Research Article Fetal Heart Rate Monitoring from...

Research ArticleFetal Heart Rate Monitoring from Phonocardiograph SignalUsing Repetition Frequency of Heart Sounds

Hong Tang1 Ting Li2 Tianshuang Qiu1 and Yongwan Park3

1Department of Biomedical Engineering Dalian University of Technology Dalian China2College of Information and Communication Engineering Dalian Minzu University Dalian China3Department of Information and Communication Engineering Yeungnam University Gyeongsan Republic of Korea

Correspondence should be addressed to Hong Tang tanghongdluteducn

Received 1 July 2016 Revised 25 November 2016 Accepted 6 December 2016

Academic Editor Jit S Mandeep

Copyright copy 2016 Hong Tang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

As a passive harmless and low-cost diagnosis tool fetal heart rate (FHR) monitoring based on fetal phonocardiography (fPCG)signal is alternative to ultrasonographic cardiotocography Previous fPCG-based methods commonly relied on the time differenceof detected heart sound bursts However the performance is unavoidable to degrade due to missed heart sounds in very lowsignal-to-noise ratio environments This paper proposes a FHR monitoring method using repetition frequency of heart soundsThe proposed method can track time-varying heart rate without both heart sound burst identification and denoising The averageaccuracy rate comparison to benchmark is 883 as the SNR ranges from minus44 dB to minus267 dB

1 Introduction

As a well-being policy pregnant women in many countriesare periodically demanded to monitor the variations in fetalheart rate (FHR) This monitoring of FHR and its variabilityprovide up-to-date information about the fetus to preventintrauterine death or permanent damage to the fetus [1]Many techniques canmonitor fetal heart rate previously Fetalmagnetocardiography (fMCG) using superconducting quan-tum interference device allows accurate assessment of beat-to-beat fetal heart rate variability [2]However the equipmentof fMCG is too expensive to be widely accessed in primaryhospital Cardiotocography (CTG) is continuous monitoringof the fetal heart rate using an ultrasound transducer placedon the motherrsquos abdomen [3ndash5] Physicians evaluate specificclinical CTG parameters by means of visual inspectionHence the accuracy of CTGmonitoring is generally depend-ing on observerrsquos expertise Fetal electrocardiogram (fECG)signal taken from the abdominal electrocardiogram of preg-nant woman is another diagnostic tool for evaluating FHR[6] However the fECG signal is often masked by maternalECG power line interference maternal electromyogram andso forth Very complex algorithms are needed to separatethe fECG signal from mixed signal before further analysis

As a totally passive methodology fetal phonocardiography(fPCG) signal collected from motherrsquos abdomen using amicrophone transducer was proposed about ten years agoto monitor FHR [7] This new technique makes long-termand frequent measurements of FHR possible They detectedthe burst shaped heart sounds from signal envelope and esti-mated FHR via the time difference of heart sound occurrence[8ndash16] Consequently the accuracy of FHR estimation relieson heart sound detection rate The performance degradesgreatly if heart sounds are missed andor wrong heartsounds are detected Denoising technique is usually used aspreprocessing due to the low energy of fetal heart sounds andmultiple interferences [17]

It is known that fetal heart sounds are originated frominteraction between fetal heart and blood flow therein Thesounds are repetitive from one cardiac cycle to another FHRmonitoring is thus equal to tracking the local repetitionfrequency of heart sound in adjacent cardiac cycles Henceheart beat identification anddenoising are then not necessary

2 Methodology

21 Repetition Frequency Estimated by Cyclic Frequency Spec-trum In the field of signal processing theory repetition

Hindawi Publishing CorporationJournal of Electrical and Computer EngineeringVolume 2016 Article ID 2404267 6 pageshttpdxdoiorg10115520162404267

2 Journal of Electrical and Computer Engineering

frequency is usually characterized by cycle frequency Itmeans occurrence rate of a repetitive event in a period oftime For example the cycle frequency of fetal heart sounds is25Hz if they repeat every 04 seconds It is assumed that 119909(119905)is a virtual digital sequence of an fPCG signal with an exactcycle period 119879 The objective of FHR estimation is to extractthe cycle frequency of the fetal heart soundThe time-varyingautocorrelation is written as

