
1

Time

Frequency Analysis
and Wavelet Transform
(Tutorial)
T
opic
The Application of
Time

Frequency
Analysis on Biomedical ECG
Signals
Student: Chen

Wei Huang
ID:
D00942010
Date: 2013.01
Graduate
Institute
of Communication Engineering
National Taiwan University

2

CONTENTS
I.
Introduction
................................
................................
.................
3
II.
Methods
................................
................................
.......................
4
A.
Time Domain
Algorithms
................................
......................
5
(a) Derivative Method I
................................
...........................
5
(b) Derivative Method II
................................
..........................
6
B.
Frequency Domain Algorithms
................................
.............
8
(a) Hilbert Transform Method
................................
..................
8
(b) Discrete Wavelet Transform Method
................................
...
9
C.
Other Algorithms
................................
................................
..
10
(a) Genetic Method
................................
................................
.
10
(b)
Geometrical Match Method
................................
...............
12
(c) Topological Mapping Method
................................
............
13
(d) Filter Bank Method
................................
...........................
13
(e) Ze
ro Crossing Method
................................
.......................
14
(f) Morphology Method
................................
..........................
15
III.
Detection
Performance Estimators
................................
............
16
IV.
One Popular Ecg Database
................................
........................
16
V.
Performance Comparisons
................................
........................
17
VI.
Conclusions
................................
................................
................
17
VII.References
................................
................................
..................
19

3

Abstract
—
B
iomedical
engineering is a big field
research and usually
requires
a lot
of
knowledge
to handle different biomedical signals through
mathematical
techniques
and Computer

Aided Design (CAD)
to
help
analyze
medical
data
in
order to get quick and accurate analyzed resu
lt. Sometimes biomedical signals
are randomly and quickly
changing to
lead that it is hard to analyze
such signals
in most cases. In this
tutorial
, it will focus on Electro
C
ardio
G
ram (ECG)
biomedical signal analysis. The ECG signal can provide the informat
ion of
human heart status and are the most important indicator among all vital body
parameters. Many heart diseases can be found by analyzing ECG waves. Thus
an ECG analyzing method with good performance (faster and more accurate
result)
is very helpful fo
r determining the characteristics of the ECG signals.
This tutorial will introduce several
ECG R

wave peak detection algorithms and
summarize the performance results between those methods.
Because bio
medical
signals are usually non

stationary,
sometimes
Fourier
T
ransform is not suitable
to apply
for
all biomedical signals
.
T
o solve such problem
s
, time

frequency
analysis and wavelet transform
will be a good choice
to
provide both time and
frequency information
at the same time.
.
Index Terms
—
Electrocardiog
ram (ECG),
R

wave detection,
Sensitivity (SE),
Positive Prediction (+P)
,
Detection Error Rate (DER)
and MIT/BIH.
I.
I
NTRODUCTION
The
ECG signal is a biological signal and can be represented by a cyclic occurrence
of patterns with different frequency
contents (QRS complex, P and T waves). By
observing the QT interval, the ST interval, and the PR interval, these differences can
lead to many physiological conditions
as shown in Fig. 1.
Nowadays the applications of ECG signal analysis are feature
extraction, feature
detection, data compression, heart rate variability (HRV) and R

wave detection. By
considering such information, the different types of diseases can be determined if
using the time

frequency analysis and wavelet transform.
ECG R

wave p
eak detection is the most important job in all automated ECG
analysis algorithms. When the position of R

wave peak is found, the locations of
other components of ECG signals such that Q, S waves can be found by considering
the relative position of R

wave p
eak and P wave is relative to the Q wave as well as T

4

wave is relative to the S wave. The normal ECG waveform is shown in Fig. 1.
Therefore, accurate detection of the R

wave peak becomes more essential in ECG
signal analysis.
Fig
.
1.
A standard and normal ECG signal waveform.
Software QRS detector is an integral and essential part of ECG signal detection.
The most
cases of
QRS detectors usually own two processing steps. The first step is to
do digital filtering of the ECG signals by
linear or nonlinear method and to find out all
possible locations of the QRS R

wave peak by peak detection algorithm. The second
step is to do peak decision rule by considering peak characteristic properties
(including peak heights from the processed ECG s
ignal and time of peak occurrence)
and to classify each R

