A stable and efficient adaptive notch filter for direct frequency estimation

We investigate the problem of direct frequency estimation. A new adaptive algorithm is developed for constrained pole-zero notch filters. The basic characteristic of this algorithm is that the notch filter is cascaded and, hence, purely parametrized by the notching frequencies. This makes the algorithm much simpler and, hence, more efficient and more robust such that the poles and zeros are automatically located on the respective constrained circle, no matter if the algorithm is implemented with infinite or finite precision. The algorithm is analyzed and compared with some existing algorithms. Several numerical examples are given as well as the corresponding simulations.