A complex adaptive notch filter using modified gradient algorithm

A modified gradient algorithm is developed for improving the convergence speed of a first-order complex adaptive IIR notch filter, which is used for estimating an unknown frequency of a complex sinusoidal signal embedded in white Gaussian noise. The new cost function using new error criterion is presented and analyzed theoretically. The proposed technique can significantly improve the convergence speed as compared with a complex notch filter using plain gradient algorithm. The computer simulations are conducted to demonstrate the validity of the proposed complex adaptive notch filter.