wave candidate as either an actual QRS complex peak or a
noise peak.
T
he automatic detection of ECG waves is important to cardiac disease diagnosis. A
good performance of an ECG analyzing method wi
ll highly affect the accurate and
reliable detection of the QRS complexes as well as the T and P waves.
Thus this
tutorial will focus on
introducing the existing
R

wave detection algorithms
for ECG
signals.
II.
M
ETHODS
Many R

wave detection algorithms have
been proposed by
r
esearchers for
the past
several decades. These detection algorithms can
be divided
in
to the following
m
athematical algorithms
including
Time domain
detection algorithms
[2][3][8][9]
.
Considering that
R

wave is characterized by of high amp
litude and
the ECG signal is
changing
quickly, these algorithms directly detect R

wave in time
domain by using
det
ecting threshold of ECG signal
with
first

order
or second

order derivative. Time

5

domain algorithms
are often good enough for real

time applica
tion
but they
are
sensitive to
interference
. Thus such existing algorithms are
suitable for
the
ECG
signal
without changing quickly sometimes
.
Frequency
domain
detection algorithms
[4][5][6][12]
. Firstly,
obtain transformation of ECG signal by linear or
nonlinear
transform, in which SNR is higher than original ECG signal.
Then apply appropriate
threshold detection rules. The
representative tran
sform includ
es
wavelet transform,
Hilbert
transform, etc. Transform domain algorithms
often have
high
detection
r
ate
and good robustness to interfer
ence
but sometimes need more detection
time.
Other
algorithms
[20][21][22][23]
i
nclud
e
template matching and
morphologic
filtering
algorithms
,
gene

based design, morphology

based design, zero

crossing design and
filter
bank design.
In the past several decades, there were many studies focusing on ECG signal
detection for QRS complex. The goal is to get higher sensitivity, higher positive
predication and lower detection error rate. In the follows, several published
algori
thms in the past years were shown in many topics of conferences and journals.
In this section,
now the detailed existing methods
will be introduced to show
development processes of the ECG detect
ion algorithm in the past years
in
dete
cting
R

wave peaks.
A.
T
ime
D
omain
A
lgorithms
(a)
Derivative
M
ethod
I
In order to attenuate noise, the signal passes through a
d
igital band

pass filter
composed of cascaded high

pass and
second

order low

pass filters. The stop
frequencies are set at 5
and 15 Hz.
The transfer
function of the low

pass filter is
The transfer function of the high

pass filter is
After filtering, the signal is differentiated to provide the
R

wave slope info
rma
tion.
The transfer function of the
differentiation is

6

After differentiation, the signal is squared point by point
.
Obtain wavefo
rm
feature
information in addition to the
slope of the R wave by
m
oving

window integration. It
is
calculated
as below.
The symbol
N is
the number of samples in the width of the
integration window.
The filtered signal and the integration signal process the
threshold detection
respectively. To be identified as the R

wave,
a peak must be detected in both the
integration and the filtered
waveforms
with adaptive thresholds.
The rules to c1assity the R

wave peak or noise peak are
presented as
below.
The
maxim
al peak detected in a regular R
R time
interval that satisf
ies
the condition of
peak height > t
hreshold
. I
f the condition is true, the peak is c
onsidered to a R

wave
peak, other peaks are considered to the
noisy peak.
If no R

wave is detected in a
regular R
R time interval,
search

back procedure is required to look for the waveforms
.
The more details can be
referred in [
1
].
(
b
) Derivative
M
ethod
II
In order to attenuate noise, the signal passes through a digital band

pass filter
composed of cascaded high

pass and second

order low

pass filters.
After this,
following steps are
differentiation,
squaring, and t
ime averaging of the
ECG
signal. A
separate derivative of the original ECG is used for wave
discrimination.
The low

pass filter is one of a class of filters
and
implemented with the difference
equation
as below.
Where
is the sampling period,
is an arbitrary integer
,
is the
differentiated ECG signal and
is the bandpassed ECG signal.
The high

pass filter is
implemented with the difference
equation
as below.

7

The difference equation for the derivative is
The nonlinear squaring function squares each output data point. Time averaging is
done by adding toge
ther the 32 most recent values from the squaring function and
dividing the total by 32.
Fig
. 2. Block diagram of
Derivative
M
ethod
II
Fig.
3.
(a) Unfiltered ECG signal (b) Output of Bandpassed filter
(c) Output after bandpass, differentiation and
squaring processes
(d) Final time

averaged signal.

