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Tutorial - IPEM 2006

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Tutorial on Biomedical Signal ProcessingDavid Simpsonds@isvr.soton.ac.ukOverview of Biomedical Signal ProcessingPre-processingAcquisitionInformationInterpretationextraction2Outline• Sampling• Fourier transforms• Developments and Discussion• Concepts, principles and examples–no maths31Signal Acquisition SystemsAmplifier / Filter(Signal conditioning)ComputerPatient / TransducerADCAnalog-to-digital converter4Digital SignalsWhat are digital signals?1601401201008060 Do we lose information?4020028 28.5 29 29.5 30 30.5 31time (s)113 114 105 99 95 107 145 123 117 108 101 97 101 153 5Analog-to-Digital (A/D) conversionAnalog Input Digital OutputAnti-alias Sampling QuantizationFilter150 150 150 150140 140 140 140130 130 130 130120 120 120 120110 110 110 110100 100 100 10028.5 29 29.5 30 30.5 28.5 29 29.5 30 30.5 28.5 29 29.5 30 30.5 28.5 29 29.5 30 30.562Blood Pressure (mmHg)Sampling TheoremIf the highest frequency contained in a signal is f , and the signal is sampled maxat a sampling rate of f > 2 f , then the s maxoriginal analog signal can be exactly recovered from the samples.Sampling rate > twice the maximum frequency in signal→ No loss of information7Signal Reconstruction(blood pressure)15014013012011010028.5 29 29.5 30 30.58time (s)Aliasing8Hz, sampled at 10 Hz, appears (aliased) as 2 Hz10.5Aliasing cannot (normally) be 0 undone-0.5-10 0.2 0.4 0.6 0.8 1time (s) ...

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Tutorial on Biomedical Signal Processing
David Simpson ds@isvr.soton.ac.uk
Overview of Biomedical Signal Processing
Acquisition
Interpretation
Outline
Preprocessing
Information extraction
• Sampling • Fourier transforms • Developments and Discussion
• Concepts, principles and examples – no maths
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3
1
51 0 41 0 130 21 0 110 01 0
28.5 29 29.5 30 30.5
Sampling
.82529295.3030.5
25.82925.93030.5
Quantization
Digital Output
Analog-to-Digital (A/D) conversion
Signal Acquisition Systems
Digital Signals What are digital signals?
Anti-alias Filter
2
97 101 153
30
4
31
30.5
29 29.5 time s
160 140 120 100 80 60 40 20 0 28
28.5
113 114 105 99 95 107 145 123 117 108 101
Patient / Transducer
25.82925.93035.0
Amplifier / Filter (Signal conditioning)
Do we lose information?
Analogtodigital converter
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51 0 140 31 0 120 11 0 01 0
51 0 140 130 120 110 01 0
51 0 140 130 120 110 01 0
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Computer
Sampling Theorem
If the highest frequency contained in a signal is f , and the signal is sampled max at a sampling rate of f > 2 f , then the s max original analog signal can be exactly recovered from the samples.
Sampling rate > twice the maximum frequency in signal No loss of information
150
140
130
120
110
100
Signal Reconstruction (blood pressure)
28.5
29 29.5 30 time (s)
30.5
Aliasing 8Hz, sampled at 10 Hz, appears (aliased) as 2 Hz
1
0.5
0
0.5
1 0
Aliasing cannot (normally) be undone
0.2
0.4 0.6 time (s)
0.8
1
7
8
9
3
Aliasing
Aliasing: high frequencies appear at lower frequencies, due low sampling rate.
