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Biomedical Instrumentation B18/BME2

Biomedical

Instrumentation B2. Dealing with noise

B18/BME2

Dr Gari Clifford


Noise & artifact in biomedical signals

Ambient / power line interference: 50 ±0.2 Hz mains noise (or 60 Hz in many data sets) with an amplitude of up to 50% of full scale deflection (FSD), the peak-to-peak ECG amplitude. Also includes ambient light changes (for PPG)

Sensor pop or contact noise: Loss of contact between the sensor and the skin manifesting as sharp changes with saturation at FSD for periods of around 1 s on the ECG (usually due to an electrode being nearly or completely pulled off);

Patient–sensor motion artifacts: Movement of the electrode away from the contact area on the skin, leading to variations in the impedance between the electrode and skin causing potential variations in the ECG and usually manifesting themselves as rapid (but continuous) baseline jumps or complete saturation for up to 0.5 second;

Electromyographic (EMG) noise: Electrical activity due to muscle contractions lasting around 50 ms between dc and 10,000 Hz with an average amplitude of 10% FSD level;

Baseline drift: E.g. respiratory motion with an amplitude of ~15% FSD at frequencies drifting between 0.15-0.3 Hz;

Hardware electronics noise: Artifacts generated by the signal processing hardware, such as signal saturation;

Electrosurgical noise: Noise generated by other medical equipment present in the patient care environment a frequencies between 100 kHz and 1 MHz, lasting for approximately 1 and 10 seconds; - may include defibrillation artifact too.

Quantization noise: Steps introduced into data

Clock drift & missing data: Sampling frequency is not constant – always use a real-time OS

Aliasing: Spurious frequencies because sampling frequency is too low or data were resampled

Signal processing artifacts: (e.g., Gibbs oscillations, IIR filters, ).

Other biological sources & sinks :(e.g., non-conductive tissues, fetal/maternal mixture, observer pulse).


Quantisation Noise

Imagine a QRS complex

The R-peak is always cut-off

This leads to additional low

and high frequency

contributions to the signal


Quantisation Noise

Signal to Noise Quantisation Ratio

(Q = # bits)

E.g. A 16-bit ADC has a maximum signal-

to-noise ratio of 6.02 × 16 = 96.3 dB.

Assumes uniform distribution of signal

If not, then reduce: E.g. If a sine wave,

then multiply by 2-½


Aliasing The corresponding behaviour in the time domain is obvious is

we consider a sinusoid of frequency fm :

Hence we have to sample at least twice every period in order

to disambiguate, and so fs > 2 fm , or equivalently ωs > 2 ωm

fs < 2 fm

fs < 2 fm

fs = fm


How fast should we sample the ECG?

fs > 2 fm ... So what is the highest frequency in the ECG?

Think about the idealised ECG

S-wave is ½ square = 0.02s = 50Hz


Signal Processing Artifacts

Spectral leakage

Windowing

Harmonics

Multiples of the

fundamental

frequency

E.g. ...


DFT recap: Sampling

Sample the time-signal by multiplication

with a train of pulses...

...which corresponds to convolution

in the frequency domain


Consider some time-domain signal, x(t),

which has frequency transform, X(ω)

FT FT-1

Review: The Fourier Transform

eix = cos(x) + isin(x)


Sampling x(t) means multiplying it by a pulse train

This means convolving X(f) with the FT of the pulse train

Review: time-sampling

pulse train time signal Convolved freq. signal


Multiply by window W(t), or convolve with a sinc W(f) in freq:

Windowing

windowed

pulse train time signal Convolved freq. signal FT[window]


The DFT

The DFT:

The DFT-1:


Where is the heart rate?



Filter distortion

Finite Impulse Response – pass band ripple, amplitude

attenuation

Infinite Impulse Filters – phase distortion


Recap – Analogue Filters

Kirchoff’s laws give:

Therefore:

Which can be discretised:



Magnitude of gains:

... and phases:

Impulse responses: (Inverse Laplace Transform of H ...

with =RC ... i.e. Response of

circuit to a Dirac delta (t).

Note u(t) is Heaviside function) and a three poles (origin, =1/RC)



Nonlinear amplification / attenuation

Nonlinear phase distortion

Different frequencies

are delayed by

different amounts


Recap – Digital Filters

A filter transforms the input signal:

X is transformed into Y by multiplying by a transfer

function H

H is composed of two types of coefficients (a & b)

The a’s multiply the input signal (X) only

The b’s include the output in the calculation

P is the feedforward order and Q the feedback order

Poles of filter are found by setting denominator of H

equal to zero


Frequency & Phase Response

Convert an impulse

function to frequency and

phase response.

E.g. bk ={0.3, 0.7, 0, -0.3, -0.7}



Filter distortion

Finite Impulse Response – pass band ripple, amplitude

attenuation

Infinite Impulse Filters – phase distortion


Gibbs Oscillations / Ringing

Consequence of

convolving

impulse response

of window (sinc

function) with

signal

In electrical

circuits= oscillation

of V or I when

electrical pulse

causes the

parasitic C & L

(from other

materials on IC)


AR models for spectral estimation

The notation AR(p) refers to the autoregressive model of

order p. The AR(p) model is written as follows:

Y t = ai Y t-i + t (1 i p)

where the ai’s are the parameters of the model and εt is a white-noise process with zero mean.

An autoregressive model is essentially an infinite

impulse response filter which shapes the white-noise

input. The poles are the resonances of the filter and

correspond to the spectral peaks in the signal.

http://en.wikipedia.org/wiki/Infinite_impulse_response

http://en.wikipedia.org/wiki/Infinite_impulse_response


AR-model vs FFT spectra (for EEG)

AR model is

parametric

Requires only a

few coefficients

Useful for

estimation on

short time series


Credits

DFT slides – Dr David Clifton

PSD slide – Dr James Pardey

b2. dealing with noise - university of oxfordgari/teaching/b18/lecture_slides/b18_lectureb... ·...

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