8

The final step of this method is to do peak detection.
A
typical large waveform
produced by the time

averaged window
is very similar to
a QRS complex. Although it
is easy to visually identify one large
peak, simple peak detection algorithms falsely
detect multiple peaks due to ripples in the wave. A simple local maxim
um
peak
detector
should have
the ability of detecting many small

amplitude peaks. Although
both peaks result from the same QRS complex, one
peak is classified as resulting
from a QRS complex, the other
s
are
classified as noise. This can bias the noise level
estimate on the high side. In contrast,
some
ripples in the baseline of the
time

averaged
signal can bias the noise estimate on the low s
ide.
The more details can
be referred in [15].
B.
Frequency
D
omain
A
lgorithms
(a)
Hilbert
Transform
M
ethod
Mathematically, the Hilbert transform is defined as
Or
where
is
the differentiated ECG input.
In the frequency domain, the signal is transformed with a filter of response
.
T
he input signal
is equivalently processed with
an all

pass filter with
shift for positive frequencies and
shift for negative frequencies. The Hilbert
transform is the
imaginary part of the analytic signal that has the input as its real
part.
Because the Hilbert transform
is the zero

crossings
and
an odd filter of the
differentiated ECG
, the Hilbert transform
will be represented as peaks in the output of
the transform.
The
output
of the Hilbert
transform on the differentiated ECG
has
been

9

explained in
terms of its odd symme
try property and signal envelope. The
all

pass
characteristic
of
Hilbert transform
prevents unnecessary
signal distortion
. I
n contrast
to the second derivative method
, it
tends to attenuate the signal at the lower
frequencies
.
Thus, the odd

phase component
of the filter
provides the necessary
modification
of the differentiated ECG
signal in order to identify the QRS peaks
while the uniform
magnitude of the filter ensures that necessary information of
the
QRS complexes is preserved. The effects of the magnit
ude
and phase of this
transform are further
used.
The first differential in discrete domain of the ECG
waveform sequence
can
be obtained by
The Hilbert transfo
rm
of the sequence
that
represents the first
differential of the ECG waveform in this
subset is then obtained using the following
methodology
. At first obtain
the Fourier transform
of the input
sequence
and set DC component to zero. Later
m
ultiply the positive and negative harmonics by
and
respectively
.
Perfo
rm
the inverse Fourier transfo
rm
of this resulting
sequence to o
btain the
Hilbert
transform
.
Finally, t
hreshold detection is used to locate the peaks in
sequence. The position of the R

wave is located by threshold
detection
if its
value is greater than 18% of the
maximum
value of the sequence.
The Hilbert
transform can have other modified forms
such as it can
combine with one or two
adaptive
thresholding method
.
The more details can be referred in [8].
(
b
)
Discrete Wavelet
Transform
Method
T
he main idea behind this algorithm was to use Discrete Wavelet Transform (DWT)
and Cubic Spline Interpolation (CSI) techniques with an improved dynamic weights
adjusting strategy to enhance the detection robustness and the signal

to

noise ratio
(SNR) of th
is ECG signal in heavy noise condition. It made use of the property that
symmetric wavelet decomposition can be used to retrieve delta

function peak location
precisely. DWT aims to separate base line drift, QRS R

wave peak and
high

frequency noise. The int
erpolation was employed to adjust the coefficients of
each decomposition level and improve time resolution of wavelet coefficients in high
decomposition levels, which generates smooth curves and suppresses noise. In

10

addition, an improved dynamic weight adj
usting strategy was adopted to assign
proper weight for each level to further enhance the signal

to

noise ratio.
Finally, a
peak detector is employed to generate R peak
candidates and an adaptive threshold
detector to locate R peaks.
Fig.
4.
Block Diagr
am of Wavelet Transform.
It
is
obvious
that wavelet coefficient has
better
time resolution
in low
decomposition levels and
has better frequency resolution
for high
decomposition
levels. When wavelet coefficients from
different levels are
found,
it is
reasonable to
improve high level resolution to achieve higher time accuracy.
In fact, all these
preserved levels are interpolated with different
gains. A
s cubic spline interpolation
technique
is used
to
evaluate new points between given
R

