PE2-3.4 Filtering for Removal of Artifacts

What this is and why it exists

Every recording in this subject arrives with unwanted material in it. Removing it is not one technique but a choice between several, and choosing badly removes signal along with the noise.

The whole topic reduces to one habit. Identify what the artefact actually is, then pick the filter that exploits how it differs from the signal.

The vocabulary

• Artefact — anything in the recording that is not the signal you wanted.
• Baseline wander — slow drift of the whole trace up and down.
• Mains interference — a narrow band of interference at the electrical supply frequency.
• Synchronized averaging — averaging repeated recordings aligned to a trigger.
• Trigger — the marker saying where each repetition begins.
• Moving average filter — an output that is the average of the last few input samples.
• Derivative operator — a filter responding to how fast the signal is changing.
• Notch filter — a filter removing one narrow band and passing the rest.
• Wiener filter — the filter that is optimal given the signal and noise spectra.
• Adaptive filter — one that adjusts itself as the signal changes.
• Reference channel — a separate recording of the interference alone.

The mental model

Match the method to the artefact, and the matching is always about a difference you can exploit.

Mains interference is narrow in frequency. The supply runs at a single frequency, fifty or sixty hertz depending on the country, and its interference sits there and at its multiples. A notch filter removes that narrow band and leaves the rest. It is the most used filter in the subject, and it is not free. It removes whatever signal was at that frequency, and it distorts phase nearby.

Baseline wander is low in frequency. It comes from breathing and from slow electrode changes, and it sits well below the signal's own band. A high-pass filter removes it, and a derivative operator does too, because differentiating suppresses slow components. Both work because the artefact and the signal separate cleanly in frequency.

Random noise on a repeatable event yields to something more powerful. If the event can be repeated and each repetition marked, add many recordings aligned to that marker. The signal is the same each time and adds up. The noise is different each time and partly cancels. The signal grows in proportion to the number of repetitions, and the noise only as its square root. So the ratio improves as the square root of the count.

That is synchronized averaging, and it is the strongest technique here. It is also the one with a requirement the others do not have. You need a trigger marking each repetition. Without one there is nothing to align, and the method cannot be used. It is how event-related potentials, which are invisible in any single recording, are recovered at all.

The moving average filter is the simplest filter that exists, and it is worth knowing what it really is. Averaging the last several samples is a low-pass filter, and its frequency response has awkward side lobes rather than a clean stopband. That explains both why it works and why it is not a good filter when the requirement is precise.

Derivative operators are the mirror. They emphasise fast changes, which is useful for finding sharp features. They also amplify noise, because noise is full of fast changes. That is why in practice they are always paired with smoothing, a combination the next topic uses directly.

The Wiener filter is the optimal linear filter given the power spectra of the signal and the noise. It is a genuine optimum and it comes with a genuine condition: you must know those spectra. In this subject you usually do not, and they change as the recording goes on.

Adaptive filtering removes exactly that assumption. The filter adjusts its own coefficients as it runs, following the changing statistics. That suits non-stationary signals, which is what these are. It also enables something the fixed filters cannot do. Record the interference on its own, on a separate channel, and an adaptive filter can learn how it reaches the signal channel. It can then subtract it, even where the two overlap completely in frequency. That is the answer to interference which no frequency-based filter can touch.

What you should now be able to explain or do

Identify an artefact by its character before choosing a filter. Say why a notch filter suits mains interference and what it costs. Explain synchronized averaging, its improvement with repetition count, and the requirement it carries. Say what a moving average filter really is and why derivative operators need smoothing. State the Wiener filter's condition, and say what a reference channel lets an adaptive filter do.

Check yourself