Improving the performance analysis of a gradient‐based adaptive IIR notch filter

Abstract

SUMMARYImprovement of performance analysis is discussed for the plain gradient-type adaptive IIR bilinear notch filters often used in the areas of communication, control, radar, and so on. Specifically, instead of the gradient linearization in the conventional analysis, nonlinear terms are introduced in the approximate expression of the gradient and an explicit expression of the estimation variance of the gradient algorithm in the steady state is derived. In regard to the step size, the convergence condition is derived that guarantees convergence of the algorithm. Its effectiveness and limitation are clarified.