1
Estimation of a Respiratory Signal from Single Channel Electrocardiogram Signal Using
Empirical Mode Decomposition
Kunal Kamble1, Vishal Lohikpure 2, Sushil Sirsat3 and Narendra Jadhav3
1 Electronics
and Tele Communication Engineering, Dr. Babasaheb Ambedkar Technological University ,
Lonere, Tal.- Mangaon, Dist.- Raigad, pin-402103.
kunal24178@gmail.com
2
Electronics and Tele Communication Engineering, Dr. Babasaheb Ambedkar Technological University ,
Lonere, Tal.- Mangaon, Dist.- Raigad, pin-402103.
vishmax20@gmail.com
3
Electronics and Tele Communication Engineering, Dr. Babasaheb Ambedkar Technological University ,
Lonere, Tal.- Mangaon, Dist.- Raigad, pin-402103.
sush.sushil1007@gmail.com
3
Electronics and Tele Communication Engineering, Dr. Babasaheb Ambedkar Technological University ,
Lonere, Tal.- Mangaon, Dist.- Raigad, pin-402103.
nsjadhav13@yahoo.com
Abstract
Respiratory signal is widely used biomedical signal for extracting
physiological or pathological information about patient. An
electrocardiogram is a transthoracic interpretation of the
fills the lungs is a poor conductor compared to the
different types of tissue that make up the thorax.[12] It is
therefore feasible, that the inspiration of air increases the
electrical impedance across the thorax. The respiratory
induced changes in thoracic impedance could lead one to
electrical activity of the heart over a period of time. Respiration
modulates heart rate such that it increases during breathing in
and decreases during breathing out & is referred as respiratory
sinus arrhythmia. Mechanical action of respiration results in the
same kind of frequency content in the electrocardiogram
spectrum. Here we are estimating the respiratory signal by
decomposing single channel electrocardiogram signal into
different intrinsic mode functions. This is especially important in
which the electrocardiogram, but not the respiration is routinely
monitored.
Keywords: Electrocardiogram, Respiratory signal, Intrinsic
mode functions, Decomposition, Residual, Vector-cardiogram.
1. Introduction
When the aim is to derive or estimate a surrogate
respiratory signal from the information contained in the
ECG signal, one have to observe the respiratory
mechanisms that induce modulations of the ECG. It has
been shown experimentally, that the filling and emptying
of the lungs during the respiratory cycle causes short term
changes in thoracic impedance distribution. The air that
conclude that inspiration would always decrease ECG
amplitude and expiration would increase ECG amplitude.
This is however not always the case. ECGs recorded from
the surface of the chest are also influenced by the relative
motion of the electrodes with respect to heart [12]. The
expansion and contraction of the chest, which accompanies
respiration, induces an apparent modulation in the
direction of the mean cardiac electrical axis which affects
beat morphology. It has been experimentally shown that
respiratory induced modulation of the electrical axis is
caused mainly by the motion of the electrodes relative to
the heart, while the thoracic impedance changes contribute
to the electrical rotation as a second order effect. These
physical influences of respiration result in amplitude
modulations of the observed ECG [9].
The Empirical Mode Decomposition (EMD) was proposed
as the fundamental part of the Hilbert–Huang transform
(HHT)[12]. The Hilbert Huang transform is carried out, so
to speak, in 2 stages. First, using the EMD algorithm, we
obtain intrinsic mode functions (IMF). Then, at the second
stage, the instantaneous frequency spectrum of the initial
sequence is obtained by applying the Hilbert transform to
the results of the above step. The HHT allows to obtain the
2
instantaneous frequency spectrum of nonlinear and
nonstationary
sequences.
These
sequences
can
consequently also be dealt with using the empirical mode
decomposition. However, this project is not going to cover
the plotting of the instantaneous frequency spectrum using
the Hilbert transform. We will focus only on the EMD
algorithm. The EMD decomposes any given data into
intrinsic mode functions (IMF) that are not set analytically
and are instead determined by an analyzed sequence alone.
The basis functions are in this case derived adaptively
directly from input data. The respiratory signal estimation
is based on the identification of the intrinsic mode
functions related to the respiratory activity [12].
1. The number of IMF extrema (the sum of the maxima
and minima) and the number of zero-crossings must either
be equal or differ at most by one.
2. At any point of an IMF the mean value of the envelope
defined by the local maxima and the envelope defined by
the local minima shall be zero.
