Vol.1, No.2, 111-116 (2009)
Copyright © 2009 Openly accessible at http://www.scirp.org/journal/HEALTH/
Non-invasive foetal heartbeat rate extraction from an
underdetermined single signal
Ranjan Acharyya1, Neil L Scott1, Paul D Teal2
1Industrial Research Ltd, Wellington, New Zealand; r.achary ya@i rl.c ri.nz, n.scottt@irl.cri.nz
2Victoria University of Wellington, Wellington, New Zealand; mailto:paul.teal@vuw.ac.nz
Received 17 June 2009; revised 20 July 2009; accepted 23 July 2009.
Extraction of foetal heartbeat rate from a single
passive sound sensor on the mother’s abdomen
is demonstrated. The extraction is based on the
assumption that a disjoint band of frequencies
exist and foetal signal is concentrated in this
band, and further that it can be represented
conveniently as a set of wavelet coefficients.
The algorithm has been applied to each stream
of data obtained from six different channels and
the detection performance is elaborated. The
algorithm has also been tested on signals from
non-pregnant abdomens to show successful
rejection of adult heartbeat. The extraction of
the desired signal is done in two stages so as to
eliminate components from the maternal heart-
Keywords: Underdetermined System; Foetal
Heartbeat Rate; Wavelet, Blind Source Separation;
Non-Invasive; Passive.
Monitoring of foetal heartrate using a non-invasive tech-
nique is still a challenging problem with a variety of
approaches [1,2]. Usually, foetal heartbeat is monitored
using a Doppler ultrasound device which transmits ul-
trasonic sound waves into the uterus. Most researchers
consider that the power used in these devices is perfectly
safe, although there are some exceptions [6]. In many
cases women prefer that ultrasound is not used on them.
Detailed motivation for development and use of accurate,
non-invasive techniques for monitoring the foetal heart
is covered in the excellent introduction of [1]. This paper
describes a method for detection of the foetal heart with
a passive acoustic monitoring device (PAM). The proc-
ess involves collection of signals with microphones and
subsequent signal processing.
The passive monitoring of foetal heartrate may be
considered as one class of Blind source separation (BSS)
problem, which has been an active research area for sev-
eral decades now. It refers to the problem of estimating
the original sources from a mixture. In most cases the
mixing system and the number of sources are unknown.
Sensors placed on the maternal abdomen provide signals
which are mixtures of an unknown number of sources
and the nature of the mixing is also unknown. In this
section a quick review of other techniques and overview
of the technique of this paper is given.
Independent Component Analysis (ICA) is a tech-
nique to obtain statistically independent components
from a mixture and a solution technique for BSS prob-
lems. One way to categorise BSS problems is based on
the number of sensor and source signals. Three different
scenarios are, the number of sensors are greater than,
equal to or less than the number of sources. The third
case, which is equivalent to solving for an underdeter-
mined system or for an overcomplete basis, resembles
the problem at hand. Detail and an in-depth analysis of
algorithms can be found in [3,4,5]. A well known algo-
rithm for sparse sources is known as DUET (degenerate
unmixing estimation techniques) [5], which does time-
frequency masking. The applicability of the algorithm
depends on a W disjoint orthogonal [5] condition of the
sources and availability of at least two sensor signals.
Extraction of foetal heartrate using ICA [7] has been
attempted in [8] and some interesting results were ob-
tained. In this paper a new algorithm is developed based
on certain assumptions on the foetal heartbeat signal.
This paper is an extension of an earlier work [9] demon-
strating estimation of the foetal heartrate by frequency
masking. A crucial difference of this paper compared to
[9] is that it avoids filtering of the signal in the time do-
main. Filtering in the time domain was done in [9] to
suppress the maternal heartbeat. The issue of suppress-
ing the maternal signal in the overlap region is addressed
in this paper by performing the filtering in two steps. In
addition to filtering in the frequency domain the resolu-
tion of the signals is enhanced by using a wavelet trans-
formation. The process is discussed in detail in later sec-
tions. The method described in this paper requires only
R. Acharyya et al. / HEALTH 1 (2009) 111-116
Openly accessible at
one mixture provided the sources satisfy certain condi-
The work reported in [10,11] using SCICA (sin-
gle-channel independent component analysis) is perhaps
the closest to this work in its assumption of disjoint fre-
quency bands for the noises in the mixtures.
