biosignal.pdf

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Biosignal Analysis

Biosignal Processing Methods

Medical Informatics 1

WS 2005/2006

J H van Bemmel, MA Musen:Handbook of medical informatics, Springer 1997

Biosignal Analysis


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Introduction

Fig. 8.1:The four stages of biosignal processing

Types of Signals

Fig. 8.2:Types of biological signals


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Types of Signals

Figure 8.3: Impulse series

Analog-to Digital Conversion

08.01Bandwidths, Amplitude Ranges, and Quantization of Some Frequently UsedBiosignals

Signal Bandwidth(Hz)

Amplituderange

Quantization(bits)

Electroencephalogram 0.2-50 600 V 4-6

Electrooculogram 0.2-15 10 mV 4-6

Electrocardiogram 0.15-150 10 mV 10-12

Electromyogram 20-8000 10 mV 4-8

Blood pressure 0-60 400 mm Hg 8-10

Spirogram 0-40 10 L 8-10

Phonocardiogram 5-2000 80 dB 8-10

Table 8.1.Bandwidths, AmplitudeRanges, and Quantization of SomeFrequently Used Biosignals.


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08.01Sampling of Signals: How Often?

Without exception, all biosignals are analog signals. Processing of biosignals by computers thereforerequires discretization (i .e., sampling and quantification). This panel explains thesampling process withoutreferring to formulas.

Thesampling theoremmathematically phrased by Shannon and Nyquist states that asignal must besampled at arate at least twice therateof the highest-frequency component present in the signal. If we useasampling rate that is too low, thesignal is distorted. If we obey the sampling theorem, thecompletesyntactic information contentof thesignal is retained. This is illustrated by the following example.

An EEG usually contains statistical, more or less sinewave-shaped fluctuations that may occur at arateofup to 30 times/second. This can also be expressed by saying that theEEG contains frequencies up to 30 Hz.Higher frequencies may also bepresent (e.g., fromother signal sources) but thesearegenerally not ofsemantic interest.

Thesampling theoremthen prescribes that weshould samplethe EEG at least at 2 x 30 =60 Hz to keep allsignal properties.Table 8.1gives thefrequency bandwidths of interest and the most commonly usedsampling rates for somebiosignals. For instance, for ECGs (bandwidth, 0.15-150 Hz) a sampling rateabovetheShannon frequency (500 Hz) is most often used. If we obey theruleof the sampling theoremit

is, in principle, possible to restore theoriginal analog signal by digital-to-analog conversion.


08.02Sampling of Signals: How Accurate?

When sampling asignal, we use ananalog-to-digital converter (A-D converter or ADC). Samples are takenat arateat least twicethe rateof thehighest-frequency component contained in the signal (i.e., the mixtureof signal plus noise, unless thenoisehas been filtered out beforehand), and thesamples are quantitated andexpressed as numbers. Thelatter is always donewith a limited accuracy and may, in principle, add so-called quantization noise to thesampled signal. This quantization noiseshould generally not exceed thenoise that is already present in thesignal, or, as expressed in moregeneral terms, discretization by theADCshould not increase theinformation entropy (seeChapter 2); syntactic and semantic signal propertiesshould be left intact.

Thedegreeof quantization can be expressed as the number of quantization steps for therangeof possibleamplitudevalues. If thesignal amplitude spans a range ofAvolts (e.g., from-A/2 to +A/2) and thequantization step isq, then the number of quantization steps ism=A/q.

In practice, letmbea power of 2: m=2n, so that thequantization of the ADC can be expressed in nbits.For instance, an ADC with an accuracy of 10 bits can discern 210=1024 different amplitudelevels,resulting in a resolution of about 0.1%, expressed as apercentage of thesignal rangeA. An ADC thatdelivers samples with 8-bit accuracy (28 =256 steps) is called an 8-bit ADC. A 1-bit ADC only determinesthesign of the signal (or whether it is larger or lower than somethreshold).

For most biosignals a6- to 12-bit ADC is sufficient; a12-bit ADC implies a resolution of 1/4096 (less than0.025%), related to a signal-to-noise ratio which is far superior to that attainablewith most signaltransducers.


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Figure 8.4: Effect of sampling frequencies

Application Areas of Biosignal Analysis

Figure 8.5: Four different situations in biosignal processing:

output signal, evoked signal, provocative test, process modelling.


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Biosignal Processing Methods

Signal-Amplitude Properties

Figure 25.1: Amplitude distribution functions

(density distribution function (ddf))


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Figure 25.2: Examples of 2D amplitude distributions


Figure 25.3: Vectorcardiogram


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Fig. 25.4: Two-dimensional amplitude ddfs for EEG amplitudes and RR intervals


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Frequency Spectra and Filtering

Figure 25.5: Examples of three biological signals with their

frequency spectra


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Figure 25.6: Frequency components.