119877119909 (119905 120591) ≜ lim119873rarrinfin

12119873 + 1

sdot119873

sum119899=minus119873

119909(119905 + 1205912 + 119899119879)119909lowast (119905 minus 120591

2 + 119899119879) (1)

where 119899 is cycle index 119879 is a real number denoting cycleperiod 120591 is time delay and 119873 determines the number ofcycles involved in analysis 119877119909(119905 120591)must be periodic becausefetal heart sounds are exactly cyclic It can be expanded intoFourier series

119877119909 (119905 120591) =+infin

sum120572=minusinfin

119877119909 (120572 120591) 1198901198952120587120572119905 (2)

where 120572 is a real number called cycle frequency The coeffi-cient of the Fourier series can be calculated by the following

119877119909 (120572 120591) = ⟨119909(119905 + 1205912) 119909 (119905 minus 120591

2) 1198901198952120587120572119905⟩119905 (3)

The operator ⟨sdot⟩119905 means the time average 119877119909(120572 120591) is calledcyclic correlation function It can be seen that it reduces tothe traditional correlation if the cycle frequency 120572 is fixed tozero 119877119909(120572 120591) can be transformed into frequency domain viaFourier transform

119878119909 (120572 119891) = intinfin

minusinfin119877119909 (120572 120591) 119890minus1198952120587119891120591119889120591 (4)

119878119909(120572 119891) is called cyclic spectral densityThephysicalmeaningof 119878119909(120572 119891) indicates that 119878119909(120572 119891) = 0 if the signal119909(119905) has anycyclic component at cycle frequency 120572 In the point of view offPCG signal 119878119909(120572 119891)must have a peak at heart rate becausethe heart sounds are dominant cyclic components at the heartrate in adjacent fetal cardiac cyclesTherefore detecting FHRis equal to detecting the basic cycle frequency of the digitalsequence The frequency spectrum is not of interest in thispaper An integral is performed to 119878119909(120572 119891) to remove thefrequency variable 119891 for the purpose of simplification

120574119909 (120572) = intinfin

infin

1003816100381610038161003816119878119909 (120572 119891)1003816100381610038161003816 119889119891 (5)

This is called cyclic frequency spectrum (CFS)Therefore theFHR is indicated by the dominant peak of 120574119909(120572)

Hr = arg max (120574119909 (120572)) times 60 (6)

where argsdot is the argument that meets the condition inthe brace and max(sdot) is the maximum operator A sharpand outstanding peak means a high degree of repetition ofheart sounds in the signal The normal FHR is commonly in[110160] bpm That is the cycle frequency in considerationis in [1827]Hz For extreme value the signals in this paperare analyzed in a greater range [1335]Hz These extremeheart rates are 80 bpm and 210 bpm which correspond tobradycardia and tachycardia respectively

To test the performance of CFS the well-known simu-lated fPCG signals proposed by Cesarelli et al [18 19] areusedThese simulated signals considered different fetal physi-ological and pathological conditions and recording situationsby simulation technique The noises considered consist ofvibrations created bymaternal body organs fetalmovementsand unwanted sounds from surrounding environmentThesesimulated signals have been openly published in PhysioNetfor freely public access and have been widely acceptedfor algorithm evaluation For example two segments of asimulated fPCG signal both have 6 s with sampling frequencyof 1 KHz where the true real-time heart rate is between140 bpm and 155 bpm seen in Figure 1There are noises whichsaturate the signal due to maternal fast body movementsacoustic sensor displacements andor high magnitude exter-nal noises CFS analysis is applied to the signal Figure 1(a)shows the low noise part of the fPCG signal in time domainFigure 1(b) shows the CFS of the signal It can be found thatthe dominant peak occurs at the cycle frequency of 235Hzthat is the FHR of this segment is 235 lowast 60 = 141 bpmFigure 1(c) shows the heavy noise part of the signal Thesignal is so heavily contaminated by noises that the heart beatscannot be identified by human visual inspection Figure 1(d)shows that the CFS still has an outstanding prominent peakas if the noise has no effect on the peak The peak is locatedat 251Hz (151 bpm) The example illustrates that CFS canindicate the repetition frequency of the heart sounds in thissegment CFS analysis takes the segment as an integral inputHence heart sound detection that is essential in previousmethods becomes not necessary in the proposedmethodThenoise is generally random and does not have any repetitionfeature So the dominant peak of CFSwill not be affected eventhe noise is so heavy to saturate the amplitude as the examplegiven in Figure 1(c)

