Convergence analysis of complex adaptive IIR notch filters

In this paper, we present a new structure for the complex adaptive IIR notch filter which is useful for the detection of complex sinusoids in communication and radar systems. The proposed structure is based on the direct form first-order complex notch filter using a gradient-based algorithm. A quantitative analysis of convergence properties is developed. It has been shown that the convergence speed does not depend on the variance of input white noise. The effects of colored Gaussian noise on convergence speed have been analyzed. By using the proposed first-order section, a new cascaded structure for the complex adaptive notch filter is also shown. The results of computer simulation are shown which confirm the theoretical prediction.