biomedical signals processing fundamentals

Course title: Biomedical signal processing
Module: Signal and image processing
Course code: BMED-3212 ECTs = 7 hrs Cr. Hr. = 4 hrs
Prerequisite: Signals and systems
Course instructor: Abel Belay, email: abelbelay98@gmail.com
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Chapter -1 Introduction to biomedical signal processing
1.1 Introduction to biomedical signals
1.2 Nature and challenges of biomedical signals
1.3 Biomedical signal processing
1.4 Matlab basics
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1.1 Introduction to biomedical signals
1.1.1 Definitions and models of biomedical signals
• Before everything else let's define what signal is. A signal is a simple valued representation of
information as a function of an independent variable.
• The registered biomedical signals from biomedical instrumentation devices are called biosignals.
In the scope of biomedical signals and sensors, biosignals are descriptors of physiological
phenomenon.
• A simple model for signal generation up to registration for acoustic signal of the chest cavity is
explained below.
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• Historical aspects: the registration of biosignals is driven by patients and physicians' needs. Apart
from verbal account, the very first diagnosis is done through the following:
• Inspection
• Palpation.
• Percussion
• Auscultation
• The main problems with these direct diagnosis systems is that;
• the proof of biosignals
• analysis of biosignals
• comparison of biosignals
• circulation of biosignals was impossible due to the subjective nature of the diagnosis.
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1.1.2 Classifications of biomedical signals
• Biomedical signals can be classified based on existence, dynamic and origin.
Figure showing the difference
among signal types based on
existence (a), dynamic (b)
and origin (c)
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1.2 Nature and challenges of biomedical signals
• Medical data are basically classified as alphanumeric, medical images from different imaging
modalities, and finally physiological signals.
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1.2.1 Signal acquisition and physiological measurement
• The basic physiological measurement trends are not so much different from basic instrumentation
schematic.
• The basic schematic diagrams show the physiological measurement (left) and instrumentation
(right).
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1.2.2. Sources of biomedical signals
• Most physiological processes manifest themselves as signals. These reflect their nature and
activities.
• Any disorder / disease in these physiological processes causes abnormalities. This is called a
pathological process which affects the health and general well-being of the system.
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• The natural existing electrical signals inducing mechanical contraction of a single cell are called
action potential.
• This is stimulated by electric current created by the movement of flow of Na+, K+, Cl- and other
ions across the cell membrane.
• The cell membrane is semi-permeable, it allows some ions or molecules to flow in while blocking
the others. In resting state the cell membrane allows K+ and Cl- ions to flow in while blocking Na+
ions.
• An action potential is the basic component of all bioelectrical signals.
• When there is stimulus the resting status of the cell changes and lets more positive ions to enter
into the cell.
• This create a positive potential which is called action potential.
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• At resting potential (when there is not trigger)
• There is less concentration of Na+ inside the cell than outside
• Outside of the cell there are more positive ions.
• To balance the charge K+ enters the cell, causing higher concentration inside the cell.
• Charge balance can't be attained due to permeability of the membrane
• A state of equilibrium is established with a certain potential difference
• Thus the potential difference at the resting potential is from -60mV to -100mV.
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• Depolarization: when the cell is excited by ionic current, the permeability of the cell membrane
changes and begins to allow Na+ ion to flow into the cell.
• While doing so, the K+ ions inside the cell began to exit the cell due to concentration gradient. But,
the flow of K+ is not as fast as Na+.
• For most cells the action potential is around 20mV.
• This process is called depolarization.
• And the cells are depolarized cells.
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• Repolarization: after a certain period of being in action potentials the cell began to rest to its
resting potential.
• At this time the membrane becomes a barrier for Na+ and lets K+ ions enter into the cell.
• This creates much of Na+ ions to exit the cell rapidly through the ion channel and K+ ion enters
through the cell by concentration gradient created by action potential.
• Na+-k+ pump is essential for resetting the balance of resting potential.
• Nerve and muscle cells depolarize rapidly. An action potential is always the same for a specific cell.
• After an action potential there is a period the cell would not respond to the stimulus known as
absolute refractory period.
• This is followed by a relative refractory period (in several ms) when another action potential by
strong stimuli is triggered in a normal situation.
• There is all or non phenomena in the relative refractory period.
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• Propagation of an action potential: an action potential propagates through the length of the muscle
unmyelinated fiber without decrease in amplitude.
• Current carrier by intracellular and extracellular fluids will depolarize the cell along. Myalinated
nerve fibers are covered by myelin sheath.
• This sheath is interrupted by nodes of ranvier, where the fiber is exposed to interstitial fluids. Sites
of excitations and changes in membrane permeability happen only at the nodes.
• And current flows from one node to another node by a process called saltatory conduction.
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1.2.3. Common biomedical signals