In Section 2, the experimental setup and the sensor
structure is shown. The assumptions on the sources are
explained in Section 3. In Section 4 the algorithm is dis-
cussed in detail. Results of the application of the algo-
rithm to a mixture of signals from a pregnant maternal
and a non-pregnant abdomen is elaborated in Section 5.
Finally, in Section 6 the conclusion and future work are
The sensor is similar to that described in [9] which was
designed for work using multiple sensors. The sensor
structure array is an array of 16 piezo film (PVDF, Poly-
vinylidene Fluoride) contact microphones of type CM-
01B in a mat placed against the mother’s abdomen. Use
of the existing 16-sensor array allowed recording multi-
ple channels simultaneously, although the algorithm
proposed here uses only a single sensor signal. The sig-
nals are conditioned in a 16 channel low noise amplifier
with band pass filtering (7.2 – 130Hz) and then recorded
in a data logger. Figure 1 shows the block diagram of
the Passive Acoustic Monitor (PAM) and Figure 2 the
complete sensor array.
The model is that the sensor signal is a mixture of sig-
nals from multiple sources including foetal heartbeat,
maternal heartbeat, other noises internal to the mother’s
abdomen and external noises from the environment. In
addition the mixing system seems to vary with time. The
most important assumption is that sound from the foetal
heart is band limited and part of the band is isolated
from the other sources, including maternal heartbeat. In
other words, sources do not share the whole band of the
foetal heart beat sound. This conclusion is motivated by
the assumption that the characteristics of sound have
direct relation to the size of the object generating the
sound. The foetal heart is considerably different in size
from the maternal heart or any other sound sources in-
side the maternal abdomen. However, it is expected that
there may be overlap of the frequency band of the foetal
heart and the maternal heart beat. The maternal heart
beat is considered to be the strongest noise present with
respect to the desired signal. In addition to being band
limited the foetal heartbeat sound is also expected to be
compact in the time domain. This implies the signal is
assumed to be absent for short periods between heart-
beats. Hence, application of wavelet transformation to
Figure 1. Block diagram of Passive Acoustic Monitor (PAM).
Figure 2. The 16 channel sensor array.
the signal is expected to enhance detection of the heart-
beat. The effect of the wavelet transformation will be
shown in the next section.
There are further assumptions on the energy content
of the signal. In each data block, after initial processing
the energy of the processed data in the foetal band needs
to be more than a specified threshold value. This is es-
sential to reduce the risk of accepting the adult heartbeat
as the foetal one. The energy of the foetal heartbeat
needs to be more than a specified threshold value at two
different stages. This has a disadvantage that if the signal
strength of the foetal heartbeat is very weak then the
algorithm can fail to detect it at any particular time. It
has been observed that the foetal heartbeat sound is loca-
tion dependent and it is strong at a certain portion of the
maternal abdomen; the strength of the signal is not equal
at every point on the abdomen. Further the position
where the signal is strongest may vary from time to time.
The algorithm has been developed to exploit the beha-
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R. Acharyya et al. / HEALTH 1 (2009) 111-116
Openly accessible at
viour of the signals given the assumptions mentioned
above. The mixture signal obtained from an acoustic
sensor is subjected to filtering in both the frequency and
wavelet domains. The procedure is an extension of the
process discussed in [9], where both maternal and foetal
heartbeat were extracted. The algorithm developed here
can be extended to extract the maternal heartbeat as well
although it is not required for estimation of the foetal
heart rate. First, we describe the components of the algo-
rithm and then provide a step by step algorithm descrip-
The first filtering step is performed in the frequency
domain. The spectrum of the mixture signal is multiplied
by a profile derived from a Gaussian mixture before in-
verse Fourier transform. The procedure to derive the
profile of the mixture of the Gaussians is as in [9]. The
Gaussian mixture so obtained is then modified such that
20 406080100 120140 160
0. 1
0. 2
0. 3
0. 4
0. 5
0. 6
0. 7
0. 8
0. 9
Frequency in Hz
Mixture of Gaussians and flat spectrum
Figure 3. The solid line is mixture of Gaussian and the dashed
line is the derived one.
