Biosignal filtering and artifact rejection

Biosignal processing, 521273S

Autumn 2012

Motivation

1) Artifact removal: for example – power line

– non-stationarity due to baseline variation

– muscle or eye movement artifacts in EEG or ECG

– Solution?: epoch rejection due to artifacts

Motivation

2) Enhancement of useful information – bandpass filtering

– finding certain signal waveforms such as eye blinks from EEG or QRS complexes from ECG

– smoothing for illustrative purposes

FIR

• Finite impulse response (FIR) filter

– Stable

– Simple to implement

– Linear phase response • Symmetrical impulse

response

• All frequencies have the same amount of delay – no phase distortion

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Source: http://www.netrino.com/Publications/Glossary/Filters.php

FIR structure

FIR

Lowpass filter, order 44 (N=45), positive symmetry. fs=256 Hz, Fp=13 Hz, Rp=4 dB, Fs=19 Hz, Rs=38 dB

0 5 10 15 20 25 30 35 40 45-0.04

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0.12

0 20 40 60 80 100 120-800

-600

-400

-200

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Frequency (Hz)

Phase (

degre

es)

0 20 40 60 80 100 120-100

-50

0

50

Frequency (Hz)

Magnitude (

dB

)

Characteristics: passband, transition band, stopband, ripple, attenuation, sampling frequency

IIR

• Infinite impulse response filters

– Feedback system

– Normally fewer coefficients that with FIR

– Used for sharp cut-off (notch filters for example)

– Can become unstable or performance degrade if not designed with care

– Pole-zero diagram

– Nonlinear phase characteristics causes phase distortion altering harmonic relationhips – frequency components have different time delays (often undesirable)

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Source: http://www.triplecorrelation.com/courses/fundsp/iiroverview.pdf

Smoothing: averaging filter

• Average of sliding window of size N samples – FIR filter

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Smoothing: Hanning filter

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Smoothing: Butterworth lowpass filtering

Butterworth lowpass filter

- Select suitable order and cutoff frequency

Synchronized averaging

• Filter noise by averaging several signals containing the same events – Often simple/complex pulses

• Signals must first be time-synchronized

Averaging of flash visual ERP’s from EEG

Notch/comb filter

• Often used for 50/60 Hz power line artifact filtering

• Narrow stop-band in basic and harmonic frequencies

• Be careful with the aliased harmonics

• Can be implemented as FIR or IIR

Ruha et al. (1997)

Notch/comb filter

Filtering result Original signal

Trend removal (detrending)

• High-pass filtering

– time-domain: difference filter

– frequency-domain: DFT

• Trend removal with other methods

– Savitzky-Golay filter

– IPG-FMH (in-place growing – FIR median hybrid)

Difference filtering, version 1

First-order difference operator: T=sampling interval )]1()([

1)( nxnx

Tny

Difference filtering, version 2

Modified first-order difference operator: - T=sampling interval - Additional pole inserted at zero frequency to steepen the transition band

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Detrending: Butterworth highpass filter

Select suitable order and cutoff frequency

Savitzky-Golay filter

• S-G filters are called polynomial or least-squares smoothing filters

• Fits a polynomial of given degree optimally to a signal window

• In a sliding time window (frame), a polynomial curve is fitted to signal, and its middle value in the frame is taken as a smoothened value

• Decomposes the signal into a trend signal and residual signal – The trend component can be interpreted as

the useful signal component or the noise component, depending on the application

• Can be realized as a fast FIR filter

0 200 400 600 800 1000 1200 1400 1600 1800 2000-4

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2

4ORIGINAL

0 200 400 600 800 1000 1200 1400 1600 1800 2000-4

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4POLYNOMIAL ORDER 3, FRAME SIZE 21

0 200 400 600 800 1000 1200 1400 1600 1800 2000-4

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4POLYNOMIAL ORDER 3, FRAME SIZE 41

IPG-FMH • In-place growing FIR-median hybrid filters

(IPG-FMH) are based on median filtering and FIR-filtering – Median filter: takes the median value within a

signal window as filter output value

• Has robust nature against noise

• Pulses longer than root signal are detected reliably, shorter pulses are removed

• Suitable also for trend estimation of signals

• Preserves sharp edges in trend better than linear low-pass filter

• Attenuates wide-band noise effectively

Wichman et al. (1990)

Wiener filtering

• Optimal filter that takes into account statistical characteristics of signal and noise processes

• Noise spectrum S and desired signal spectrum Sd must be known or estimated

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LMS adaptive filtering (least mean square)

• Situation: an interfering signal component is summed to the actual biosignal

• Filter aims to subtract the interfering signal x from the “noisy” biosignal y

• The interference signal x is usually measured independently and simultaneously with another sensor device

• In an ideal situation, the interference signal x is identical to the interference component in y; only the amplitude and sign must be determined before subtraction (one filter weight is enough)

• Sometimes only a correlated version of the interference can be measured; the filter adapts the interference signal shape optimally to the interference signal component that appears in y (many filter weights are needed)

• Be careful with the possible delay between the interference signal and biosignal

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LMS adaptive filtering (least mean square)

• Based on steepest descent optimization algorithm, where the n filter weights are updated at every sample iteratively according to local gradients on error surface

• Learning rate parameter

– 0 < < 1/lmax

– lmax : largest eigenvalue of data correlation matrix

– should be adaptive if data is nonstationary

• Proper initialization of filter weights is important – E.g., letting the filter adapt for a while

without outputting anything (works on-line)

– E.g., running filter backwards in time to initialize (works off-line)

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Example: removing respiration effects from heart rate data

Example: removing ocular artifacts from EEG

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Adaptive filtering of ECG

Selected references

Journal articles on two trend detectors • Wichman R, Astola JT, Heinonen PJ, Neuvo YA (1990) FIR-Median Hybrid Filters with excellent

transient response in noisy conditions. IEEE Trans. Acoust., Speech, Signal Processing 38:2108-2117.

• Original Savitsky-Golay paper: http://pubs.acs.org/cgi-bin/archive.cgi/ancham/1964/36/i08/pdf/ac60214a047.pdf

Books on signal processing basics • Ifeachor EC, Jervis BW. Digital Signal Processing: A Practical Approach. Addison-Wesley,

reprint 1996, pp. 279-287, 375-383, 550-551, 561-563, 697-706.

• Orfanidis, SJ. Introduction to Signal Processing. Prentice-Hall, Englewood Cliffs, NJ, 1996, pp. 434-441.