• Common biomedical signals are ECG, EEG, ENG, PCG EGG, ERG, OCG ...etc. In this course the base
detailed view will be given to ECG, EEG and EMG.
• ECG (electrocardiogram): this is a signal generated by an action potential originated in the heart (
specially at SA fiber).
• This creates a PQRST - curve. This curve (especially the - R curve) gives better information for
diagnosis of heart disease and arrhythmia.
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• EEG (electroencephalogram): this is a signal from the brain cells. There are a number of electrodes
involved for measuring the alpha, Beta, gamma and theta waves. They are very much used in
accessing the sleeping action of the brain activities.
Representation of 10-20 EEG electrode
system placement , pg: nasopharyngeal,
a: auricular, fp: prefrontal, f: frontal, p:
parital, c: central, o: occipital, t: temporal,
cb: cerebellar, z: midline, odd number in
the left and even numbers in the right,
(a) delta rhythm; (b) theta rhythm; (c) alpha rhythm; (d) beta rhythm; (e)
blocking of the alpha rhythm by eye opening; (f) 1 s time markers and 50 µV
marker.
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• EMG (electromyogram): this electrical based biomedical signal is formed due to the contraction of
muscle cells. It is a triggered potential which will be transduced through on surface (non-invasive)
or invasive AgCl electrodes.
• It is usually the sum of the responses of a number of muscle fibers. The summation of the
responses of muscle units is called multiple-unit EMG (MUEMG).
• This is because most stimuli trigger a number of muscle cells and most importantly to move (for
movement of) a single part of the skeleton needs the contraction of a number of muscle fibers.
• It is mostly used to detect the abnormality in the muscle cells (muscular dystrophy) and other
likely disorders.
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• Electroneurogram (ENG): it is used to measure the conduction velocity of the nerve cell. Use a
needle or on surface AgCl electrode.
• This signal is affected by power lines greatly, so as a result of its band width and small amplitude
(10 microvolts).
• Nerve fibers 45-70 m/s
• Heart muscles 0.2-0.4ms
• Between atria and ventricle 0.05-0.04 m/s
• Most of the time any nerve disease may increase the latency.
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• Phonocardiogram (PCG): the heart sound signal may be a traditional biomedical signal. The PCG is
a vibration of sound related to the contractile activity of the cardihemic system (the heart and the
blood together).
• The transducer is implemented to convert the vibration to electrical signal (accelerometers or
microphones or pressure transducers are placed on the chest for this purpose).
• The carotid pulse: this is a pressure signal recorded over the carotid artery as it passes near the
surface of the body at the neck; it is the extension of the pressure on the aorta that is felt on the
neck due to its proximity.
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• Electrogastrogram (EGG): the electrical activity of the stomach consists of rhythmic waves of depolarization
and repolarization of its smooth muscle cells.
• The activity begins in the mid- corpus of the stomach with intervals of 20s in humans. An external electrode
could sense these signals.
• Using it for diagnosis is not possible yet.
• Other biomedical signals: Signals from catheter tip sensors, Speech signal, Vibromyogram, Vibroarthrogram,
Otoacoustic emission (OAE) signals and other bioacoustic signals.
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1.2.4 Challenges and difficulties in biomedical signal acquisition and analysis
• Accessibility of variables to measurement
• Inter relationships and interaction among physiological systems:
• Effect of instrumentation or procedure on the system
• Physiological artifacts and interference
• Energy limitations
• Patient safety
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1.3 Introduction to biomedical signal processing of the
1.3.1 Why are signals processed?
• To remove unwanted signal components that are corrupting the signal of interest.
• To extract information by rendering it in a more obvious or more useful form.
• To predict future values of the signal in order to anticipate the behavior of its source
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1.3.2 Objectives of biomedical signal analysis/processing
• Some objectives of biomedical signal analysis and processing
• Information extraction
• Diagnosis
• Monitoring
• Therapy and control
• Evaluation
1.3.3 Application of computer in medicine biomedical signal
• Nowadays, from the advancement of computer technologies and evolution of ubiquitous
computers, it has become more simple to make a computer itself as a medical instrument. This is
by using complementary medical software. Usually these medical software are application
software. The basic software architecture is shown below.
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1.3.3 Application of computer in medicine and biomedical signal
• Nowadays, from the advancement of computer technologies and evolution of ubiquitous
computers, it has become more simple to make a computer itself as a medical instrument.
• This is by using complementary medical software. Usually these medical software are application
software. The basic software architecture is shown below.
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• To transform any computer to biomedical instrumentation device, there exist two basic decisions
to make these are; the choice of disk operating system and the high level language that should be
implemented.
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Chapter -2 Discrete time signals and systems
2.1 Classifications of signals and systems
2.2 Discrete time signals
2.3 Discrete time systems
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2.1 Classification of signals and systems
2.1.1 Classification of signals
• Real and complex signal
• Deterministic and random signals
• Even and odd function
• Periodic and non-periodic signals
• Continuous time and discrete time signals
• Analog and digital signal
• Energy and power signals
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Exercise check if the following sequences are even-odd,
periodic or aperiodic and energy or power

