Abstract
In this paper, we propose an adaptive notch filter that realizes the phase shift of the all-pass filter by the expression of Fourier sine series. The method to control the weights of the all-pass filter composed by IIR filter is known well. However, these adaptive notch filters have not been put to practical use since the peculiar stability problem of IIR filter and the problem concerning the determination method of the degree of IIR filter exist. The proposed adaptive notch filter is always stable since the all-pass filter is composed by an exponential filter. Moreover, the adaptive algorithm is a simple gradient based algorithm and the convergence of weights is guaranteed. The degree of the all-pass filter only depends on the required steepness of the elimination characteristic and does not depend on the number of narrowband signals that should be eliminated. Moreover, it can be said that the proposed method is a suitable method for practical use since the elimination characteristic hardly influenced by the broadband signal added to the narrowband signal. Finally, the analytical results and the above mentioned feature are strictly verified by computer simulation.