Example: EEG sampled at 60 Hz. Mains (50Hz) would reappear in EEG at 10 Hz, i.e. in theα-band (8-13 Hz)
10 10 0
10 10 0
Example Speech with noise at 5 kHz
00
original
10000
aliased
5000 frequency (Hz)
10000
10
Sampling frequency f =22050 s
Sampling frequency f =5512 Hz s
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With and without anti-alias filter f =5512 Hz s original (aliased) 5 filtered 10
10 10 0 1000 2000 frequency (Hz) Cutoff frequency: 2000 Hz
Sampling frequency (no filter) f =5512 Hz s
5 10
original (aliased) filtered
500 550 600 650 frequency (Hz)
700
Sampling frequency (with filter) f =5512 Hz12 s
4
Anti-alias filtering
Low-pass filter the signalbeforedigitizing (analog signal), to avoid aliasing
1. Select maximum frequency of interest 2. Select cut-off frequency (f ) of anti-c alias filter a little above this maximum 3. Select sampling rate f > 2* f s c (usually use f > 3* f , because filters s c are not perfect) 13
500
0
500 200
50
0
Quantization The out ut of a ADC is integer
50
50 200 210 230 • Dynamic rang +/- 500 micrclipping • 8 bits poor quantization
Fourier Transform
220
230
mic range: 50 microV
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• (Almost) all signals can be considered as (infinite) sums of (infinitesimal) cosine waves x(t)X(f) time domainfrequency domain • Discrete Fourier Transform: x(n)X(n)
N1N1 j(2π/N)in1j(2π/N)in X(i)=x(n)ex(n)=X(i)e ∑ ∑ n=0Ni=0
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5
50
0
10
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2
0 0
4
2
0
2
4 0
EEG Signal
50 100 frequency (Hz)
50 100 frequency (Hz)
harmonics i=0, 1, 2, 3, 20, 42
10
5
0
5
10 0
1
2 time
3
16
Discrete Fourier Transform original
reconstructed
0.1 0.08 0.06 0.04 0.02 0 0
4
500 1000 1500 17 frequency (Hz)
Selecting a Frequency Band EEG – T6/A6 Selecting only theαfrequency band (8-13 Hz)
40 20 0 20 40 60 80
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29.5
30
30.5
5
4
3
2
1
0 0
very rapid change and slow variations are eliminated: α- activity is enhanced
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10 0
6
Phase spectrum Original phase i .. 2 Phase is important for 1.5 shape and delay of signal 1 0.5 3 0 2 0.5 1 1 0 1.5 0 0.5 1 1.5 2 time 1 Random phase 2 1.5 3 0 5 10 15 20 1 frequency (Hz) 0.5 0 0.5 random phase Delay: 1 1.5 Add linear trend to phase 0 0.5 1 1.5 2 time (s) 19
0.06
0.04
0.02
0 0
0.04
0.03
0.02
0.01
0 0
Examples
3 x 10 5
4
3
2
1
0
500 1000 frequency (Hz)
500 1000 frequency (Hz)
1500
1500
3 x 10 2
1.5
1
0.5
0 0 3 x 10
5 4 3 2 1 0 0
5000 frequency (Hz)
5000 frequency (Hz)
Frequency range
This example: f =22050 Hz s
5000 frequency (Hz)
Sampling rate f max
=
f s 2
10000
21
10000
10000
7
3 x 10 5
4
3
2
1
0
65
DFT
70 75 frequency (Hz)
80
Provides a discrete spectrum: Assumes the data is periodic
Frequency (spectral) olution: 1 f= T
0.2
0
0.2
0.4 0
1000 2000 3000 time (ms)
Fourier Transform vs. Power Spectral Analysis • Fourier Transform: for analysis of a signal • Power Spectrum (PS): for analysis of a statistical (stochastic) process – Recorded signal is a ‘sample’ of process – Estimate of statistical properties of process – Loss of information on recorded signal • Signal cannot be recovered from PS • No phase information
0
0.5
1 tim e [s ]
22
1.5
More methods Noise reduction – Filters (linear and non-linear) – Noise and artefact recognition – Optimal filters (prior information / assumptions) – Multi-channel (P rincipa l and Independent component analysis; adaptive noise cancellation) Time-frequency – Spectrogram – W igner-V ille etc. – W avelets – Do we need them? Signals and Systems – Correlation and coherence (simple, multiple, parti a l, directed) – Modelling • black box vs. physiological – System identification • linear / non-linear • time (in)variant Pattern recognition and classification – Rule-based – Statistical methods – Learning (n eural networks) Statistical analyses – Estimation errors – Inter- and intra-subject variability – Conventional / computationally intensive (Monte Ca rlo, bootstrap)
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Discussion
• ‘Know your signal’ and look at it – Features – Noise and artefact? • Define your question – Is that really the problem? • Know the methods – Assumptions? – Limitations and pitfalls – Interpretation – Is there a simpler alternative? • Consider results – Does it make sense? – So what? • Inferences Common sense – the most important tool25
Next courses
• Signal Processing for Cochlear Implants – 6-7 November, 2006 (TBC) • Demystifying Biomedical Signals: Principles and Applications – 15 - 19 January, 2007 • Biomedical Applications of Signal Processing – 26 - 30 March, 2007
For further information • www.soton.ac.uk/~mtpbsp • ds@isvr.soton.ac.uk
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