2.1 Classification of signals and systems
2.1.2 Classification of systems
• Continuous, discrete-time and digital system
• Deterministic and random
• Causal and non-causal
• Static and dynamic
• Linear and non-linear
• Time variant and time-invariant
• Invertible and non-invertible
• Stable and unstable
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Exercise check if the following systems are causal,
linear, time invariant and stable

2.2.1 Discrete time signals
• Discrete time signal is a signal having a discrete time value unlike in continuous time signals.
• If the independent variable is discrete in time, the signal deﬁned at discrete instants of time is
called discrete-time signal..
• Thus, a continuous signal is continuous both in time and amplitude, while a discrete-time signal is
continuous in amplitude but discrete in time.
• A digital signal is one that is discrete in both time and amplitude.
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Continuous signals
T, F , 𝜭 , 𝜔
𝜔=2T, T=1F
Thus, -∞<𝜔<∞ and accordingly -∞<F<∞ for
a continuous time signal x(t).
Discrete signals
N, f 0 , Fs, Ts , 𝜔0
𝜔=2∏/N, N=1/f0, t=nTs, Fs=1Ts
ωo =2π/N , when N=2, then ωo =|π|. Thus, -
π<𝜔o< π and accordingly -1/2<fo<1/2 for a
discrete time signal x[n].

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• Elementary operations in discrete time signals
• Multiplication
• Addition
• Scalar multiplication
• Time shifting
Sketching values time (shift, scale), x(t) = t, t+2, t-2, -t
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Other time operations

• Discrete signal representation
• Sequence
• Graphical
• Tabular
• Functional 𝑥[𝑛] = 𝑒𝑛
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• Unit sample sequence
• Unit step
• Unit ramp
• Exponential
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Different exponential
functions for different a

2.3.1 Discrete time systems
• Discrete time systems are mathematical functions or procedures that will be done on an input
signal and provide an output.
2.3.2 Discrete time systems response
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Also system sketch schematics

