# Time-Frequency Analysis and Wavelet Transform (Tutorial)

AI and Robotics

Oct 24, 2013 (4 years and 11 months ago)

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-
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

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
-
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)
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

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
-
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

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

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
-
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
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
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
-

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

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
in this method
to improve time resolution of wavelet

coefficients in high
decomposition
levels, which generates

smooth curves and suppresses noise. In

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

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
.

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

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
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
-
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

2011

[7]

Derivat ion

N/A

Two fixed schemes

Differention, Slope est imation

2011

[8]

Hibert t ransform

Band
-
Pass filt er

FFT, RR int erval est imation

2008

[9]

Wavelet transform

N/A

scheme

Discret e Wavelet Transform, Cubic Spline Int erpolation

2012

[10]

Morphology

Low
-
Pass filt er

Dilat ion, Erosion, Opening and Closing

2012

[11]

Wavelet transform

Band
-
Pass filt er

Four
-
scale discret e wavelet
transform

2010

[12]

Wavelet transform

Band
-
Pass filt er

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

Median est imator, Search back, Peak level estimation

1985

[15]

Derivat ion

Band
-
Pass filt er

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

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

Feat ure ext raction, Zero crossing count

1995

[23]

Genet ic algorit hm

Band
-
Pass filt er

Polynomial filter, Genetic maxima det ection

VII.

R
EFERENCES

[1]

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-
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-
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[13]

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-
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-
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