25.03Wavelet Analysis

In Fourier analysis, asignal is thought to be composed of sines and cosines. By using theFourier transform,asignal can be decomposed in these basic functions. Thesamples of thetransformed signal (Fouriercoefficients) represent thecontribution of sineand cosine functions at different frequencies. A disadvantageof Fourier analysis is that it is difficult to composea signal that is limited in time, by using functions that,by definition, stretch out into infinitetime. It is thereforedifficult for aFourier function to approximatesharp changes in a signal. For example, avery simpleand time-limited signal, a spike, is decomposed byFourier transformation into an infinitenumber of sines and cosines (seealso Fig 25.6afor thedecomposition of a block signal).

A way to tackle this problemis throughwavelet analysis. It uses thesameprincipleas Fourier analysis,namely, that signals arecomposed of basic functions, calledwavelets. The most important differencebetween thesewavelets and the sines and cosines used in Fourier analysis is that wavelets are limited intime. Theprocedure for wavelet analysis is to choosea suitable wavelet prototype function (also calledmother wavelet or analyzing wavelet) that meets certain constraints. A ll composing functions arederivedby stretching or scaling themother wavelet both in time and in amplitude. Using a wavelet transform, thesignal is decomposed into thesescaled versions of the mother wavelet. In fact, the composing cosines usedin Fourier analysis can also be seen as stretched, scaled, and shifted versions of amother-cosine. In Fourieranalysis, the composing functions areinfinite in thetime domain because they represent exactly onefrequency. In wavelet analysis, thecomposing wavelets havea limited extent both in the timedomain and

in thefrequency domain, where contributions fromfrequenciesoutside acertain areaarenegligible.

Themost important result of the wavelet transformis thelocationof the composing wavelets in time. Sharp, time-limited signal partswill berepresented by wavelets that arescaled down in duration.As in Fourier analysis, the contribution of thecomposing waveletsto thesignal provides information about the temporal properties ofthesignal on different timescales. Additionally, the locations of thecomposing wavelets provideinformation about the position of aspecific signal property. Figure25.7shows two examples of a

mother wavelet, both fromthe well-known Coiflet wavelet family.


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Figure 25.7: Two examples of a mother wavelet.


Figure 25.8: Frequency spectra of an ECG.


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Figure 25.9: Schematic representation of filters.


Figure 25.10: ECG and its band-pass filtered version.


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Frequency Spectra and Filtering15.01Relationships between True Positive (TP), True Negative (TN), False Positive(FP), and False Negative (FN)

Decision Model

+ -

+ TP FN 100%Truth

- FP TN 100%

Table 15.1. Relationships between TruePositive (TP), T rue Negative(TN), FalsePositive (FP), andFalse Negative(FN).

15.02Il lustration of Sensitivity, Specificity, and Predictive Value

Decision Model

+ -

+ a b a +bTruth

- c d c +d

a +c b +d a +b +c +d

Table 15.2. Illustration of Sensitivi ty, Specificity, and Predictive Value (seetext).

sensitivity=a/(a+b)specificity=d/(c+d)

ppv=a/(a+c)npv=d/(b+d)


Figure 15.6: Distributions of systolic blood pressure of hypertensive

and nonhypertensive people: a) population survey, b) primary care,c) cardiac clinic


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Figure 15.7: Distributions of the primary population of Fig. 15.6.


Figure 15.8: ROC curves of the population of Fig. 15.7

TN (100-FP) vs. FN (100-TP).


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Signal-to-Noise Ratio

Figure 25.11: Coherent averaging in an ECG recording.

Signal-to-Noise Ratio

25.04Coherent Averaging

In coherent averaging we computethe sumof, say,Kwaveforms s0, which areextracted after detectionfroma noisy signal x0(t) =s0(t) +n0(t). Theoriginal signal varianceis S0 =s0

2 and thenoise variance isN0=n0

2, so that theSNR is:

SNR0 =S0/N0.

Thesumof theKsignal waveformss0 will result in awaveforms1 which isKtimes as large as the originalwaveform, that is,s1 =Ks0. The resulting signal dispersion is alsoKtimes as large:s1=Ks0. The varianceofs1 is thenS1=s1

2=K2s02.

Weassumethat thenoisehas anormal distribution. TheKnoisy waveformsn0 are also summed to a newnoisy signal, n1. I t can be proven that thevariance ofn1 isK(and notK

2) times as large as thevarianceofn0so thatN1=n1

2=Kn02. The SNR after summation is then:

SNR1 =S1/N1 =K2s0

2/Kn02 =Ks0

2/n02 =KS0/N0 =KSNR0.

This implies that theSNR has improved linearly with thenumber of summed waveforms.


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Signal Detection

25.01Four Different Detection Situations for the Decision D that an eventS is Present

Situationa Description S D

TP Theevent is present AND is correctly detected 1 1

FP Theevent is not present AND is incorrectly detected 0 1

TN Theevent is not present AND is correctly not detected 0 0

FN Theevent is present AND is incorrectly not detected 1 0

Table 25.1. Four Different Detection Situations for the Decision D that an eventS is Present.

aTP, truepositive; TN, truenegative; FP, falsepositive; FN, falsenegative.

Signal Detection

Figure 25.12: Detection and estimation may reinforce each other.


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Signal Detection

Figure 25.12: An artificial signal of amplitude-modulated impulses.

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