2.3.2 Discrete time systems response
• For the linear time invariant systems calculate the convolution sum.
• 𝑥 𝑛 =
1
5
𝑛
𝑢[𝑛] h 𝑛 = (−1)𝑛𝑢[𝑛]
• 𝑥 𝑛 =
1
5
𝑛
𝑢[𝑛] h 𝑛 = (
1
3
)𝑛𝑢[𝑛]
• Determine the convolution and correlation of the following two signals.
• 𝑥1 𝑛 = [… 0,2, −1,3,7, 1, 2, −3,0, … ]
• 𝑥2 𝑛 = [… 0,2, −1,2, −2, 4, 1, −2,5,0 … ]
• Methods for computing linear convolution
• Matrix method
• Graphical method
• Circular convolution
• Deconvolution
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2.3.3 Characterization of discrete time systems
• Characterization of discrete time systems
• Discrete time systems can be represented by difference equation. Linear difference equation that can be
written as a sum of constant coefficient can be recursive or non recursive.
• Non- recursive difference equation: A non-recursive LTI discrete-time system is one that can be characterized
by a linear constant coefficient difference equation of the form
• Recursive difference equation:
• Solution of difference equation
Solve for y(t)
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2.3.4 Representation of discrete time system in frequency domain
DTFT (discrete time fourier transform)
• The Fourier transform is one of several mathematical tools that is useful in the analysis and design of LTI systems.
Another is the Fourier series.
• These signal representations basically involve the decomposition of the signals in terms of sinusoidal (or complex
exponential) components. With such a decomposition, a signal is said to be represented in the frequency domain.
• Most signals of practical interest can be decomposed into a sum of sinusoidal signal components. For the class of
periodic signals, such a decomposition is called a Fourier series. For the class of finite energy signals, the
decomposition is called the Fourier transform.
• From physics we know that each color corresponds to a specific frequency of the visible spectrum. Hence the
analysis of light into colors is actually a form of frequency analysis.
• Frequency analysis of a signal involves the resolution of the signal into its frequency (sinusoidal) components.
Instead of light, our signal waveforms are basically functions of time.
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• DTFT
• In discrete time fourier transform, the time is discrete while the frequency is not. Here the angular frequency
could assume any value.
• A causal LTI system is represented by the following Difference
Equation.
• (i) Find the impulse response of the system h(n),
as a function of parameter a. Also find magnitude and phase
Response of the system.
• (ii) For what range of values would the system be stable?
• The frequency response of the systems is given by:
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• Frequency response of discrete time systems
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2.3.5 Representation of sampling in frequency domain
• The sampling of continuous time signals to discrete is given below. Let xp(t) is continuous signal.
• Let p(t) is
• Thus,
• From convolution theorem:
• Finally, the sampled signal will be:
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2.3.5 Representation of sampling in frequency domain
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2.3.6 Discrete time random signals
• Discrete time random signals are characterized by the statistically behaviors. For example white noise is a
random signal.
• It can be characterized by the statistical properties like, mean, variance and auto correlation with certain
delay.
• The mean is 0
• The auto correlation is only non zero at 0 but does not exist for other values of n.
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Chapter -3 Analysis of discrete time LTI systems
3.1 Analysis in Z-transform
3.2 Discrete time fourier transform and discrete
fourier transform
3.3 Fast fourier transform and its application

3.1.1 Definition property and inverse z-transform
• The Z transform is an equivalent form of Laplace transform in the discrete signals.
• The direct Z transform is given by: X z = 𝑛=0
∞
𝑥 𝑛 𝑧−𝑛, where z = 𝑟𝑒𝑖𝜔 , 𝑧−𝑛 = (𝑟𝑒𝑖𝜔)−𝑛= 𝑟−𝑛𝑒−𝑖𝜔𝑛
• Z transform identifies the presence of exponentially increasing or decreasing oscillation in a given signal x[n].
The Z transform is used to determine stable and unstable systems.
• The Z transform only exists for the converging values of the power series 𝑥 𝑛 𝑧−𝑛. The domain is called
region of convergence (ROC).
• Determine the Z transform for the following
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• Properties of the ROC
• The properties of the ROC are summarized below. We assume that X(Z) is a rational function of z.
• Property 1: The ROC does not contain any poles.
• Property 2: If x[n] is a finite sequence (that is, x[n] = 0 except in a finite interval Nl1<n<N2, where N1, and
N2, are finite) and X(z) converges for some value of z, then the ROC is the entire z-plane except possibly z = 0
or z = ∞.
• Property 3: If x[n] is a right-sided sequence (that is, x[n] = 0 for n < N, < ∞) and X(z) converges for some
value of z, then the ROC is of the form
• Where rmax equals the largest magnitude of any of the poles of X(z). Thus, the ROC is the exterior of the
circle lzl= rmax in the z-plane with the possible exception of z = m.
• Property 4: If x[n] is a left-sided sequence (that is, x[nl = 0 for n > N, > - ∞ ) and X(z) converges for some
value of z, then the ROC is of the form
• where rmax is the smallest magnitude of any of the poles of X(z). Thus, the ROC is the interior of the circle
lzl=rmin in the z-plane with the possible exception of z = 0.
• Property 5: If x[n] is a two-sided sequence (that is, x[n] is an infinite-duration sequence that is neither right-
sided nor left-sided) and X(z) converges for some value of z, then the ROC is of the form where r, and r, are the
magnitudes of the two poles of X(z).
• Thus, the ROC is an annular ring in the z-plane between the circles lzl= r, and lzl = r2 not containing any
poles. 45

