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Year : 2020  |  Volume : 7  |  Issue : 3  |  Page : 141-147

Role of harmonics and subharmonics in peripheral pulse analysis

1 Department of Bio-Medical Engineering, MGM College of Engineering and Technology, Navi Mumbai, Maharashtra, India
2 Department of Bio-Technology, MGM Institute of Health Sciences, Navi Mumbai, Maharashtra, India
3 Department of Medicine, MGM Institute of Health Sciences, Navi Mumbai, Maharashtra, India

Date of Submission16-May-2020
Date of Acceptance25-May-2020
Date of Web Publication18-Aug-2020

Correspondence Address:
Dr. G D Jindal
Department of Bio-Medical Engineering, MGM College of Engineering and Technology, Kamothe, Navi Mumbai, Maharashtra.
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/mgmj.mgmj_47_20

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Elastic compliance of the blood vessels contributes high-frequency components in the peripheral pulse, which are analyzed with the help of the power spectral density of the signal. The frequency corresponding to heart rate in a subject is called his fundamental harmonic or first harmonic, frequency twice the heart rate is called second harmonic, and so on. The contribution of these harmonics is assessed by performing Fourier transform on the peripheral blood volume or flow pulse signal for sufficient duration, which yields power spectral density of the peripheral pulse. Dedicated software, known as pulse harmonic analyzer, has also been developed for performing harmonic analysis of the peripheral signal. It not only yields a contribution of higher harmonics in the pulse but also subharmonics (frequencies smaller than the heart rate of the subject). Researchers have observed suppression of second harmonics in subjects aging more than 30 years, suppression of high-frequency components in the power spectral density of the pulse in the coronary artery disease and enhancement of the first harmonic in hypertensives and subjects susceptible to diabetes during the past four decades. Subharmonic components are observed to be related to variability in heart rate, pulse volume, and pulse morphology, which has the potential to become a method of choice for continuous real-time variability monitoring in intensive care units. These observations are reviewed in this paper briefly.

Keywords: Harmonic analysis, heart rate variability, peripheral pulse, subharmonics

How to cite this article:
Jindal G D, Bhat SN, Sawant MS, Deshpande AK. Role of harmonics and subharmonics in peripheral pulse analysis. MGM J Med Sci 2020;7:141-7

How to cite this URL:
Jindal G D, Bhat SN, Sawant MS, Deshpande AK. Role of harmonics and subharmonics in peripheral pulse analysis. MGM J Med Sci [serial online] 2020 [cited 2020 Sep 28];7:141-7. Available from: http://www.mgmjms.com/text.asp?2020/7/3/141/292376

  Introduction Top

Plethysmography is the noninvasive recording of the instantaneous volume of an object. It is a commonly used method for recording blood volume changes in any part of the body without causing any harm or discomfort to the patient. Although several plethysmographic methods exist for specific applications, electrical impedance, or photo,[1],[2] plethysmography is routinely used for blood volume investigations in any part of the body. This is because of the electrical and optical properties of the blood, which vary from individual to individual depending on his hemoglobin concentration. Photo plethysmograph (PPG) can record blood volume changes in the fingers, toes, or earlobes, and impedance plethysmograph (IPG) can record the same in the rest of the body. PPG is an established method for continuous noninvasive monitoring of oxygen saturation in the blood in critical patients in the intensive care units.

Electrical IPG takes into cognizance the electrical resistivity of the blood. Since blood is a good conductor of electricity as compared to the remaining constituents of the limbs such as bone, muscle, fat, and skin, the amount of blood in any part of the body is inversely proportional to the electrical impedance offered by the body segment. Therefore, pulsatile blood volume changes in the limb segment caused by the rhythmic contraction of the heart can be recorded as pulsatile impedance changes. A large volume of work has been done on this technique by a large number of researchers around the globe and it is still a method of choice for continuous monitoring of cardiac output noninvasively. PPG, based on the optical properties of the blood, is an ideal choice for the measurement of blood flow at terminal points (fingers, toes, or ear-lobe) and it does not require electrical contact between the patient and instrument.