wave candidates
,
it is
employed in the
preprocess
ing step to
find out
the wavelet c
oefficients.
From here, we can observe that
symmetric wavelet is suited
to precisely locate the
R

wave
peaks in
the
ECG signal. There is a local
maximum in the wavelet
coefficients
to find out
the
locations of
R

wave
pea
ks
.
Using
the local maxim
um
of
wavelet
coefficients is the
essential point
of
such an
algorithm.
S
pline
interpolation is
adopted
in this method
to improve time resolution of wavelet
coefficients in high
decomposition
levels, which generates
smooth curves and suppresses noise. In
addition, an
adaptive
coefficient
weight
ing
strategy is
used to improve the SNR in
heavy noise condition.
Such method sometimes has better
accuracy
on detection on
ECG signals but may need more
computation time.
The more details can be referred
in [9],[12].
C.
Other
A
lgorithms
(
a
)
Genetic Method
There is an
approach to design optimal QRS detectors
which
used a detector
including the linear or
nonlinear polynomial filter
to
enhance the QRS complexes as

11

well as a simple and adaptive maxima detector. The design of such a QRS detector
required the definition of the characteristics of the polynomial filter as well as the
selection of its coefficients and the parameters of the ma
xima detector. Some of these
variables were set by the human designer, the others were chosen by a genetic
algorithm. In genetic algorithm application, it used several filters including the
Quasi

Linear filter and the Quadratic filter to apply to consecuti
ve samples and
selected samples.
Fig.
5.
Block Diagram of Genetic Method.
In polynomial filters, the output signal
at time
is the value taken by a
polynomial of order
of a set of
input samples
.
and
where
is the time delay with respect to time
.
The maximum detector is used to detect the maxima of the filter output.
To avoid
false detections in the presence of noise,
QRS

like artifacts, and filter responses, only
the
maxima
that have amplitude greater than a threshold
.
Genetic algorithm has
allow
ed
optimizing the parameters of the maxima
detector
and the coefficients of the filter according to a single
criteri
on: minimizing the
number of
erroneous
detections. While this objective
function is commonly used in
the optimization of detectors
having fe
w parameters, it has never been adopted in
designing more
complicated QRS enhancing filters or detectors.
The joint
optimization of the two stages of detectors has
made optimally adapted to each other.
This has allowed for
the discovery of parameters which
yield robust and efficient

12

QRS
detectors even with very simple layouts and only a few operations
per sample.
The more details can be referred in [23].
Fig.
6.
Block Diagram of
Geometrical Match
Method.
(
b
)
Geometrical
M
atch
Method
One
approach
was developed which is
based on a geometrical matching
rule
evaluated using a decision function in a local moving

window procedure. The
decision function was a normalized measurement of a similarity criterion comparing
the windowed input signal with the re
ference beat

pattern into a nonlinear

curve space.
A polynomial expansion model described the reference pattern. For the curve space,
an algebraic

fitting distance was built according to the canonical equation of the unit
circle. The geometrical matching a
pproach operated in two stages including training
and detection. In the first stage, a learning method based on genetic algorithm
estimated the decision function from training beat

pattern. In the second stage, a
level

detection algorithm evaluated the dec
ision function to establish the threshold of
similarity between the reference pattern and the input signal.
The first step is to define
geometrical
matching.
it is similar to pattern recognition.
T
he goal of matching procedure is to
determine the similari
ty between two entities.
It
is
propose
d
to evaluate the matching between the pattern and the
analyzed signal
according to a nonlinear geometric metric.
The second step is to define data set and geometric curve.
A measurement vector
describes the signal pat
tern to be detected.
The selection of the most effective features
reduces the
dimensionality on the measurement vector. The proposed decision

13

function will be trained to take into account the discriminatory
features of the pattern,
evaluating the concept o
f

similarity.
In literature, this problem involves a
preprocessing stage
referred as the feature extractor machine
.
The third step is to do polynomial model estimation. It
must be capable to generate
the polynomial parameters
.
The more details can be refe
rred in [21].
(
c
)
Topological
M
apping
Method
A
topological mapping
is used from
one dimensional sampled ECG signals to two
dimensional vectors for a real

