Convergence analysis of complex adaptive IIR notch filters with colored noisy signal

In this paper, we present a method to obtain the convergence properties of adaptive complex IIR notch filters. The adaptive detection of a complex sinusoid with additive noise has been investigated. The effects of the colored noise on the convergence speed have been presented. The bias in the frequency estimate assuming colored input noise has also been derived for the single sinusoid case. The results of computer simulation are shown which confirm the theoretical prediction.