• ROC for different signal types
46

• Properties of Z-transform
47

• Z-transform common signals
48

• Inverse Z-transform
• Application of Z-transform
49

3.2 Discrete time fourier transform and discrete fourier transform
3.2.1 Discrete time fourier transform and discrete fourier transform
50
Discrete time fourier transform Discrete fourier transform
• In discrete time fourier transform, the time is
discrete while the frequency is not. Here the
angular frequency could assume any value.
• In discrete fourier transform the angular
frequency is made discrete with a specific
frequency numbers.

• DFT
• In discrete fourier transform the angular frequency is made discrete with a specific frequency numbers.
• Consider a ﬁnite discrete sequence x[n]; 0 <x[n]< N – 1, that the DTFT of the sequence x[n] is given by:
• The is a continuous function of angular frequency that ranges from –pi to pi.
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• Properties of DFT
52
Determine the N point DFT of the sequences

• Fast Fourier transform
• The direct evaluation of each value of X[k] requires N complex multiplications and N complex additions. As
such, N*N complex multiplications and N(N-1) complex additions are necessary for the computation of an N-
point DFT.
• Consequently, for large N, the computational complexity in terms of the arithmetic operations is high in direct
evaluation of the DFT.
• Therefore, a number of efﬁcient algorithms have been developed for the computation of the DFT. These
efﬁcient algorithms collectively have become known fast Fourier transforms.
• The FFT algorithms decompose successively the computation of the discrete Fourier transform of a sequence
of length N into smaller and smaller discrete Fourier transforms. The two most basic FFT algorithms are:
• Decimation in time
• Decimation in frequency
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3.3.1. Decimation in time radix-2
• This decomposes the sequence into smaller ones.
• Determine the DFT of the following.
• X(n)={1,0,1,1,0,1,1,0,1,0,0,1,1,1,1,0}
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3.3.1 Decimation in time
• Inverse DFT
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3.3.2. Decimation in frequency (radix-2)
• The basic idea in the decimation-in-time (DIT) algorithm was to decompose the input sequence successively
into smaller and smaller subsequences. In the case of decimation-in-frequency (DIF) algorithm, we
decompose the N-point DFT sequence X[k] successively into smaller and smaller subsequences.
• Consider an input sequence x(n), and divide it into two halves. Then, the DFT of x(n) can be written as
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3.3.2. Decimation in frequency
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Chapter -4 Digital filters
4.1 Infinite impulse response filter
4.1.1 Design approximations
4.1.2 Design structure
4.2 Finite impulse response filter
4.2.2 Design structure
4.3 Effect of finite word length

