CHAPTER 10CHAPTER 10. BIOSIGNAL PROCESSING

Specific Behavioral ObjectivesSpecific Behavioral ObjectivesDescribe the different origins and types of biosignals.g yp gDistinguish between deterministic, periodic, transient, and random signals.Explain the process of A/D conversion.Define the sampling theorem.p gDescribe the main purposes and uses of the Fourier transforms.Define the Z transform.Describe the basic properties of a linear system.Describe the concept of filtering and signal averaging.Explain the basic concepts and advantages of fuzzy logic.Describe the basic concepts of artificial neural networks.

10 1 INTRODUCTION10.1 INTRODUCTIONBi i l (bi l i l i l )• Biosignals (biological signals) :– space, time, or space‐time records of a biological event.– electrical, chemical, and mechanical activitieselectrical, chemical, and mechanical activities– contain useful information that can be used to understand the 

underlying physiological mechanisms, which may be useful for medical diagnosismedical diagnosis

• Biosignal Processing : – a process to retrieve the useful information– Acquisition and Analysis :

• Acquisition : a variety of sensors• Common analysis methods : amplification, filtering, digitization,Common analysis methods : amplification, filtering, digitization, processing, storage

• Sophisticated processing methods : signal averaging, wavelet analysis, and artificial intelligent techniquesy g q

10.2 PHYSIOLOGICAL ORIGINS OF BIOSIGNALS

l l• Bioelectric Signals :– Action potentials generated by excitable cells 

using intracellular or extracellular electrodesusing intracellular or extracellular electrodes– ECG, EGG, EEG, EMG, etc

• Biomagnetic Signals : g g– Biomagnetism is the measurement of the 

magnetic signals that are associated with specific physiological activityspecific physiological activity

– typically linked to an accompanying electric field from a specific tissue or organ. (electromagnetism)

– SQUID (Superconducting Quantum Interference Device) magnetometerInterference Device) magnetometer

– MEG, MNG, MGG, MCG, etc.

10.2 PHYSIOLOGICAL ORIGINS OF BIOSIGNALS

• Bio he i al Si al• Biochemical Signals– Concentration of various chemical agents in the body– Ions, pO2, pCO2, 

• Biomechanical Signals– Produced by mechanical functions of biological systems– include motion displacement tension force pressure and flowinclude motion, displacement, tension, force, pressure, and flow

• Bioacoustic Signals– a special subset of biomechanical signals that involve vibrations 

(motion)(motion).– Heart sound and respiratory sound  measured by using acoustic 

transducers such as microphones and accelerometers.• Biooptical Signals• Biooptical Signals

– generated by the optical, or light‐induced, attributes of biological systems.Fl h t i ti f th i ti fl id (f t h lth– Fluorescence characteristics of the amniotic fluid (fetus health monitoring), Dye dilution method to measure CO, Oxygen saturation

10.3 CHARACTERISTICS OF BIOSIGNALS

l f d h f• Classification according to various characteristics of signal

waveform shape statistical structure and temporal properties– waveform shape, statistical structure, and temporal properties– Continuous vs Discrete signals : x(t) vs x(n)– Deterministic vs Random (Stochastic)( )

• Mathematical functions :• Statistical techniques : 

Stationary vs Nonstationary– Stationary vs Nonstationary

– Periodic and Transient  : x(t) = x(t+kT) – Example : HRV (random) in ECG (periodic)

x(t)=sin(ωt)p p

y(t)=e‐0.75tsin(ωt)

10 4 SIGNAL ACQUISITION10.4 SIGNAL ACQUISITIONO f l A• Overview of Biosignal Data Acquisition– Unwanted interference or noise : exogenous or endogenous

High precision low noise equipment is often necessary to– High‐precision low‐noise equipment is often necessary to minimize the effects of unwanted noise

– the information and structure of the original biological signal of interest should be faithfully preserved.

Electrical E e i asignal

Figure 10.4 bioinstrumentation system

10 4 SIGNAL ACQUISITION10.4 SIGNAL ACQUISITION

A l f d

( )T jω

• Sensors, Amplifiers, and Analog Filters

Sensor should not adversely

G

– Sensor should not adversely affect the properties and characteristics of the signal it is 

i Frequency1f 2f 3f 4f 5f 6f

measuring– Amplifier and Filter :  OP Amp 

circuits

Frequency

- f1 : HPF cut-off

• To boost amplitude• To compensate for distortion caused by the sensor

- f2 : lower limit of biosignal freq.- f3 : power-line freq.- f4 : upper limit of biosignal freq.caused by the sensor

• To meet the specifications of the data acquisition system (analog‐to digital converter)

- f5 : LPF cut-off & anti-aliasing- f6 : A/D sampling freq

to‐digital converter)

10.4.3 A/D Conversion

• Continuity :analog vs digital

아날로그신호아날로그신호

디지털신디지털신호

Conversions between Analog & Digital

(1) A/D 변환 : 아날로그신호를디지털신호로변환- 표본화(sampling) : 시간축상의이산화양자화( ti ti ) 진폭축상의이산화- 양자화(quantization) : 진폭축상의이산화

(2) D/A 변환 : 디지털신호를아날로그신호로변환

디지털

아날로그

Sampling Theorem

신 에 함된최대 파수성분(f ) 다Sampling of Signals: How Often?

- Nyquist Rate : 신호에포함된최대 주파수성분(fc)보다최소 2배이상(2fc)의빠르기로표본화하면 정보의손실없이원래의신호를완벽하게복원할수 있다.