It should be noted that the heart sounds are not perfectlyperiodic due to the heart rate variability (HRV) So theheart sounds are quasi-periodic The degree of the periodicproperty can be reflected by the sharpness of the peak Thatis the more periodic the heart sounds become the sharperthe dominant peak will be In the extreme case if the heartsounds having ultimate recording time are perfectly periodicthe CFS will have only one nonzero magnitude at the cyclefrequency On the contrary if the heart rate varies muchthe degree of periodic property of the heart sounds reducesgreatly then the peak of the CFS will become flat In anotherextreme case the heart sounds appear randomly then theCFS will not have any dominant peak In this sense therepetition frequency of heart sounds reflects the averagefrequency of heart rate So the repetition frequency can beused as a metric of fetal heart rate

Journal of Electrical and Computer Engineering 3

2 4 60Time (s)

minus5

0

5A

mpl

itude

(mV

)

(a)

2 25 3 3515Cycle frequency (Hz)

0

05

1

Nor

mal

ized

ampl

itude

(b)

minus2

minus1

0

1

2

Am

plitu

de (m

V)

2 4 60Time (s)

(c)


0

05

1

Nor

mal

ized

ampl

itude

(d)

Figure 1 Fetal heart rate detection for an fPCG signal (a) A low noise fPCG signal (b) CFS analysis Cycle frequency indicated by thedominant peak is 235Hz (141 bpm) (c) A heavy noise fPCG signal (d) CFS analysis Cycle frequency indicated by the dominant peak is251Hz (151 bpm)

Table 1 Summary of the tests

Record number SNR (dB) Heart rate variation (bpm) Accuracy rate1 minus44 108ndash159 9232 minus66 108ndash159 9193 minus81 108ndash156 9014 minus102 108ndash159 8915 minus148 108ndash168 8976 minus172 108ndash156 9017 minus201 108ndash177 8858 minus238 111ndash153 8889 minus256 111ndash168 82010 minus267 108ndash168 810Note the accuracy rate is defined in (9)

22 Time-Varying Estimation Using SlidingWindow To tracktime-varying FHR a sliding window covering the fPCGsignal is used Therefore (5) becomes time-dependent

120574119909 (120572 119905) = intinfin

infin

1003816100381610038161003816119878119909 (120572 119891 119905)1003816100381610038161003816 119889119891 (7)

where 119878119909(120572 119891 119905) is a cyclic spectral density over a timewindow [119905 minus 120577 119905 + 120577] So 120574119909(120572 119905) can be called time-varyingcyclic spectrumThe width of the sliding window is 2120577 Fromthe repetition feature of heart sound it can be concludedthat the width of the sliding window must be greater thantwo cardiac cycles to ensure that the fetal heart beats at least


minus4

minus2

0

2

4A

mpl

itude

(mV

)

50 100 150 200 250 300 350 400 4500Time (s)

(a)

50 100 150 200 250 300 350 400 4500Time (s)

80100120140160

Hea

rt ra

te (b

pm)

(b)

Figure 2 Time-varying fetal heart rate monitoring (a) An fPCG signal with saturated noise (b) Detected time-varying fetal heart rate

two times in the window Otherwise there is no repetitionfeature in the windowed signal The time-varying FHR canbe tracked by searching the peak in 120574119909(120572 119905)

Hr (119905) = arg max (120574119909 (120572 119905)) times 60 (8)

So the instantaneous FHR can be detected by the peaklocation of the time-varying cyclic frequency spectrum

An fPCG signal is 478 s in time length as seen in Fig-ure 2(a) The signal is contaminated by saturated noise Theestimated SNR isminus157 dB A sliding windowwith width of 8 sand overlap of 01 s is applied to the signalThe detected time-varying FHR is shown by the black solid line in Figure 2(b)The tracking trajectory accurately reflects the FHR variationsAccelerations and decelerations are clearly observed in thetrajectory