4.1 Infinite impulse response filter
• A filter is a device that passes electric signals at certain frequencies or frequency ranges while
preventing the passage of others. — Webster.
• In addition, there are filters that do not filter any frequencies of a complex input signal, but just add a
linear phase shift to each frequency component, thus contributing to a constant time delay. These are
called all-pass filters.
• The most important step in digital filter design is to obtain a realizable transfer function H(z). After
finding out the stability of H(z), different techniques can be used to design the digital filters.
• The most common technique used are filter design from analog filters, bilinear transformation, digital
filter design from analog filters.
Analog low pass filter design
• Different approximations are used to design lowpass analog filters, the common ones are mentioned
here;
• Butterworth
• Chebyshev I
• Chebyshev II
• Elliptic
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• Filter specifications
• Pass band edge frequency Ω𝑝
• Stop band edge frequency Ω𝑠
• Peak ripple value in pass band 𝛿𝑝
• Peak ripple value in stop band 𝛿𝑠
• Peak pass band ripple 𝛼𝑝
• Minimum stop band ripple 𝛼𝑠
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• Butterworth approximation
• The magnitude square response of Butterworth approximation is given by;
• Two parameters totally characterize the Butterworth filter character; the cutoff frequency Ω𝑐 and order
N.
• The Butterworth low pass filter has a flat magnitude at Ω = 0. The gain in dB is given by
10𝑙𝑜𝑔|𝐻𝑎 𝑗Ω |2
, the gain is -3dB when Ω = Ωc. The loss in dB is given as:
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• The magnitude of the Butterworth filter can be made as a function of s, this is by making s=j Ω.
• Then through normalization, the Ωc=1. the whole equation can be written as:
• Then the normalized impulse response of the filter is given by:
• Where pi for i=1,2,3……N, the left hand side poles.
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• Summary of filter design
71

• Design of analog filters from analog filters
• The analog highpass, bandpass, and bandstop filters can be designed using analog frequency
transformations.
• First, the analog prototype lowpass filter specifications are derived from the desired specifications of
the analog filter using suitable analog-to-analog transformation.
• Finally, the transfer function of the desired analog filter is determined from the transfer function of the
prototype analog lowpass transfer function using the appropriate analog-to-analog frequency
transformation.
• The lowpass-to-lowpass, lowpass-to-highpass, lowpass-to-bandpass, and lowpass-to-bandstop analog
transformations are considered next.
• Lowpass to lowpass
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Butterworth Chebyshev I Chebyshev II Elliptic
Low pass to low pass
Low pass to high pass
Low pass to band pass
Low pass to band stop
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Transforming analog filter to digital filter
• There are two methods of deriving the digital filter from the analog filter. Disadvantages of impulse
invariance method Bilinear transformation method
• Impulse invariance method
• Bilinear transformation
• Impulse invariance method stages
• Derive the s domain of the analog filter as a sum of partial fraction.
𝐻𝑎 𝑠 =
𝑘=1
∞
𝐴𝑘
𝑆 − 𝑃𝑘
• Use the inverse Laplace-transform to find the time domain signal
ℎ𝑎 𝑡 =
𝑘=1
∞
𝐴𝑘𝑒𝑃𝑘𝑡
𝑢(𝑡)
• Use discrete transformation to discretize the system, t = 𝑛𝑇𝑠
ℎ𝑎 𝑛 =
𝑘=1
𝑁
𝐴𝑘𝑒𝑃𝑘𝑛𝑇𝑠𝑢(𝑛)
• Use the z-transform of the discrete time system
𝐻 𝑧 =
𝑘=1
𝑁
𝐴𝑘
1 − 𝑒𝑃𝑘𝑇𝑠𝑧−1 74

• Disadvantages of impulse invariance method
• Aliasing
• One to many mapping of analog frequencies
• The frequency has to be bandlimited for implementing this design scheme.
• Examples
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• Bilinear transformation method stages
• Specify the digital filter parameters through frequency warping.
• Ω = tan(
𝜔
2
)
• Analog filter specification through low pass prototype transformation.
• Analog filter transfer function to digital using bilinear transformation.
• Digital filter transfer function and frequency response verification
• The relation between the analog frequency and the digital frequency is not linear. Thus, it introduces
distortion.
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4.1.2 Structure of IIR filters
• Direct form I
• The transfer function of an Nth-order IIR ﬁlter is of the form
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• Direct form II
80

