Abstract
AbstractIn this paper, a new algorithm for the detection of a single sinusoid corrupted by Gaussian noise using IIR adaptive bandpass/notch filter is presented. As the first step, the relation between the convergence speed and the filter Q‐factor in IIR adaptive bandpass filter is analyzed. Based on the result of analysis, an algorithm is derived in which the filter Q‐factor and the adaptive control signal generator Q‐factor are made continuously variable so that they are inversely proportional to the distance between the filter center frequency f0 and the frequency f of the sinusoid to be detected. This makes both the convergence speed of f0 and f and the resolution high. Then it is found that limiting the maximum amplitude response of the adaptive control signal generator to a value proportional to sin 2πf can suppress the coefficient fluctuation after convergence effectively. By this approach, an IIR adaptive filter with a high Q can easily be realized. As the next step, an additional high‐speed and highly stable adaptive algorithm is proposed in which the step size of the filter coefficient update is made to vary inversely with the filter Q‐factor. A realization of the IIR adaptive notch filter is also presented. Finally, the usefulness of the proposed adaptive algorithm is verified by a computer simulation.
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