05 10 15 20 25 30 35
-0. 25
-0. 2
-0. 15
-0. 1
-0. 05
0. 1
0. 2
Time in msec
Wavelet coefficients and filtered signal
Figure 4. Comparison between filtered signal and its wavelet
coefficients (dashed).
a range of values around the peak of the mixture are set
to unity. This makes the frequency profile flat around the
middle portion. The reason for this modification is that
the peak energy frequency bin may vary from foetal
heart to heart or it may fluctuate from beat to beat.
Therefore a general form of frequency profile in the
first stage of filtering seems to be more appropriate.
Figure 3 shows the frequency profile derived in [9] and
the profile that is utilized in this paper. The mixture sig-
nal is filtered by this derived spectrum.
After filtering, the energy of the signal is compared to
the energy of the signal prior to filtering. The filtered
signal must meet the energy criterion which is set by a
specified threshold value, in order to proceed to the next
stage of processing, which is carried out for the portions
of signals which are expected to have a foetal heartbeat.
Next, a stationary wavelet transform (SWT) of type
Discrete Meyer as defined in MATLAB, is applied to the
signal. The number of coefficients in each level of sta-
tionary wavelet transform has the same number of sam-
ples as the original signals. The approximate coefficients
of the 5th level are considered [12]. Figure 4 shows a
small block of the filtered signal and the corresponding
5th level wavelet coefficients.
As can be seen in the figure, the portion where the
foetal heart beat is expected i.e. higher energy portion of
the signal is inflated. Next, the locations of the foetal
heartbeat in a block are estimated by determining the
peaks of the energy of the wavelet coefficients. The al-
gorithm should detect the peaks corresponding to each
heartbeat. Often the change of sign of the derivative is
used for detecting a peak. However, the foetal heart sig-
nal is essentially oscillatory in nature, each heartbeat
event includes several oscillation peaks hence, the
change of sign of the derivative would return many
peaks which are not of interest. To get rid of this prob-
lem the change of sign of derivative algorithm is applied
twice. An algorithm returns the first peak estimator as
the points of change of sign of the derivative. The same
algorithm is then applied to the absolute values of the set
of first peaks to determine the overall peak estimates.
Figure 5 shows the peaks detected by the algorithm in
the first and second stages. The arrows mark the final
peaks detected by the algorithm. The two stage peak
detector is an alternative to the other peak estimation
methods that require a strict threshold value.
The peaks obtained from the second stage are close to
the actual maxima, as observed by eye.
The signal around the peaks so selected is expected to
be made up of foetal heartbeat signal. At this stage a few
peaks may remain from maternal heartbeats. Next, the
signal is multiplied by a window function around the
peak values. The window function is shown in Figure 6.
The purpose of this window function is to attenuate all
other sources near the desired foetal heartbeat. Emphasis
may be given to the point that the objective of this paper
is to recover the foetal heartbeat rate rather than the
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05 10 15 20 25 3035
Peaks detected by the algorithm
Time in msec
Figure 5. The ‘o’ are the peaks obtained first and arrow shows
the accepted peaks.
05 10 15 20 25 30 35 4045
Time in msec
Window function
Figure 6. Window to multiply the time domain signal.
waveform. The use of the window function may change
the actual waveform of the foetal heartbeat but it is ex-
pected not to affect the foetal heartbeat rate. This ends
the first stage of the algorithm.
The signal obtained after applying the window func-
tion is subjected to another filtering step in the frequency
domain. The spectrum of the signal is once again multi-
plied by a profile derived from a set of Gaussians before
inverse Fourier transformation. These new set of Gaus-
sians are obtained in the same way as before [9]. How-
ever, the band of the spectrum is shifted towards higher
frequencies. For example if the frequency range of the
mixture of Gaussians were 15 to 45 Hertz earlier the
derived frequency range would be from 30 to 60 Hertz.
The motivation for this shifting is to pass the signals
which have only foetal heart beat. As mentioned before,
the lower part of foetal spectrum overlaps with the ma-
ternal heartbeat spectrum. The second step is expected to
minimize the energy in the overlap and hence the con-
tribution from the maternal heartbeat. To remove the
maternal part this second step of filtering is performed.