3 Experiments

31 Time Resolution and Cycle Frequency Resolution Thepri-mary purpose of the sliding window is to limit the extentof the subsequence to be analyzed so that the cyclic charac-teristics are approximately constant over the duration of thewindow The more rapidly the repetition frequency changesthe shorter the window should be So it is reasonable toconclude that as the window length becomes longer thepeak will become sharper that is the repetition frequencyresolution increases On the other hand as thewindow lengthdecreases the ability to resolve changes with time increasesConsequently the choice of window length becomes a trade-off between repetition frequency resolution and time resolu-tion With the preknowledge of the change rate of FHR thewindow length can be empirically selected as 5ndash10 s to obtainan acceptable trade-off

32 Performance of Fetal Heart Rate Monitoring Using theRepetition Frequency To evaluate the proposed methodit is necessary to test the performance under controlledconditions This is achieved by the simulated fPCG signals[18 19] Each signal lasts 478 s These signals considereddifferent fetal physiological and pathological conditions andrecording situations by simulation technique The noiseconsidered consists of vibrations created by maternal bodyorgans fetal movements unwanted sounds from surround-ing environment and so forthThe SNR ranges from minus44 dBto minus267 dB Visual check by human eyes shows that fetalheart sounds cannot be recognized as the SNR is lower than

minus15 dB The FHR in each signal is tracked by the proposedmethod If the difference between the detected heart rate andthe benchmark is within plusmn5 bpm the detected heart rate isconsidered accurate The accuracy rate is defined as

accuracy rate

= number of beats within difference ⩽ 5 bpmtotal number of beats

(9)

A summary of the tests is presented in Table 1 It can be foundthat the proposed method can accurately track the fetal heartrate even the SNR is lowered to minus267 dB where the heartsounds are totally covered by the noiseThe key point why theproposedmethod is so robust to noise is because it detects therepetition frequency of heart sounds instead of detecting thetime difference of heart sounds

33 Performance Comparison to the Previous Methods Twotypical previous methods are selected to be compared to theproposed method in this subsection One is a rule-basedmethod proposed by Kovacs et al [16] where the FHR wasevaluated by searching S1-S2 pairs The other method is anadvanced method proposed by Varady et al [14] where theFHR was estimated by the periodicity of heart sound burstsfrom cross-correlation of signal envelope Both methodsneed detection of the fetal heart sound burst Hence theperformance of the two methods is heavily dependent on thedetection accuracy of fetal heart sound burst Ten simulatedfPCG signals with SNR varying from minus44 dB to minus267 dBare used to evaluate the three methods and the results aregiven in Table 2 It is found that the rule-based methodand the advanced method outperform the proposed methodin low noise environments However both the rule-basedand the advanced methods degrade greatly due to the fastincreasing of missing rate for sound burst detection withdecreasing SNR The proposed method does not need soundburst detection It is to estimate the repetition frequency ofheart sound which is less affected by random noise Hencethe FHR estimation is robust to noise even if the sound burstis destroyed by heavy noise because the repetition feature stillremains

4 Conclusions

fPCG is a promising technique to monitor fetal heart rateHowever the performance of previous methods generally


Table 2 Performance comparison

Record number SNR (dB) The proposed method Rule-based method[16]

Advanced method[14]

1 minus44 923 954 9622 minus66 919 954 9613 minus81 901 941 9634 minus102 891 903 9455 minus148 897 826 9046 minus172 901 608 8677 minus201 885 mdash 8248 minus238 888 mdash 6369 minus256 820 mdash mdash10 minus267 810 mdash mdashNote (a) the accuracy rate is defined in (9) (b) ldquomdashrdquo means that so many heart sound burst pairs were missed that the accuracy rate was very low

depends on the detection rate of heart sound bursts froman fPCG recording The authors find that the fetal heart ratecan be evaluated by the repetition frequency of heart soundswhich can be extracted from peaks in the cyclic frequencyspectrum without sound burst detection and denoising Thefeature of repetition can remain even if the SNR is loweredto minus267 dB As the SNR is lower than minus15 dB the proposedmethod outperforms the two typical previous methods

Competing Interests

The authors declare that there are no competing interests reg-arding the publication of this paper

Acknowledgments

This work was supported in part by the National Natural Sci-ence Foundation of China (Grant nos 61471081 and 61601081)and Fundamental Research Funds for the Central Univer-sities (Grant nos DUT15QY60 DUT16QY13 DC201501056and DCPY2016008)

