PE2-3.4 Filtering for Removal of Artifacts
You can apply synchronized averaging and moving average filters in the time domain, use derivative-based operators and notch filtering in the frequency domain, and design a Wiener or adaptive filter for artefact removal.
Choosing the filter is a matter of knowing what the artefact is: mains interference is narrowband so a notch works, baseline wander is low frequency so a high-pass or derivative operator works, and random noise on a repeatable event yields to synchronized averaging. Synchronized averaging is the most powerful technique here and it needs something the others do not — a trigger marking each repetition. The Wiener filter is optimal only when you know the signal and noise spectra, which is exactly the assumption adaptive filtering removes.
Work through these
Statistical preliminaries
The statistics needed before any filtering: what noise is, and how it combines with signal. Short, and everything below depends on it.
Time domain filtering: synchronized averaging
Averaging repeated recordings aligned to a stimulus, which pulls a signal out of noise far larger than itself. It is how event-related potentials are recovered at all.
Time domain filtering: the moving average filter
The simplest filter there is, and its frequency response. Knowing that a moving average is a low-pass filter with awkward side lobes explains its limits.
Moving average filter to integration; derivative-based operators
Two related operations, one smoothing and one sharpening. Derivative operators amplify noise, which is why they are always paired with smoothing in practice.
Frequency domain filtering: the notch filter
Removing one narrow band, which is almost always mains interference. It is the most used filter in the subject and it distorts the signal near that frequency.
Optimal filtering: the Wiener filter
The filter that is optimal given the statistics of signal and noise. It requires knowing those statistics, which is the assumption to keep in view.
Adaptive filtering
Filtering that changes as the signal changes, which is what non-stationary biomedical signals need. It is also how a reference channel can cancel an artefact.
Selecting the appropriate filter for a given artefact
The item that ties the topic together: matching the filter to the artefact. Choosing badly removes signal along with noise, which is the failure to avoid.
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