time detection of the QRS complexes of ECG signals.
In order to describe a change of curvature, it
derived a modified spatial velocity
(MSV) to locate QRS complexes more easily. In this method, firstly it should choose
the mapping parameters including time delay and mapping dimension to obtain a clear
representation of the QRS complex in the new space f
or a discrimination of QRS
complex from other components, such as P and T waves. Secondly it should find out
the relation between noise and phase portrait which is essential to reduce
high

frequency noise components. Finally the detection method was to ac
cept only
the QRS complex spectral components by filtering. It used only one low

pass filter to
remove high

frequency components relative to the QRS complex spectral components.
In summary, this algorithm reliably detected QRS complexes using the rate of
c
urvature of the vector loop. The distinct feature of this method was a change of
signal dimension to the new dimension vector loop. This topological mapping made
overall processing steps simpler and very robust to low

frequency noise or artifact.
For this
method, it is at first to choose mapping parameters including time delay
and mapping dimension. By o
btain
ing
proper reconstruction parameters
and
a clear
representation
of the QRS complex
, it is a
purely geometrical
cons
ider
ations and
guarantees a maximum
distance of trajectories represented
in the new dimension.
The second step is to find out the relationship between noise and phase portrait.
The
high

frequency noise
includes
power line
interference, electrode contact noise,
muscle contractions
and the
low

frequency noise
includes
base line drift
. I
n
high

frequency
noise, the structure of phase portrait could not be recognized
and it
can be removed by using filter.
In
low
frequ
e
ncy noise, the structure of phase portrait
does
no
t
hi
de and is clearly recog
nizable.
The more details are shown
in [16].
(
d
)
Filter Bank Method

14

A
multi

rate digital signal processing algorithm
is used
to detect heart beats in the
electrocardiogram (ECG). The algorithm incorporated a filter bank (FB) which
decomposed the ECG into
sub

bands with uniform frequency bandwidths. The F
ilter
B
ank

based algorithm enabled independent time and frequency analysis to be
performed on a signal. Features computed from a set of the sub

bands and a detection
strategy was used to fuse decisions fro
m multiple one

channel beat detection
algorithms. Further improvements to the algorithm may be easily achieved by using
more features of the frequency components of the ECG.
FB contains a set of analysis and
synthesis filters. The analysis filters
decompose
an incoming
signal into specific frequency bands or sub

bands. Processing
can be
performed on each sub

band independently. The set
of synthesis filters can then
combine the processed sub

bands
to result in a processed version of the input signal.
Thus,
a FB

based algorithm involves decomposing a signal into
frequency sub

bands,
processing these sub

bands according to
the application at hand, and then sometimes
reconstructing the
processed sub

bands.
The choice of filter bank
is important that the
FB used to process the ECG have
certain characteristics. The
analysis and synthesis filters should have linear phase.
Linear
phase ensures that the
R

wave
points in the ECG
.
The
perfect reconstruction
property was also incorporated into the
design of the
FB because an overall goal is to
develop one set
of filters to accomplish multiple ECG processing tasks
.
The more
details can be referred in [20].
(
e
)
Zero Crossing Method
It is
an algorithm based on a feature obtained by counting the number of zero
crossings per segment. The algorithm operates for feature extraction, event detection
and localization of R peak by counting zero crossings. It was a feature signal that was
largely independent of sudden changes in the amplitude level of the signal and was
robust against noise and pathological signal morphologies. It was shown that this
feature could be used for a computationally simple algorithm with a high detection
performance. Due to this simple principle, QRS detection can be realized at low
computatio
nal costs.
In feature extraction step, d
ue to these
spectrum
characteristics
of the ECG
components, it is reasonable to filter the
ECG signal at first in order to attenuate the
mean, the
P

wave,
T

wave, and the high frequency noise
.
T
he
band
passed
filtered

15

signal
oscillates around zero.
From observation, it is obvious that
many zero crossings
are in
non

