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Detection, estimation and filtering of desired signal in the presence of noise are some of the most common and practical problems in the analysis of time domain. The analysis in the time domain often involves the comparison of two different signals and stochastic signals are usually more profitably analyzed in the time domain. Extraction of signals are considerably improves quality of signal. In many signal processing applications is to decompose an original signal into its primitive or fundamental constituents and to perform simple operations separately on each component, thereby accomplishing extremely sophisticated operations by a combination of individually simple operations. Noise reduction and signal decomposition are among important and practical issues in time-domain signal analysis. This book presents an Adaptive Notch Filter (ANF) to achieve both these objectives. For noise reduction purpose, the presented adaptive filter successfully extracts a single sinusoidal of a possibly time varying nature from a noise-corrupted signal.