• Signal flow graph
81

• Cascaded
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ECG signal processing
• ECG signal acquisition and preprocessing
• It contains analysis
• Correct interpretation
• Procedures and automatic positioning of the ECG leads
• There are 10 common steps for ECG evaluation
• Rhythm
• Heart rate
• Cardiac axis
• P-wave
• PR- interval
• Q-wave
• QRS-complex
• QT interval
• ST-segment
• T-wave

• High-frequency noise in the ECG: The noise could be due to the instrumentation amplifiers, the
recording system, pickup of ambient EM signals by the cables, and so on.
• The signal illustrated has also been corrupted by power-line interference at 60 Hz and its harmonics,
which may also be considered as a part of high-frequency noise relative to the low-frequency nature of
the ECG signal.
• Motion artifact in the ECG: Low-frequency artifacts and base-line drift may be caused in chest-lead ECG
signals by coughing or breathing with large movement of the chest, or when an arm or Leg is moved in
the case of limb-lead ECG acquisition.
• The EGG is a common source of artifact in chest-lead ECG. Poor contact and polarization of the
electrodes may also cause low-frequency artifacts. Base-line drift may sometimes be caused by
variations in temperature and bias in the instrumentation and amplifiers as well.
• Base-line drift makes analysis of iso-electricity of the ST segment difficult. A large base-line drift may
cause the positive or negative peaks in the ECG to be clipped by the amplifiers or the ADC.

• Potential solutions to the problem
• Time domain filters
• Synchronized averaging filter
• Moving average filters
• Frequency domain filter
• Butterworth lowpass filters
• Adaptive filter

• Purpose of ECG
• Identification of various pathological conditions, myocardial infraction, chest pain, dysrhythmias
• Obtain the baseline ECG for comparison prior to surgery or routine diagnosis.
• Gold standard for diagnosis of cardiac arrythmias, but also used for pulmonary embolism and
hypothermia.
• 12 lead ECG
• 6-recordial leads, 4-limb leads . Thus 10 leads = 12

ECG processing
• ECG waveform recognition
• Cardiac conduction pathway: the self excitable sinoatrial node in the right atria generates an impulse.
This impulse enters left atria resulting in simultaneous contraction (P-wave).
• Then impulse passes to atrioventricular node which is the inferior wall of right atria. The time travel
from SA node to AV node is PQ-segment. From the AV node it passes to bundle of HIS (specified group of
cells located in the septum). This divides into branches.
• The septal depolarization and beginning of ventricular depolarization. The purkinje fibers carry the
impulse to myocardium (QRS-complex). This ends the conduction pathway.

ECG processing
• ECG waveform recognition
• Automaticity (initiate impulse), excitability (ability to respond), conductibility (ability to transmit) and
contractability (ability to contract and pump) are the physiological properties of myocardiocytes.
• There are bipolar (I, II, III) and unipolar leads (aVr, aVl, aVf).
• The common pathologies of heart can be exactly located using these leads.
• Lateral leads (v5,v6, aVl, I), anterior leads (v3,v4), septal leads (v1, v2), inferior leads (aVf, III, II).
• 25mm/s 1mm/25mm/s = 0.04sec
• 60sec => 300 large squares
• HR = 300/no. RR intervals (large squares)
• For regular rhythm the RR intervals are consistent.
• For an irregular 30 large squares x 10
• Normal => 60-100 bpm
• Bradycardia => <60bpm
• Tachycardia => >100 bpm

• Adaptive filter for ECG
• Design an optimal filter to remove a nonstationary interference from a nonstationary signal.
• An additional channel of information related to the interference is available for use. The filter should
continuously adapt to the changing characteristics of the signal and interference.
• The filter should be adaptive; the tap-weight vector of the filter will then vary with time. The
principles of the adaptive filter, also known as the adaptive noise canceler(ANC)
• The filter should be optimal.

• The bandwidth of interest of the ECG signal, which is usually in the range 0.05 - 100 Hz
• This includes the 60 Hz component; hence simple lowpass filtering will not be appropriate for removal
of power-line interference.
• Lowpass filtering of the ECG to a bandwidth lower than 60 Hz could smooth and blur the QRS complex
as well.

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