QRS
segments and only a small number of zero crossings
are
during the
QRS complex.
Fig. 7. Block Diagram of
Zero Crossing Method
In event
detection
step
, a
n event begins when the feature signal
(number of zero
crossings per segment) falls
under
a
n
adaptive threshold
.
The
event
ends when the
signal rises above the threshold.
Both the beginning and the end of the event are
in
the
boundaries of
the search interval for the temporal
localization of the R

wave. If
adjacent events are temporally
very close (multiple events), they will be combined
into one single event. The beginning of the combined
event is the beginning of the
first event, and the
end of the combined event is the end of the last event.
In temporal
localization of the R

wave
step
,
t
he detection of
the QRS complex is
completed by the determination of
the temporal location of the R

wave. If only one
ECG
channel is used for the detection of the R

wave,
the
temporal location is
d
etermined by a combined maximum
and
minimum
search.
Using
the maximum or
the minimum position of the search
interval as the temporal location of the R

wave
is
a simple decision boun
dary
.
The more details can be
described
in [22].
(
f
)
Morphology
Method
It is
an algorithm to remove background noise and baseline wandering from
original ECG signal by morphological filter , which uses two most fundamental
mathematical morphological operators (erosion and dilation). The modulus
accumulation and combination are uti
lized to act as a low

pass filter to enhance the
QRS complex and improve the signal

to

noise ratio. Finally peak extraction is done
by adaptive thresholding and decisions. In morphology, opening and closing are two
extended morphological operators and cou
ld also work as morphology filters with
clipping effects to cut down peaks and fill up valleys from ECG signals. Although this
paper presented a morphology

based algorithm for QRS detection which is different
from other frequency

based methods, the calcula
tions of erosion and dilation
operations for ECG signals takes more computation time.
The more details can be
referred in [10].

16

III.
D
ETECTION
P
ERFORMANCE
E
STIMATORS
For the R

wave detection of the ECG signals, there are three parameters to be
proposed as sta
ndard. There are
Sensitivity (SE), Positive Prediction (+P) and
Detection Error Rate (DER)
.
The three parameters
are used to evaluate the detection
performance
of R

wave detection of the ECG signals for all existing detection
algorithms
and their
corresponding meanings are described as below.
TP is the numbers of a correctly detected true beat (actual R

wave). FN represents
that the numbers of a missed true beat by the proposed algorithm. FP means the
numbers of a false beat detection. Thus the detection performance parameters of
Sensitivity (S
E), Positive Prediction (+P) and Detection Error Rate (DER) are
calculated by using
above
equations respectively.
IV.
O
NE
P
OPULAR
E
CG
D
ATABASE
In order to compare the detection performance for t
h
ose
proposed algorithm
s
in the
world, a common ECG signal datab
ase is very important for this. It is very lucky that
one database website is used and all related algorithms for ECG R

wave peak
detection are
using the
MIT/BIH Arrhythmia Database
[1].
The characteristic
features about this database are described as belo
w with more detailed information.
The database is public to everyone and it can be gotten by those people who are
interested in such ECG research
for
FREE
.
It contains 48 half

hour and two

channel ambulatory ECG recordings.
The subjects
are
25 men aged
from
32 to 89 years

old (Records 201 and 202 came from the same
male subject)
and 2
2
women aged
from
23 to 89 years

old
.
From the current data
distribution of those recordings, the total 11 records from healthy persons are

17

including 113, 115, 116, 117, 208
, 210, 212, 215, 223, 231 and 234. Other 37 records
belong to sick persons. These recordings have 11

bit resolution over 10mV and are
sampled at 360Hz and each recording has 650000 sampling points. The ground truth
data is obtained from the current MIT/BI
H database website [1] and the total number
of the ground truth beats is 112647 beats.
For all recordings with many different beat types, the five beat types (+, ~, , x and !)
could be removed from the ground truth data because they are not standard ECG
waveform. The beat types of +, ~ and  belongs to isolated QRS

like artifact. The beat
types of ! and x are ventricular flutter wave and non

conducted p

wave respectively.
The total number of final ground truth beats without considering these five beat typ
es
is 109494 beats.
V.
P
ERFORMANCE
C
OMPARISON
S
In order to compare the detection performance, the three parameters
Sensitivity
(SE), Positive Prediction (+P) and Detection Error Rate (DER)
described before are
listed here again. For the Sensitivity and
Pos
itive Prediction
parameters, their values
are as higher as possible for representing the better performance. For the Detection
Error Rate parameter, its value is as lower as possible for representing the better
performance.
After collecting the performance results from all existing published algorithms,
From
TABLE
I
, it can be seen the total ground truth beats of
all existing
published
algorithms
,and the values of SE, +P and DER respectively
on different ECG R

wave
peak dete
ction algorithms
.
VI.
C
ONCLUSIONS
In summar
ies
for all existing detection algorithms, even they used different methods
or mixed methods on both time domain and frequency domain, the ONLY one goal is
to get better performance on
Sensitivity (SE), Positive
Prediction (+P) and Detection
Error Rate (DER)
on the ECG signals for improving
R

wave peak detection accuracy
of electrocardiogram (ECG) signals
and
obtain
ing
better performance gain.