The peripheral pulse detected by IPG or PPG starts with a steep rise consequent to cardiac ejection, reaching the summit at peak systole, then descending gradually characterized by a notch (the dicrotic notch) in the middle of descent and finally reaching the baseline asymmetrically till the next cardiac ejection. The notch is observed to be reduced with the advancement in age. The peripheral pulse closely resembles the shape of an arterial pressure wave recorded with a catheter.

The shape of the peripheral pulse depends on the thickness of blood vessels, contractility of the heart, and vascular smooth muscle in the vessel wall. Therefore, the condition of the blood vessel can be assessed from the morphology of the peripheral pulse. [Figure 1] shows three different types of arterial pulses recorded from the fingers or toes in a variety of conditions. A physiologically normal pulse has a fast slope, small crest, fast return to the baseline during systole, and slow return to the baseline during diastole as shown in (A). Invariably, a notch is present in the down slope of the pulse separating the systole and the diastole. In the case of arterial occlusion, the crest is delayed and rounded and the return to the baseline is also slow as shown in (B). In case of insufficient arterial perfusion the pulse wave has a fast slope, small crest, and fast return to the baseline throughout as shown in (C).
Figure 1: Morphology of the PPG pulse (A) in a normal subject, (B) in a patient with arterial occlusion, and (C) in a subject with generalized atherosclerosis. The normal pulse is characterized by fast rise, round crest, and a slow return to the baseline as shown in (A). In the case of arterial occlusion, the rise is slow, and the crest is round and broad with a slow return to the baseline as shown in (B). In the case of deficient arterial perfusion pressure, the rise of the pulse is sharp, crest in rounded and small, and a fast return to the baseline as shown in (C).

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Fading of the dicrotic notch in pathological conditions can be identified either by direct observation as is usually done for electrocardiograms or electroencephalograms or by HARMONIC analysis. In general, for a pulse rate of 72 per minute (frequency 1.2 Hz), 2.4, 3.6, 4.8, and 6.0 are called second harmonic, third harmonic, fourth harmonic, fifth harmonic, and so on. Frequency 1.2 Hz, in this case, is called first or fundamental harmonic. In the harmonic analysis, the general contribution of these harmonic frequencies is obtained by Fourier transform (FT) and is represented as power spectral density (PSD). Diminution of the dicrotic notch can be quantitatively appreciated by a decrease in the power of the second harmonic.

Like higher harmonics, for a sufficiently long signal (around 300s) the contribution is observed in frequencies smaller than 0.5 Hz. These are called subharmonics. Jindal et al.[3] have attributed these subharmonics to variability of the signal, probably caused by the autonomic nervous system (ANS), renin-angiotensin system or baroreceptor reflex.

Sherebrin and Sherebrin[4] have performed a harmonic analysis of peripheral pulses in age-stratified data. They formed three age groups of 10–29, 30–59, and 60–89 years based on their previous observation that there was a marked decrease in extensibility in the human aorta above the age of 30 years and further minimal change beyond 60 years. The PSD of second to sixth harmonics has shown a considerable decrease in the power of second and sixth harmonics at P < 0.05. Similarly, Jindal et al.[5] have performed short-term Fourier transform (STFT) of peripheral pulses obtained using IPG and have shown a marked difference in the PSD obtained in a patient with coronary artery disease (CAD) in comparison to that of a normal subject. It was observed that high-frequency (HF) components were suppressed by nearly two-thirds in CAD. Similar dominance of lower harmonics in the pressure waveform was observed by O’Rourke and Winter[6] in elderly subjects and attributed to aortic impedance change with aging. Wang et al.[7] have attributed higher harmonics of the peripheral pulse to the heart, liver, kidney, spleen, and lungs in serial order. Wan-An Lu[8] has reported the importance of each harmonic in the pulse spectrum having physiological and pathological relevance in the circulation.

In view of the above, Jindal et al.[9] developed a software application called pulse harmonic analyzer (PHA), which could read the prerecorded peripheral pulse data, obtain its PSD, identify different harmonics, compute various parameters of the harmonics, display PSD and numerical parameters on the screen, and transfer the computed parameters to an Excel sheet. Offspring of diabetic patients, at high risk of acquiring Type II diabetes having nearly 25% probability per diabetic parent, were compared against control subjects using PHA.[3] All these applications of pulse harmonic analysis are briefly reviewed in this paper.

