9346933.ppt

Lecture 1 BME452 Biomedical Signal Processing (copyright Ali Işın, 2013) 1
NEAR EAST UNIVERSITY
FACULTY OF ENGINEERING
DEPARTMENT OF BIOMEDICAL ENGINEERING
BME452 Biomedical Signal Processing
Lecture 1
Introduction

Lecture 1
Course overview
Instructor: Ali Işın
Email: aliisin@hotmail.com

Assessment
Midterm examination: %30
Final examination = 60%
Attendance= 10%
Course Material: Lecture Slides
Lecture 1

Syllabus
 BME452
 Fundamentals of digital signal processing/Introduction
to signals
 Signal sampling and reconstruction
 Signal conditioning
 Frequency analysis and power spectrum estimation
 Digital filtering methods
 Feature extraction
 Classification algorithms
 Statistical Methods
 Application-ECG Signal Analysis

Lecture 1
Introduction
 In this lecture, we’ll learn the fundamental
concepts on signals and an introduction to
some specific signals

Signals
 What is a signal?
 A signal is a function of independent variables
such as time, distance, position, temperature,
pressure, etc.
 Most signals are generated naturally but a
signal can also be generated artificially using
a computer
 Can be in any number of dimensions (1D, 2D
or 3D)

Signals (cont)
 1D/2D/3D signals
 1D signal=f(x); x=time, distance, etc.
 2D signal=f(x,y); x,y= spatial positions
 3D signal=f(x,y,z); x,y,z=spatial positions
 Time series
 1D signals with amplitude, pressure,
intensity, etc. as a function of time, f(t)
 2D/3D signals
 Are normally images as functions of 2 or 3
spatial coordinates

Biological signals
 What are biological
signals?
 Biological signals are
time series signals
generated by some
biological mechanism
 Represented as small
amplitudes of voltages
(or other units) as a
function of time
 Some examples are
shown on the table
Generated/
caused by
Name
Heart Electrocardiogram
(ECG)
Brain Electroencephalogram
(EEG)
Muscle Electromyogram
(EMG)
Blood
pressure
changes
Arterial Blood
Pressure (ABP)
Blood
oxygen level
Oxygen Saturation
(SpO2)

Examples of biological signals
 EEG
 Oscillating electrical potentials recorded from the
scalp surface.
 Very small in amplitude (V range).
 Generated by neuronal activations in the brain.
 Evoked potentials – a specific type of EEG evoked
during a stimulus like visual, auditory, etc.
 ECG
 Electrical potentials recorded from the chest
(mainly), arms, legs.
 Generated by electrical activity of the heart,
which results in heart pumping blood
 EMG
 Electrical potentials recorded from the skin.
 Generated by skeletal muscle activity.
 ABP
 Pressure recorded on the upper arm (units-
mmHg)
 Generated by changes in blood pressure
0 100 200 300 400 500 600 700
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
Sampling points
Amplitude
(microV)
EEG signal
0 100 200 300 400 500 600 700
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
Sampling points
Amplitude
(microV)
EMG signal
ECG pictures from S.K.Mitra, DSP 3e

Examples of biological signals (cont)
Figure from Biolectrical Signal
Processing in Cardiac and
Neurological Applications, L.
Sornmo and P. Laguna
 Multimodal
signals
 Sometimes, more
than one type of
signal are
recorded but each
signal would
require different
analysis technique

Speech and Musical sound signal
 Speech and sounds are
recorded as air pressure
changes as a function of
time
 Speech
 Note the amplitude and
time span of each word
 Musical sound
 Cello: Attack, steady
state, delay
 Bass drum: Attack, delay
 Cello: Pseudo-periodic
 Bass drum: Aperiodic
Pictures from S.K.Mitra, DSP 3e
‘I like digital signal processing’
Cello Bass drum

Image and video signals
 Images
 light intensity as a function of 2D
coordinates
 Black and white or grey scale images
(I=0-255)
 Colour images: I=red(0-255),
green(0-255), blue(0-255)
 Video
 Sequence of images, called frames
 Is a function of 3 variables = 2 spatial
coordinates and time
Pictures/audio/visual from S.K.Mitra, DSP 3e

