Simplified adaptive algorithm for constrained notch filters with guaranteed stability

The stability issue in adaptive notch filters is investigated from a structural viewpoint. A new adaptive algorithm for direct frequency estimation is developed using a constrained pole-zero notch filter. The basic characteristic of this algorithm is that the notch filter is realised in a cascade form, with each stage implemented in a normal realisation. A simplified version of the gradient signals is derived, which makes the algorithm very efficient. It is shown that this proposed adaptive notch filter is bounded-input-bounded-output stable. Numerical examples with simulations, where the proposed algorithm performs well in terms of convergence and guaranteed stability, are given to support the theoretical results