Qr-decomposition based adaptive notch filters

Adaptive notch filters (ANF) are a special case of IIR adaptive filters that are able to track and cancel a time-varying sinusoid or a narrow band interference signal from a broad band signal. These filters update zeros and poles of the notch filters based on an objective function that minimizes the output signal energy. An ANF algorithm can only be used in practical applications if the underlying adaptive algorithm is inherently stable. QR-decomposition algorithms are known for their stability in finite precision environment. A QR-decomposition based adaptive notch filter is introduced and derived which is capable of estimating and canceling multiple narrow band interferers or sinusoids. The simulation results show that the convergence speed of the proposed method is equivalent to the recursive prediction-error (RPE) algorithm.