Seismic signals
 Elastic waves generated by
ground movements from
earthquake, volcanic eruption or
underground exposition
 Earth body propagation
 P waves - faster
 S waves – slower
 P and S waves are studied
in 3D
 Horizontal: north-south
 Horizontal: east-west
 Vertical
 Another wave: surface wave –
not so important
Pictures S.K.Mitra, DSP 3e

Signal Analysis
 Signals carry information
 A signal which does not carry information or carries
information not desired is known as noise/noisy signal
 Aim of signal analysis
 Extract useful information carried by the signal to suit
the application
 Methods
 The methods for signal analysis will depend on the
type of the signal and nature of the information being
carried by the signal
 There are some common methodologies and some
specific ones for specific signals

Classification of signals
 Signals can be classified into various types by
 Nature of the independent variables
 Value of the function defining the signals
 Examples:
 Discrete/continuous function
 Discrete/continuous independent variable
 Real/complex valued function
 Scalar (single channel)/Vector (multi-channels)
 Single/Multi-trial (repeated recordings)
 Dimensionality based on the number of independent
variables (1D/2D/3D)
 Deterministic/random
 Periodic/aperiodic
 Even/odd
 Many more….

Classification - Discrete/continuous signals
 Normally, the independent variable is time
 Continuous time signal
 Time is continuous
 Defined at every instant of time
 Discrete time signal
 Time is discrete
 Defined at discrete instants of time - it is a sequence of
numbers
 Four classifications based on time/amplitude -
continuous/discrete:
 Analogue, digital, sampled, quantised boxcar

Classification - Discrete/continuous signals (cont)
 Analogue signal
 Continuous time signal with continuous amplitude, eg. music
stored on cassette tape.
 Digital signal
 Discrete time signal with discrete valued amplitudes
represented by a finite number of digits, eg. music stored on
hard disk.
 Sampled data signal
 Discrete time signal with continuous valued amplitudes (i.e.
amplitude can take any value)
 Digital signal is thus quantised sampled data signal
 Quantised boxcar signal
 Continuous time signal with discrete valued amplitudes

Classification - Discrete/continuous signals (cont)
Amplitude- continuous
Time-continuous
Amplitude- continuous
Time-discrete
Amplitude- discrete
Time-discrete
Amplitude- discrete
Time-continuous
Figures from S.K.Mitra, DSP 3e

Random vs deterministic signal
 Deterministic signal
 A signal that can be predicted using some methods like a
mathematical expression or look-up table
 Easier to analyse
 Random (stochastic)
 A signal that is generated randomly and cannot be predicted ahead
of time
 Most biological signals fall in this category
 More difficult to analyse

Time and frequency analysis/operation
 Analogue signal
 Only time analysis/operation can be performed
 Discrete-time signal
 Both time and frequency analysis/operation can be performed (on
their own or jointly)
-1
0
1
An analogue signal
Continuous time
Amplitude
-2
-1
0
1
2
Continuous time
Amplitude
A partially multiplied analogue signal
0 200 400 600 800 1000
-2
-1
0
1
2
Discrete time (sampling points)
Amplitude
Frequency and time operated discrete-time signal
0 200 400 600 800 1000
-1
0
1
Discrete time (sampling points)
Amplitude
A discrete time signal

Time domain operations
 Scaling
 Multiplication of a signal by a constant, 
 Amplification if the  (gain) >1
 Attenuation if the  <1
 Eg.: y(t)=x(t)
 Delay/advance
 Delays or advances the signal, y(t)=x(t) by a certain time, t0
 Eg.: Delay, y(t)=x(t-t0); Advance, y(t)=x(t+t0)
 Addition/subtraction
 Addition/subtraction of signals to obtain a combined signal
 Eg.: y(t)=x1(t)+x2(t)+x3(t)

Time domain operations (cont)
 Product
 Product of two or more signals
 Eg.: y(t)= x1(t).x2(t)
 Differentiation/Integration
 Differentiation/Integration of a signal to produce a new signal
 Eg:
 Combination of operators
 It is common to combine operators to generate a new signal
 Eg.:
 Analogue/discrete-time operators
 Scaling, addition/subtraction, delay, product – implemented in both
analog and discrete-time signals
 Differentiation/integration – implemented in analog signals, only an
approximation can be implemented with discrete-time signals
dt
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t
y )
(
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1D time series – some mathematical notations
 A 1D time series
 y=f(t) for continuous independent variable
time
 y=f(n) for discrete independent variable n
 Every value of f(n) is called a sample
 Discrete-time signal can be generated by
sampling a parent continuous-time signal at
uniform intervals of time
 Then, discrete variable n can be normalised
to assume integer values as a representation
of t.

