient modeling can tackle the inherent inharmonicity of the notes emitted by a string instrument. Finally, a complete adaptation algorithm for the model parameters, derived from Nehorai's ANF recursive prediction error algorithm, is described.