18

T
ABLE
I
P
ERFORMANCE COMPARISO
N
WITH OTHER PUBLISHED
ALGORITHMS AND TH
E PROPOSED ALGORITHM
IN THE PAPER ON THE
STANDARD
MIT/BIH
A
RRHYTHMIA DATABASE
Al gori thm
Total Beats
FN
FP
SE
+P
DER
[7]
109508
199
405
99.82%
99.63%
0.55%
[8]
97794
195
411
99.80%
99.58%
0.62%
[9]
90989
296
375
99.67%
99.59%
0.74%
[10]
109510
279
199
99.75%
99.82%
0.44%
[11]
109492
224
154
99.80%
99.86%
0.35%
[12]
102934
101
191
99.90%
99.81%
0.28%
[13]
107344
2112
884
98.03%
99.17%
2.79%
[14]
109267
340
248
99.69%
99.77%
0.54%
[15]
116137
277
507
99.76%
99.56%
0.68%
[16]
109481
335
137
99.69%
99.87%
0.43%
[20]
90909
374
406
99.59%
99.55%
0.86%
[21]
60431
1246
521
97.94%
99.13%
2.92%
[22]
91283
277
390
99.70%
99.57%
0.73%
[23]
109963
441
545
99.60%
99.50%
0.90%
For all existing detection algorithms with better performance, we can
observe that
t
he original
ECG
data is
FIRSTLY
processed by using filter
to do
baseline extraction
of ECG signals in order to reduce false detections caused by the various types of
interference which are present in ECG signals
.
SECONDLY
, the
specific method
s in
time domain or frequency domain or mixed methods
are used
to obtain
R

wave
candidates.
At the
THIRD
step, use one or two adaptive thresholding methods to sift
for true R

wave peak of the ECG signals.
From the previous section
s
, we can observe
there
are always some tr
ade

off
conditions on computation time and
performance
(SE, +P and DER)
for different
ECG R

wave detection methods.
There is one summary table for th
e
se
proposed
methods which
are
shown in TABLE II.

19

T
ABLE
II
S
UMMARY OF
A
LGORITHMS
Year
Algorithm
Method
Filter
Thresholding
Comments
2011
[7]
Derivat ion
N/A
Two fixed schemes
Differention, Slope est imation
2011
[8]
Hibert t ransform
Band

Pass filt er
One adapt ive scheme
FFT, RR int erval est imation
2008
[9]
Wavelet transform
N/A
One adapt ive
scheme
Discret e Wavelet Transform, Cubic Spline Int erpolation
2012
[10]
Morphology
Low

Pass filt er
One adapt ive scheme
Dilat ion, Erosion, Opening and Closing
2012
[11]
Wavelet transform
Band

Pass filt er
One adapt ive scheme
Four

scale discret e wavelet
transform
2010
[12]
Wavelet transform
Band

Pass filt er
One adapt ive scheme
Biort hogonal spline wavelet t ransform, Mallat algorithm
2008
[13]
Hibert t ransform
Band

Pass filt er
Two fixed schemes
Hamilt on

Tompkins, Squaring and t ime

average est imation
1986
[14]
Derivat ion
Band

Pass filt er
One adapt ive scheme
Median est imator, Search back, Peak level estimation
1985
[15]
Derivat ion
Band

Pass filt er
Two adapt ive schemes
Squaring and moving

average estimation
1996
[16]
Topological mapping
Low

Pass filt er
One
fixed scheme
Spat ial velocity wit h 2D vectors
1999
[20]
Filt er bank
Band

Pass filt er
Two adapt ive schemes
Magnit ude and phase reconstruction, subband handling
2007
[21]
Geomet rical match
N/A
One fixed scheme
Polynomial model estimation
2003
[22]
Zero
crossing
Band

Pass filt er
One adapt ive scheme
Feat ure ext raction, Zero crossing count
1995
[23]
Genet ic algorit hm
Band

Pass filt er
One adapt ive scheme
Polynomial filter, Genetic maxima det ection
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R
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