2D image/video – some mathematical notations
 2D images
 I=f(x,y), where I is the intensity of red, green and blue (RGB)
colours in a certain range (normally 0-255)
 x and y are the co-ordinates of the pixel
 Example, f(1,1)={255,255,255} would mean that the pixel at (1,1)
is white
 2D videos
 Videos are simply sequences of images (known as frames)
 I=f(x,y,t), where I is the intensity of red, green and blue colours
 Since we are dealing with discrete-time videos, we would have
I=f(x,y,n)
 Example, f(7,8,10)={0,0,0} would mean that the pixel at (7,8)
during discrete time (i.e. frame number), n=10 is black.
 Black and white (Grey Scale) images/videos
 The intensity would be grey level values (normally in the range 0-
255) instead of RGB values

Classification – period/aperiodic
 Periodic
 Continuous time-signal is
periodic if it exhibits
periodicity, i.e. x(t+T)=x(t),
-<t< where T=period of
the signal
 The smallest value of T is
called the fundamental
period, T0
 A periodic signal has a
definite pattern that repeats
over and over with a
repetition period of T0
 For discrete-time signals,
x(n+N0)=x(n),-<n<
 A signal, which does not
have a repetitive pattern is
aperiodic
Figures from Digital Signal Processing,
S.Salivahanan, Vallavaraj,
C.Gnanapriya
Periodic signal (discrete-time)
Periodic signal (continuous-time)

Singular functions
 Singular functions
 Important non-periodic signals
 Delta/unit-impulse function is the most basic and all other singular
functions can be derived from it
Unit impulse functions
Unit step functions
Unit ramp functions
Unit pulse function






 1
)
(
;
0
,
0
)
( dt
t
t
t 
 0
0
,
0
,
1
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)
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


n
n
n

0
0
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0
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
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u
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Figures from Digital
Signal Processing,
S.Salivahanan,
Vallavaraj,
C.Gnanapriya

Classification –even/odd
 Even signal
 Signal exhibit symmetry
in the time domain
 x(t)=x(-t) or x(n)=x(-n)
 Odd signal
 Signal exhibit anti-
symmetry in the time
domain
 x(t)=-x(-t) or x(n)=-x(-n)
 A signal can be expressed as a sum of its even
and odd components
 x(t)=xeven(t)+xodd(t)
 where xeven(t)=1/2[x(t)+x(-t)], xodd(t)=1/2[x(t)-x(-t)]

Filtering
 An important frequency domain operation
 A filter performs this operation
 Passes certain frequency components with
minimal distortion and blocks nearly all other
frequency components
 Passband – range of allowed frequencies
 Stopband – range of blocked frequencies

What is frequency?
 Frequency measures the
periodicity (i.e.
repetitiveness)
 No of cycles per second
 It is measured in Hz
 = 1/fundamental period (s)
 In the figure, there are 4
fundamental cycles in 0.5 s
 1 cycle per 0.125 s
 So, Freq=1/0.125 = 8 Hz
y
t (s)
0.5

