Tutorial - IPEM 2006

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Tutorial on Biomedical Signal ProcessingDavid [e-mail] 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) ...

Informations

• Publié par: Issi
• Nombre de lectures: 22
• Langue: English

Extrait

Tutorial on Biomedical Signal Processing

David Simpson [e-mail]

Overview of Biomedical Signal Processing

Acquisition

Interpretation

Outline

Preprocessing

Information extraction

• Sampling • Fourier transforms • Developments and Discussion

• Concepts, principles and examples – no maths

2

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 Input

Analog-to-Digital (A/D) conversion

Signal Acquisition Systems

Digital Signals What are digital signals?

Anti-alias Filter

2

97 101 153

30

4

ADC

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

6

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

5

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

11

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 Hz 12 s

4

Anti-alias filtering

Low-pass filter the signal before digitizing (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 micr clipping • 8 bits poor quantization

Fourier Transform

220

230

mic range: 50 microV

14

• (Almost) all signals can be considered as (infinite) sums of (infinitesimal) cosine waves •x(t)⇔X(f) time domain⇔frequency domain • Discrete Fourier Transform: x(n)⇔X(n)

N−1N−1 −j(2 π /N)in 1 j(2 π /N)in X(i)=x(n)e⇔x(n)=X(i)e ∑ ∑ n=0 N i=0

15

5



50

0

10

8

6

4

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

50

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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2

8

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 tool 25

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 • [e-mail]

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