A Complex Adaptive Notch Filter

A complex adaptive notch filter is developed, for tracking single-sided (a.k.a. analytic or complex) tones immersed in background noise. A complex all-pass based realization is pursued which inherits useful properties from its real counterpart: independent tuning of the notch frequency and attenuation bandwidth, easy realization of the complementary band-pass filter, unbiased frequency estimation, and faster convergence and tracking than a gradient descent algorithm.