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Noise reduction and signal decomposition are among important and practical issues in time-domain signal analysis. This paper presents an adaptive notch filter (ANF) to achieve both these objectives. For noise reduction purpose, the proposed adaptive filter successfully extracts a single sinusoid of a possibly time-varying nature from a noise-corrupted signal. The paper proceeds with introducing a chain of filters which is capable of estimating the fundamental frequency of a signal composed of harmonically related sinusoids, and of decomposing it into its constituent components. The order of differential equations governing this algorithm is 2n+1, where n is the number of constituent sinusoids that should be extracted. Stability analysis of the proposed algorithm is carried out based on the application of the local averaging theory under the assumption of slow adaptation. When compared with the conventional Fourier …