시간축 주파수축

Aliasing-1undersampling effect

Spectrum Effect Waveform Effect

Aliasing 2Aliasing - 2

Figure 10.6 A 360Hz sine wave is sampled every 5ms (i.e., at 200 samples/s). This sampling rate will adequately sample a 40Hz sine wave, but not a 360Hz sine wave.

Quantization EffectSampling of Signals: How Accurate?

Resolution of N-bit quantization = 2N-1 steps(ex: 8 bit quantization for 1(V) signal = 1/255(ex: 8 bit quantization for 1(V) signal 1/255

= 3.92(mV) Resolution)

A/D Conversion

QUIZ

외래환자로부터측정한 10초동안의근전도(EMG) 신호를디지털데이터

로변환하여 760MByte의 CD Rom으로저장하라”는 order에대해 CD

Rom 1장에최대 몇 명의환자 데이터를수록할수 있을지계산하시오.

(단, 근전도 신호의 최대 주파수 성분은 1.5(kHz)이며, 근전계의 출력은 최

대 1(V)의 크기 신호를 제공하는데 향후 분석 목적상 250(㎶) 까지의 분해

능을요구한다.)

10.5 FREQUENCY DOMAIN REPRESENTATION OF BIOLOGICAL SIGNALS

10 5 1 Periodic Signal Representation:10.5.1 Periodic Signal Representation: The Trigonometric Fourier Series

: fundamental frequency

: harmonics

Joseph Fourier initiated the study of Fourier series in order to solve the heat equation.

Fourier SeriesFourier Series• Example Problem 10.6Example Problem 10.6

MATLAB ImplementationMATLAB Implementation

Figure 10.8 (a) MATLAB result showing the first 10 terms f f h dof Fourier series approximation for the periodic square 

wave of Fig. 10.7a. (b) The Fourier coefficients are shown as a function of the harmonic frequency.

10 5 2 Compact Fourier Series10.5.2 Compact Fourier Series

Th f i id d i b itt b i l i• The sum of sinusoids and cosine can be rewritten by a single cosine term with the addition of a phase constant;

• Example Problem 10.7

10.5.3 Exponential Fourier Seriesp

Euler’s formula :

Relationship to trigonometry :

Proofs : using Talyor series,

10 5 3 Exponential Fourier Series10.5.3 Exponential Fourier Series• Complex exponential functions are directly related to sinusoids and cosines;

• Euler’s identities:

Meaning of the negative frequencies?

It requires only i t ti

negative frequencies?

• Example Problem 10.8

one integration.

p

Harmonics AnalysisHarmonics Analysis

Fi 10 10H i ffi i f h i Figure 10.11Harmonic reconstruction of the aortic pressure waveform.

Figure 10.10Harmonic coefficients of the aortic pressure waveform

10 5 4 Fourier Transform10.5.4 Fourier Transform

I l f• Fourier Integral or Fourier Transform;– Used to decompose a continuous aperiodic signal into its 

constituent frequency componentsconstituent frequency components.

X( ) is a co ple alued fu ctio of the co ti uous f e ue cy– X(ω) is a complex valued function of the continuous frequency, ω.– The coefficients cm of the exponential Fourier series approaches 

X(ω) as T →∞.– Aperiodic function = a periodic function that repeats at infinity

• Example Problem 10.9

10 5 5 Properties of the Fourier Transform10.5.5 Properties of the Fourier Transform

• Linearity

• Time Shifting / Delay

• Frequency Shifting

• Convolution theorem

10 5 6 Discrete Fourier Transform10.5.6 Discrete Fourier Transform• DTFT (Discrete Time Fourier Transform)  : Fourier 

transform of the sampled version of a continuous signal;

– X(ω) is a periodic extension of X’(ω) ‐ Fourier transform of a continuous signal x(t) ;• Periodicity :e io i i y• Poisson summation formula*:

*which indicates that a periodic extension of function    can be constructed from the samples of function

• DFT (Discrete Frourier Transform) : Fourier series of a periodic extension of the digital samples of a continuous 

samples of function   

N ‐ 1signal;

10 5 6 Discrete Fourier Transform10.5.6 Discrete Fourier Transform• Symmetry (or Duality)y y ( y)

– if the signal is even:  x(t) = x(‐t)– then we have – For example, the spectrum of an even square wave is a sinc 

function, and the spectrum of a sinc function is an even square wave. 

• Extended Symmetry

t ωFourier Series

t ωFourier Transform

t ω t

Fourier Series Fourier Transform

t ω t ωDiscrete Fourier Transform Discrete Fourier Series

10 5 6 Discrete Fourier Transform10.5.6 Discrete Fourier Transform• fast Fourier transform (FFT) :

– an efficient algorithm to compute the discrete Fourier transform (DFT) and its inverse. ( )

– There are many distinct FFT algorithms.A FFT i a ay to o ute– An FFT is a way to compute the same result more quickly: computing a DFT of N points in h b hthe obvious way, using the definition, takes O(N2) arithmetical operations, while pan FFT can compute the same result in only O(NlogN) operations. p

Figure 10.12 (a) 100 Hz sine wave. (b) Fast Fourier transform (FFT) of 100 Hz sine wave.

Figure 10.13 (a) 100 Hz sine wave corrupted with noise. (b) Fast Fourier transform (FFT) of thenoisy 100 Hz sine wave.