References

[1] M Romano L Iuppariello A M Ponsiglione G Improta PBifulco andM Cesarelli ldquoFrequency and time domain analysisof foetal heart rate variability with traditional indexes a criticalsurveyrdquoComputational andMathematical Methods inMedicinevol 2016 Article ID 9585431 12 pages 2016

[2] R T Wakai ldquoAssessment of fetal neurodevelopment via fetalmagnetocardiographyrdquo Experimental Neurology vol 190 S1 pp65ndash71 2004

[3] R M Grivell Z Alfirevic G M Gyte and D Devane ldquoAnte-natal cardiotocography for fetal assessmentrdquo Cochrane Data-base of Systematic Reviews no 1 Article ID CD007863 2010

[4] H Cao D E Lake J E Ferguson C A Chisholm M P Gri-ffin and J R Moorman ldquoToward quantitative fetal heart ratemonitoringrdquo IEEE Transactions on Biomedical Engineering vol53 no 1 pp 111ndash118 2006

[5] M Romano M Bracale M Cesarelli et al ldquoAntepartum car-diotocography a study of fetal reactivity in frequency domainrdquo

Computers in Biology and Medicine vol 36 no 6 pp 619ndash6332006

[6] M Anisha S S Kumar and M Benisha ldquoMethodologicalsurvey on fetal ECG extractionrdquo Journal of Health amp MedicalInformatics vol 5 article 469 2014

[7] F Kovacs C Horvath A T Balogh and G Hosszu ldquoFetalphonocardiographymdashpast and future possibilitiesrdquo ComputerMethods and Programs in Biomedicine vol 104 no 1 pp 19ndash252011

[8] F Kovacs N Kersner K Kadar and G Hosszu ldquoComputermethod for perinatal screening of cardiac murmur using fetalphonocardiographyrdquo Computers in Biology and Medicine vol39 no 12 pp 1130ndash1136 2009

[9] F Kovacs C Horvath A T Balogh and G Hosszu ldquoExtendednoninvasive fetal monitoring by detailed analysis of data mea-sured with phonocardiographyrdquo IEEE Transactions on Biomed-ical Engineering vol 58 no 1 pp 64ndash70 2011

[10] V S Chourasia A K Tiwari and R Gangopadhyay ldquoTime-frequency characterization of fetal phonocardiographic signalsusing wavelet scalogramrdquo Journal of Mechanics in Medicine andBiology vol 11 no 2 pp 391ndash406 2011

[11] M Moghavvemi B H Tan and S Y Tan ldquoA non-invasive PC-based measurement of fetal phonocardiographyrdquo Sensors andActuators A Physical vol 107 no 1 pp 96ndash103 2003

[12] V S Chourasia A K Tiwari and R Gangopadhyay ldquoA novelapproach for phonocardiographic signals processing to makepossible fetal heart rate evaluationsrdquo Digital Signal ProcessingA Review Journal vol 30 pp 165ndash183 2014

[13] M Ruffo M Cesarelli M Romano P Bifulco and A FratinildquoAn algorithm for FHR estimation from foetal phonocardio-graphic signalsrdquo Biomedical Signal Processing and Control vol5 no 2 pp 131ndash141 2010

[14] P Varady L Wildt Z Benyo and A Hein ldquoAn advancedmethod in fetal phonocardiographyrdquo Computer Methods andPrograms in Biomedicine vol 71 no 3 pp 283ndash296 2003

[15] J Chen K Phua Y Song and L Shue ldquoA portable phonocar-diographic fetal heart rate monitorrdquo in Proceedings of the IEEEInternational Symposium on Circuits and Systems (ISCAS rsquo06)May 2006

[16] F Kovacs M Torok and I Habermajer ldquoA rule-based phono-cardiographic method for long-term fetal heart rate monitor-ingrdquo IEEE Transactions on Biomedical Engineering vol 47 no1 pp 124ndash130 2000


[17] S Vaisman S Yaniv Salem G Holcberg and A B Geva ldquoPas-sive fetal monitoring by adaptive wavelet denoising methodrdquoComputers in Biology and Medicine vol 42 no 2 pp 171ndash1792012