Filtering (cont)
 Low-pass filter (LPF)
 Passes all low-
below the cut-off
frequency, fc and
blocks all higher
above fc
 Eg.: Consider a
combination of 3
sinusoidal signals, 2
Hz, 5 Hz and 11 Hz.
 The final output
signals after LPF at
fc=8 Hz and fc=3 Hz
are shown.
%MATLAB codes
f=2, fs=256;
for i=1:1000,
y(i)=sin(2*pi*i*(f/fs));
end
plot(y);
axis([0 1000 -1.5 1.5]);
0 200 400 600 800 1000
-1.5
-1
-0.5
0
0.5
1
1.5
0 200 400 600 800 1000
-1.5
-1
-0.5
0
0.5
1
1.5
0 200 400 600 800 1000
-1.5
-1
-0.5
0
0.5
1
1.5
0 200 400 600 800 1000
-3
-2
-1
0
1
2
3
+
+
=
Combined signal
LPF, fc=8 hz
0 200 400 600 800 1000
-3
-2
-1
0
1
2
3
LPF, fc=3 hz
0 200 400 600 800 1000
-1.5
-1
-0.5
0
0.5
1
1.5
Only 2 Hz signal
remains
Only 2 Hz and 5 Hz
signals remain

Filtering (cont.)
 High-pass filter (HPF)
 Passes all high-frequency
components above the
cut-off frequency, fc and
blocks all lower
below fc
 Eg.: Consider the same
combination of 3
sinusoidal signals, 2 Hz,
5 Hz and 11 Hz.
 The final output signals
after HPF at fc=3 Hz and
fc=8 Hz are shown.
0 200 400 600 800 1000
-3
-2
-1
0
1
2
3
0 200 400 600 800 1000
-1.5
-1
-0.5
0
0.5
1
1.5
0 200 400 600 800 1000
-1.5
-1
-0.5
0
0.5
1
1.5
0 200 400 600 800 1000
-1.5
-1
-0.5
0
0.5
1
1.5
0 200 400 600 800 1000
-3
-2
-1
0
1
2
3
+
+
=
Combined signal
HPF, fc=8 hz
HPF, fc=3 hz
0 200 400 600 800 1000
-1.5
-1
-0.5
0
0.5
1
1.5
Only 5 Hz and 11 Hz
signals remain
Only 11 Hz signal
remains

Filtering (cont.)
 Band-pass filter (BPF)
 Passes all frequency
components between edge
passband frequencies,
fp1<freq(allow)<fp2 and blocks
all frequencies below and
above edge stopband
frequencies, freq(block)<fs1;
freq(block)>fs2
combination of 3 sinusoidal
signals, 2 Hz, 5 Hz and 11
Hz.
 The final output signal after
BPF at fp1=4 Hz, fp2=6 Hz,
fs1=3 Hz, fs2=7 Hz is shown
0 200 400 600 800 1000
-1.5
-1
-0.5
0
0.5
1
1.5
0 200 400 600 800 1000
-1.5
-1
-0.5
0
0.5
1
1.5
0 200 400 600 800 1000
-1.5
-1
-0.5
0
0.5
1
1.5
0 200 400 600 800 1000
-3
-2
-1
0
1
2
3
+
+
=
Combined signal
BPF
0 200 400 600 800 1000
-1.5
-1
-0.5
0
0.5
1
1.5
Only 5 Hz signal
remains

Filtering (cont.)
 Band-stop filter (BSF)
 Passes all frequency
components lower and higher
than edge passband
frequencies, freq(allow)<fp1;
freq(allow)>fp2 and blocks all
frequencies between
fs1<freq(block)<fs2
combination of 3 sinusoidal
signals, 2 Hz, 5 Hz and 11
Hz.
 The final output signal after
BSF at fp1=3 Hz, fp2=7 Hz,
fs1=4 Hz, fs2=6 Hz is shown
0 200 400 600 800 1000
-1.5
-1
-0.5
0
0.5
1
1.5
0 200 400 600 800 1000
-1.5
-1
-0.5
0
0.5
1
1.5
0 200 400 600 800 1000
-1.5
-1
-0.5
0
0.5
1
1.5
0 200 400 600 800 1000
-3
-2
-1
0
1
2
3
+
+
=
Combined signal
BPF
0 200 400 600 800 1000
-1.5
-1
-0.5
0
0.5
1
1.5
5 Hz signal is
filtered out, only
2 Hz and 11 Hz
signals remain

Study guide (Lecture 1)
 From this week’s lecture, you should
know
 The common types of signals
 The different classifications of signals
 Time domain operations
 Basic concepts of filtering
 Computation of period, frequency
End of lecture 1

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