The maternal heartbeat is much stronger than the foetal
one and hence this type filtering helped recover the foe-
tal signal from the noise floor. Similar to the previous
step, the filtered signal must meet an energy criterion
which is set by a specified threshold value, in order to
consider it to be a foetal heartbeat. In the final steps the
signal is passed through a peak detector twice (like the
previous step) so that only those parts of the signal with
relatively large peaks can be considered as foetal heart-
The complete steps of the algorithm are given below:
• The data is divided into equal sized blocks. Each of
which is filtered by the following steps. In our case the
block size is 14400 samples; 6 seconds of data at the
sampling frequency 2400 samples per second.
• Multiply in the frequency domain the block of data
by the mixture of Gaussians derived as in [9] with flat all
pass section at mid band.
• Check the energy content of small blocks of con-
tiguous 2000 samples and compare the ratio of total en-
ergy before and after filtering. If a block has a ratio of
the energy, after and before filtering greater than the
threshold value of 0.005 the block is accepted for the
next step of processing. A small block of 2000 samples
is chosen instead of 14400 samples so the a whole block
of 6 sec data is not lost.
• Perform a stationary wavelet transform and retain
the approximate coefficients (low pass filtered part) of
level 5 for further processing. The Discrete Meyer
wavelet is utilized.
• Find the peaks of each block by passing data
through a peak detector twice. The peak detector is
based on the change of sign of the derivative of the sig-
nal. The peak detector output is passed on if it exceeds
the specified threshold value of 0.0067.
• Multiply the frequency content of the block of data
with the spectrum derived from the mixture of Gaussians
with flat all pass in the mid band.
• Window the signal with a 1000 sample window
about each peak.
• Multiply the frequency content of the block of
wavelet coefficients with the mixture of Gaussians and
perform an inverse Fourier transform.
• Check the energy content of small blocks of wave-
let coefficients of 2000 samples and compare the ratio of
total energy before and after filtering. If a block has a
ratio of the energy of the signal after and before filtering
is greater than the threshold value of 0.1 the block is
accepted for the next step of processing.
• Find the peaks of each block by passing data
through a peak detector twice. Pass all peaks exceeding a
specified threshold value of 0 .02.
• Count the number of peaks per minute to find the
heart beat rate.
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• Multiply the signal with a window of 1000 samples
so that only selected portions of the energy are kept to
produce an audible confidence signal.
The algorithm was applied to four different datasets.
Two sets of data came from pregnant women and two
from non-pregnant abdomens. The purpose was to verify
that the algorithm can detect foetal heartbeat while not
falsely detecting a heartbeat when none is present. Data
sets were collected with equipment comprising either 6
or 16 sensor. The sensor elements are identical while the
6-sensors equipment samples at 2400 data samples per
second and the 16-sensor at 300 samples per second.
Data sets were regularized by decimating the 2400 data
to 300. As the Gaussian mixture algorithm was designed
for 2400, both data types were then up-sampled to 2400
samples per second. It has been observed that the foetal
05 10 15 20 25 30 35 4045
0. 2
0. 4
0. 6
0. 8
Time in secs
Foetal heartbeat in 40 seconds
Figure 7. Foetal heartbeat for 40 seconds.
Time in secs
Foetal heartbeat in 5 seconds
Figure 8. Foetal heartbeat for 5 seconds.
heart beat sound is prominent at one sensor at a time.
This has been noticed in two different sets of data.
Figures 7 and 8 show the foetal heartbeat for a period
of 40 seconds and 5 seconds respectively. In the 40 sec-
ond data one can observe that the foetal heartbeat sound
has been missed a few times. From the signals illustrated,
a heartbeat rate of 144 beats per minute can easily be
estimated. A separate Doppler sensor used at the same
time reported a rate between 135 and 160 beats per min-
ute. Similar results were obtained from the other foetal
data set.
Data were collected from non-pregnant abdomens for
a total of 10 minutes being 5 minutes each from two
people. There were 16 channels and altogether the total
number of adult heartbeats expected was 11520 assum-
ing 72 heartbeat per minute. The number of false detec-
tions as foetal heart beat signal was 154 which is 1.3%
of 11520. In addition the 154 falsely detected pulses
were randomly scattered which indicated that they won’t
contribute significantly to the calculations of foetal heart
It has been shown that foetal heartbeat rate can be ex-
tracted from a single microphone sensor non- invasively.
The rejection of the adult heart rate by the algorithm is
established. Future research will look into adjustment of
the processing parameters adaptively. In addition the
frequency profile of foetal heart beat may be adjusted
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