[18] M Cesarelli M Ruffo M Romano and P Bifulco ldquoSimulationof foetal phonocardiographic recordings for testing of FHRextraction algorithmsrdquo Computer Methods and Programs inBiomedicine vol 107 no 3 pp 513ndash523 2012

[19] Simulated fetal PCGs July 2015 httpwwwphysionetorgphy-siobankdatabasesimfpcgdb

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Propagation




Navigation and Observation



DistributedSensor Networks



frequency is usually characterized by cycle frequency Itmeans occurrence rate of a repetitive event in a period oftime For example the cycle frequency of fetal heart sounds is25Hz if they repeat every 04 seconds It is assumed that 119909(119905)is a virtual digital sequence of an fPCG signal with an exactcycle period 119879 The objective of FHR estimation is to extractthe cycle frequency of the fetal heart soundThe time-varyingautocorrelation is written as

119877119909 (119905 120591) ≜ lim119873rarrinfin

12119873 + 1

sdot119873

sum119899=minus119873

119909(119905 + 1205912 + 119899119879)119909lowast (119905 minus 120591

2 + 119899119879) (1)

where 119899 is cycle index 119879 is a real number denoting cycleperiod 120591 is time delay and 119873 determines the number ofcycles involved in analysis 119877119909(119905 120591)must be periodic becausefetal heart sounds are exactly cyclic It can be expanded intoFourier series

119877119909 (119905 120591) =+infin

sum120572=minusinfin

119877119909 (120572 120591) 1198901198952120587120572119905 (2)

where 120572 is a real number called cycle frequency The coeffi-cient of the Fourier series can be calculated by the following

119877119909 (120572 120591) = ⟨119909(119905 + 1205912) 119909 (119905 minus 120591

2) 1198901198952120587120572119905⟩119905 (3)

The operator ⟨sdot⟩119905 means the time average 119877119909(120572 120591) is calledcyclic correlation function It can be seen that it reduces tothe traditional correlation if the cycle frequency 120572 is fixed tozero 119877119909(120572 120591) can be transformed into frequency domain viaFourier transform

119878119909 (120572 119891) = intinfin

minusinfin119877119909 (120572 120591) 119890minus1198952120587119891120591119889120591 (4)

119878119909(120572 119891) is called cyclic spectral densityThephysicalmeaningof 119878119909(120572 119891) indicates that 119878119909(120572 119891) = 0 if the signal119909(119905) has anycyclic component at cycle frequency 120572 In the point of view offPCG signal 119878119909(120572 119891)must have a peak at heart rate becausethe heart sounds are dominant cyclic components at the heartrate in adjacent fetal cardiac cyclesTherefore detecting FHRis equal to detecting the basic cycle frequency of the digitalsequence The frequency spectrum is not of interest in thispaper An integral is performed to 119878119909(120572 119891) to remove thefrequency variable 119891 for the purpose of simplification

120574119909 (120572) = intinfin

infin

1003816100381610038161003816119878119909 (120572 119891)1003816100381610038161003816 119889119891 (5)

This is called cyclic frequency spectrum (CFS)Therefore theFHR is indicated by the dominant peak of 120574119909(120572)

Hr = arg max (120574119909 (120572)) times 60 (6)

where argsdot is the argument that meets the condition inthe brace and max(sdot) is the maximum operator A sharpand outstanding peak means a high degree of repetition ofheart sounds in the signal The normal FHR is commonly in[110160] bpm That is the cycle frequency in considerationis in [1827]Hz For extreme value the signals in this paperare analyzed in a greater range [1335]Hz These extremeheart rates are 80 bpm and 210 bpm which correspond tobradycardia and tachycardia respectively

