Two discrete oscillator based adaptive notch filters (OSC ANFs) for noisy sinusoids

We propose two adaptive notch filters (ANFs) for sinusoids embedded in a noisy environment. Both of the ANFs, as usual, are structurally composed of a time-variant infinite-impulse-response (IIR) filter that serves as a line-enhancer and an adaptive mechanism that serves as a frequency estimator. The novelty of ANFs is that the derivations of the coefficient-updating algorithms for the adaptive mechanisms are both inspired by a discrete oscillator model and, moreover, are both independent of the structures of the line-enhancement filters chosen. A second-order IIR bandpass filter is selected to serve the line-enhancement portions for both of the two ANFs. Analyses and computer simulations show that the performances of the proposed ANFs are very promising.