The algorithm as proposed by Huang is based on
producing smooth envelopes defined by local maxima and
minima of a sequence and subsequent subtraction of the
mean of these envelopes from the initial sequence. This
requires the identification of all local extrema that are
further connected by cubic spline lines to produce the
upper and the lower envelopes. The procedure of plotting
the envelopes is shown in Figure [10].
2. Empirical Mode Decomposition
Decomposition results in a family of frequency ordered
IMF components. Each successive IMF contains lower
frequency oscillations than the preceding one. And
although the term "frequency" is not quite correct when
used in relation to IMFs, it is probably best suited to define
their nature.[10] The thing is that even though an IMF is of
oscillatory nature, it can have variable amplitude and
frequency along the time axis.
2.1 Steps involved in EMD
1. Identify the extrema (maxima and minima) of the signal
x (t).
2. Find the upper envelope of the x (t) by passing a natural
cubic spine through the maxima.
3. Find the lower envelope of the minima.
4. Compute mean of the upper and lower envelopes and
designate as m(t).
5. Get an IMF candidate using the formula hn (t) = x(t) –
m(t).
6. Check whether the hn(t) is an IMF, and is not repeat, the
process from step 1 if hn(t) is an IMF then set
r(t) = x(t) - hn(t).
2.1 Intrinsic mode function
EMD decomposes a signal x (t) into its components called
intrinsic mode functions (lMFs) hn(t), n =1, 2, ...,N and the
residual r(t)
N
x(t )   hn (t )  r (t )
n 1
An IMF resulting from the EMD shall satisfy only the
following requirements:
Fig. 1 Plotting the envelopes and their mean
Figure 1 gives the analyzed sequence in the thin blue line.
The maxima and minima of the sequence are shown in red
and blue, respectively. The envelopes are given in green.
The mean is calculated based on the two envelopes and is
shown in Figure 1 as the dashed line. The mean value so
calculated is further subtracted from the initial sequence.
The above steps result in the extraction of the required
empirical function in the first approximation. To obtain the
final IMF, new maxima and minima shall again be
identified and all the above steps repeated [12].
3
Fig. 2 Respiratory induced modulation of ECG signal
4. Simulation Results
1
0.8
0.6
0.4
Fig. 2 Block diagram
0.2
0
This repeated process is called sifting. The sifting process
is repeated until a certain given stoppage criterion is met.
Selection of sifting stoppage criteria is one of the key
points affecting the decomposition result as a whole. We
will get back to the discussion of this issue a bit later. If the
sifting process is successfully completed, we will get the
first IMF. The next IMF can be obtained by subtracting the
previously extracted IMF from the original signal and
repeating the above described procedure once again. This
continues until all IMFs are extracted. The sifting process
usually stops when the residue, for example, contains no
more than two extrema.
-0.2
-0.4
-0.6
-0.8
-1
0
5
10
15
20
25
20
25
Fig. 2 Modulated Single channel ECG signal
intrinsic mode functions
0.8
0.6
0.4
0.2
3. Respiratory Signal estimation
If the ECG signal is decomposed till the Nth level of
decomposition, and the detail signal of 9th decomposition
is reconstructed, we get the RS. The value of N depends
upon the sampling rate. This is because the maximum
frequency that can be represented is taken equal to fs/2,
where fs is the sampling frequency. Because of the fact that
the range frequency of RS is 0.2 Hz – 0.4 Hz, it is
necessary to compute the decomposition, level
corresponding to this range [10]. In our case the data taken
is sampled at 200 Hz and the decomposition level selected
is the 9th level.[12]
0
-0.2
-0.4
-0.6
-0.8
0
5
10
15
Fig. 3 First intrinsic mode function
4
References
intrinsic mode functions
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
0
5
10
15
20
25
Fig. 4 Fifth intrinsic mode function
intrinsic mode functions
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
0
5
10
15
20
25
Fig. 5 Required respiratory signal
Power Spectral Density
70
Power/frequency (dB/rad/sample)
60
50
40
30
20
10
0
-10
-20
-30
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Normalized Frequency ( rad/sample)
0.9
1
Fig. 6 Power spectral density
4. Conclusion and Future Work
In this work empirical mode decomposition method is
utilized to estimate the respiratory signal from single
channel ECG signal. Wavelet decomposition is also used
to extract respiratory signal from single channel ECG
signal but it has been shown that empirical mode
decomposition leads to better results. Some researchers,
recently, are developing further improvements on EMD
technique that make these new algorithms very useful and
powerful instruments for indirect monitoring. This
technique can also be used for the extraction of heart
sound signal from auscultation process and for the
analysis of heart sound signal in different critical cases.
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