To test the performance of CFS the well-known simu-lated fPCG signals proposed by Cesarelli et al [18 19] areusedThese simulated signals considered different fetal physi-ological and pathological conditions and recording situationsby simulation technique The noises considered consist ofvibrations created bymaternal body organs fetalmovementsand unwanted sounds from surrounding environmentThesesimulated signals have been openly published in PhysioNetfor freely public access and have been widely acceptedfor algorithm evaluation For example two segments of asimulated fPCG signal both have 6 s with sampling frequencyof 1 KHz where the true real-time heart rate is between140 bpm and 155 bpm seen in Figure 1There are noises whichsaturate the signal due to maternal fast body movementsacoustic sensor displacements andor high magnitude exter-nal noises CFS analysis is applied to the signal Figure 1(a)shows the low noise part of the fPCG signal in time domainFigure 1(b) shows the CFS of the signal It can be found thatthe dominant peak occurs at the cycle frequency of 235Hzthat is the FHR of this segment is 235 lowast 60 = 141 bpmFigure 1(c) shows the heavy noise part of the signal Thesignal is so heavily contaminated by noises that the heart beatscannot be identified by human visual inspection Figure 1(d)shows that the CFS still has an outstanding prominent peakas if the noise has no effect on the peak The peak is locatedat 251Hz (151 bpm) The example illustrates that CFS canindicate the repetition frequency of the heart sounds in thissegment CFS analysis takes the segment as an integral inputHence heart sound detection that is essential in previousmethods becomes not necessary in the proposedmethodThenoise is generally random and does not have any repetitionfeature So the dominant peak of CFSwill not be affected eventhe noise is so heavy to saturate the amplitude as the examplegiven in Figure 1(c)

It should be noted that the heart sounds are not perfectlyperiodic due to the heart rate variability (HRV) So theheart sounds are quasi-periodic The degree of the periodicproperty can be reflected by the sharpness of the peak Thatis the more periodic the heart sounds become the sharperthe dominant peak will be In the extreme case if the heartsounds having ultimate recording time are perfectly periodicthe CFS will have only one nonzero magnitude at the cyclefrequency On the contrary if the heart rate varies muchthe degree of periodic property of the heart sounds reducesgreatly then the peak of the CFS will become flat In anotherextreme case the heart sounds appear randomly then theCFS will not have any dominant peak In this sense therepetition frequency of heart sounds reflects the averagefrequency of heart rate So the repetition frequency can beused as a metric of fetal heart rate


2 4 60Time (s)

minus5

0

5A

mpl

itude

(mV

)

(a)


0

05

1

Nor

mal

ized

ampl

itude

(b)

minus2

minus1

0

1

2

Am

plitu

de (m

V)

2 4 60Time (s)

(c)


0

05

1

Nor

mal

ized

ampl

itude

(d)





120574119909 (120572 119905) = intinfin

infin

1003816100381610038161003816119878119909 (120572 119891 119905)1003816100381610038161003816 119889119891 (7)



minus4

minus2

0

2

4A

mpl

itude

(mV

)

50 100 150 200 250 300 350 400 4500Time (s)

(a)

50 100 150 200 250 300 350 400 4500Time (s)

80100120140160

Hea

rt ra

te (b

pm)

(b)



Hr (119905) = arg max (120574119909 (120572 119905)) times 60 (8)



3 Experiments




accuracy rate


(9)



4 Conclusions





Advanced method[14]



Competing Interests


Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










2 4 60Time (s)

minus5

0

5A

mpl

itude

(mV

)

(a)


0

05

1

Nor

mal

ized

ampl

itude

(b)

minus2

minus1

0

1

2

Am

plitu

de (m

V)

2 4 60Time (s)

(c)


0

05

1

Nor

mal

ized

ampl

itude

(d)





120574119909 (120572 119905) = intinfin

infin

1003816100381610038161003816119878119909 (120572 119891 119905)1003816100381610038161003816 119889119891 (7)



minus4

minus2

0

2

4A

mpl

itude

(mV

)

50 100 150 200 250 300 350 400 4500Time (s)

(a)

50 100 150 200 250 300 350 400 4500Time (s)

80100120140160

Hea

rt ra

te (b

pm)

(b)



Hr (119905) = arg max (120574119909 (120572 119905)) times 60 (8)



3 Experiments




accuracy rate


(9)



4 Conclusions





Advanced method[14]



Competing Interests


Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus4

minus2

0

2

4A

mpl

itude

(mV

)

50 100 150 200 250 300 350 400 4500Time (s)

(a)

50 100 150 200 250 300 350 400 4500Time (s)

80100120140160

Hea

rt ra

te (b

pm)

(b)



Hr (119905) = arg max (120574119909 (120572 119905)) times 60 (8)



3 Experiments




accuracy rate


(9)



4 Conclusions





Advanced method[14]



Competing Interests


Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Advanced method[14]



Competing Interests


Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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