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An adaptive filter is a system with a linear filter that has a transfer function controlled by variable parameters and a means to adjust those parameters according to an optimization algorithm. Because of the complexity of the optimization algorithms, almost all adaptive filters are digital filters. Adaptive filters are required for some applications because some parameters of the desired processing operation (for instance, the locations of reflective surfaces in a reverberant space) are not known in advance or are changing. The closed loop adaptive filter uses feedback in the form of an error signal to refine its transfer function. Generally speaking, the closed loop adaptive process involves the use of a cost function, which is a criterion for optimum performance of the filter, to feed an algorithm, which determines how to modify filter transfer function to minimize the cost on the next iteration. The most common cost function is the mean square of the error signal. As the power of digital signal processors has increased, adaptive filters have become much more common and are now routinely used in devices such as mobile phones and other communication devices, camcorders and digital cameras, and medical monitoring equipment. The recording of a heart beat (an ECG), may be corrupted by noise from the AC mains. The exact frequency of the power and its harmonics may vary from moment to moment. One way to remove the noise is to filter the signal with a notch filter at the mains frequency and its vicinity, but this could excessively degrade the quality of the ECG since the heart beat would also likely have frequency components in the rejected range. To circumvent this potential loss of information, an adaptive filter could be used. The adaptive filter would take input both from the patient and from the mains and would thus be able to track the actual frequency of the noise as it fluctuates and subtract the noise from the recording.

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Adaptive filter

Filter (signal processing)

In signal processing, a filter is a device or process that removes some unwanted components or features from a signal. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. However, filters do not exclusively act in the frequency domain; especially in the field of many other targets for filtering exist.

Kalman filter

For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. Kálmán, who was one of the primary developers of its theory.

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Students learn digital signal processing theory, including discrete time, Fourier analysis, filter design, adaptive filtering, sampling, interpolation and quantization; they are introduced to image pr

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Robust heart rate estimation using wrist-type photoplethysmographic signals during physical exercise: an approach based on adaptive filtering

Jean-Marc Vesin, Sibylle Fallet

Photoplethysmographic (PPG) signals are easily corrupted by motion artifacts when the subjects perform physical exercise. This paper introduces a two-step processing scheme to estimate heart rate (HR)

Institute of Physics2017

Oscillations have been increasingly recognized as a core property of neural responses that contribute to spontaneous, induced, and evoked activities within and between individual neurons and neural en

Public Library of Science2013

Efficient Schemes for Adaptive Frequency Tracking and their Relevance for EEG and ECG

Jérôme Sébastien Van Zaen

Amplitude and frequency are the two primary features of one-dimensional signals, and thus both are widely utilized to analysis data in numerous fields. While amplitude can be examined directly, freque

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