EE 5345
Biomedical Instrumentation
Lecture 18: slides 343-361
Carlos E. Davila, Electrical Engineering Dept.
Southern Methodist University
slides can be viewed at:
http:// www.seas.smu.edu/~cd/ee5345.html
EE 7345/5345, SMU Electrical Engineering Department, © 2000
343
Data Compression Performance
n
Compression Ratio (CR):
total number of bits before compression
CR =
total number of bits after compression
n
Percent Root Mean Square Difference (PRD):
M −1
PRD =
∑ ( x[n] − x$[n])
n=0
M −1
2
[
]
x
n
∑
2
× 100
n=0
EE 7345/5345, SMU Electrical Engineering Department, © 2000
344
Case Studies
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Jalaleddine
Aydin
EE 7345/5345, SMU Electrical Engineering Department, © 2000
345
ECG Signal Processing
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ECG Component Detection
ECG Arrhythmia Detection
High Fidelity ECG via Signal Averaging
Measurement of Heart Rate
EE 7345/5345, SMU Electrical Engineering Department, © 2000
346
ECG Component Detection
R
T
P
Q S
0.6 s
typical HR: 70 bpm
P: atrial depolarization
R: ventricular depolarization
T: ventricular repolarization
EE 7345/5345, SMU Electrical Engineering Department, © 2000
347
R-Wave Detection
•different R-R intervals
•different R-wave heights
ECG:
Detector Output:
Automated R-wave detection useful for:
•heart rate measurement.
•detection of tachycardia (high HR), bradycardia
(low HR), or ventricular fibrillation.
EE 7345/5345, SMU Electrical Engineering Department, © 2000
348
Noise Sources in ECG
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motion artifact (can be wide-band)
60 Hz interference
baseline drift (generally amplifier related)
These noise sources can significantly degrade
the quality of the ECG. Simple amplitude thresholding
does not produce good R-wave detection.
EE 7345/5345, SMU Electrical Engineering Department, © 2000
349
General Approaches to R-Wave Detection
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Non-Syntactic: rely on characteristic features of QRS
complexes to perform the detection-simple.
Syntactic: based on grammatical inference-can get
complicated.
Hidden Markov Models: based on a probabilistic model of
R-wave occurrence times-complicated.
We’ll cover all three approaches.
EE 7345/5345, SMU Electrical Engineering Department, © 2000
350
Non-Syntactic QRS Detection
source: J. Pan and W. Tompkins, “A Real-Time QRS Detection Algorithm,”
IEEE Transactions on Biomed. Engr. vol. 32, pp. 230-236, March 1985.
bandpass
filter
T1
d/dt
(
)2
MA
filter
T2
dout
delay
EE 7345/5345, SMU Electrical Engineering Department, © 2000
351
Bandpass Filter
lowpass
filter
highpass
filter
1− z )
(
H( z) =
(1 − z )
−6 2
lowpass filter:
−1 2
⇒ y[n] = 2 y[n − 1] − y[n − 2] + x[n] − 2 x[n − 6] + x[n − 12]
EE 7345/5345, SMU Electrical Engineering Department, © 2000
352
Highpass Filter
− 1 + 32z + z )
(
H ( z) =
(1 − z )
−16
−32 2
−1
⇒ y[ n ] = − y [n − 1] − x[ n ] + 32 x[ n − 16] + x [n − 32]
Squaring Function:
y[n] = x[n]2
EE 7345/5345, SMU Electrical Engineering Department, © 2000
353
Moving Average (MA) Filter
1
y[n] =
( x[n − ( N w − 1)] + x[n − ( N w − 2)]+L+ x[n])
Nw
Nw: length of MA (FIR) filter
Threshold Devices:
x[n]
T
b
 H , x[n] ≥ T
b=
 L, x[n] < T
(comparator)
EE 7345/5345, SMU Electrical Engineering Department, © 2000
Rules for Non-Syntactic Detector
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Thresholds T1 and T2 are adjusted from beat-to-beat in
order to compensate for trends in R-wave peak amplitude.
Processing delays are compensated for.
If an R-wave is not detected after a set time interval, the
algorithm reprocesses the data going back to the previous
detection, using a new lower set of thresholds.
Algorithm also detects non-QRS peaks such as P and T
waves using a different lower set of thresholds.
EE 7345/5345, SMU Electrical Engineering Department, © 2000
355
Detection Assessment
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False Positive: R-wave detected when none was present.
False Negative: R-wave not detected when one was
present.
Results of Pan-Tompkins algorithm applied to the
MIT/BIT arrhythmia database:
0.437% false positive rate (5% typical)
0.239% false negative rate
•some subjects show high detection failure.
•no noise was added to the data to simulate poor
recording conditions.
EE 7345/5345, SMU Electrical Engineering Department, © 2000
356
Syntactic Detection of R-Waves
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Based on theory of formal languages called grammars.
Grammars are used to describe all signals (sentences)
belonging to a given class (language).
A class is represented by a given set of known sentences
called a training set.
We wish to estimate the class associated with a given
sentence based on what we know from the training set.
There are a number of different grammars, we will
consider only finite state grammars.
EE 7345/5345, SMU Electrical Engineering Department, © 2000
357
Finite State Grammars
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Grammar has associated with it a finite set of states,
{S0, S1, …, SN-1, T1, T2, …, TM}
and a finite set of symbols:
{a, b, …, f}
Sentences generated by this grammar are composed of the
symbols {a, b, … , f} and are determined by a set of rules
which are best represented by a graph.
Graph starts at start state S0 and ends at one or more
terminal states T1, T2, …, TM.
EE 7345/5345, SMU Electrical Engineering Department, © 2000
358
Graph for Finite State Grammar
S0
a
b
S1
b
a
T1
b
S2
a
T2
possible sentences: b,
abbbaa,
abbbbbbab,
aaa, etc.
EE 7345/5345, SMU Electrical Engineering Department, © 2000
359
Finite State Automata
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Given a sentence from an unknown finite state grammar,
would like to be able to determine whether that sentence
comes from a certain grammar.
This can be done with a finite state automaton.
The automaton has associated with it a finite number of
states
{Q0, Q1, …, QN-1}
The automaton reads in symbols from a sentence, the
symbols define state transitions. If certain final states are
arrived at, startin from Q0, the sentence is accepted as
belonging to a certain grammar.
EE 7345/5345, SMU Electrical Engineering Department, © 2000
360
Finite State Automaton for Grammar on slide
330
Q0
a
b
Q1
b
a
Q3
b
a
Q2
a
Q4
Any sentence ending in state Q3 or Q4 is accepted, otherwise it is rejected.
abbbbbbbbaa: accepted
abb: rejected
EE 7345/5345, SMU Electrical Engineering Department, © 2000
361