  Manifestation of aging on harmonics Top

Sherebrin and Sherebrin[4] used two 935-nm light-emitting diodes (LEDs) separated by 12mm with a phototransistor at their center and placed the assembly in the middle of third phalanx of the index finger of the subject. Energizing LEDs, phototransistor output is recorded after passing through a bandpass filter (single-pole multiple feedback) with a center frequency of 1 Hz and a Q of 0.05 in order to have baseline stability and a minimum attenuation of signal components in the range between 0.1 and 10 Hz. The waveform is displayed on a chart recorder. The output signal was also digitized and fast Fourier transform (FFT) was performed to get the frequency spectrum of the peripheral pulse and displayed on the computer monitor.

They collected data on 54 subjects excluding those with cardiovascular sickness and those taking related medication. They stratified the data into three age groups: 10–29, 30–59, and 60–89 years named as young (Y), middle (M), and elder (E) age group, respectively. [Table 1] gives the relative mean power of second to sixth harmonic with respect to first harmonic for all the three groups and also the probability value of statistically insignificant difference at 95% confidence level in three mutual comparisons (P < 0.05 shows a statistically significant difference between the two groups). Significant differences were observed between Y–M and Y–E groups for second harmonics and between M–E for sixth harmonic relative mean power. The elder age group shows little additional worsening than the middle age group. The difference in the shape of the peripheral pulse wave and the disappearance of the dicrotic notch with age has also been observed by them, which is caused by reduced wave reflection. The notch is a striking feature that has changed with age.
Table 1: Harmonic analysis of age-stratified groups

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Thus, their study concluded with a sharp decline in the relative power of the second harmonic and fading of the dicrotic notch with age.


Jindal et al.[1] have recorded peripheral pulse at the right wrist using peripheral pulse analyzer (PPA) based on principle of IPG. It comprises an electrical impedance measuring unit interfaced to a laptop personal computer (PC). With the subject in supine the carrier electrodes are applied around the elbow and palm in the right hand and sensing electrodes are applied 3–4cm apart around the proximal and distal part of the wrist. Rate of change of electrical impedance (dZ/dt), which indirectly gives rate of change of blood volume in the limb segment bound by sensing electrodes, is recorded for a period of 300s using biosignal acquisition system (BAS) software built in PPA system. The digital data (sampling rate 500 per second) are saved in the system for further processing and analysis.

Analysis is carried out using variability analyzer (VARANA) software resident in PPA system. The data file is loaded, opened, and processed for peak detection. For a given peak, 511 samples on the left side and 512 samples on the right side of the peak are given as input for short-term FFT after passing through Hanning window. FFT of these 1024 data samples is computed and PSD is displayed in one of the graphic panels of the system. Based on sampling rate these 1024 Fourier coefficients correspond to 500 Hz. Therefore, first harmonic is expected between second and third Fourier coefficient. The morphology index (MI) is then computed from the FFT data using following formula:

where PSD (i) is the sum of squares of real and imaginary Fourier coefficient as obtained from FFT. The first two coefficients are ignored as they have high values due to the DC component in the signal.

[Figure 2] shows the output of this algorithm in terms of peripheral pulses and their short-term FFT. Only 32 coefficients are shown for the purpose of clarity. (A) and (B) show a peripheral pulse and its PSD in a control subject and similarly (C) and (D) in a patient with CAD after angioplasty. In control subjects, the value of MI is observed to be around 0.9 and in subjects with CAD the same is observed to be in the range of 0.3 to 0.5 due to dominance of lower frequency components as evident from the figure. In this case, there is an overall reduction in the HF components rather than just second or sixth harmonic as observed in manifestations of aging.{Figure 2}

  Development of pulse harmonic analyser software and clinical application Top

In view of the above observations, application software called PHA has been developed.[9][Figure 3] shows the graphical user interface (GUI) panel for the same. One can load the prerecorded DAT FILE or TEXT FILE by clicking on the buttons provided by the button pellet in the bottom right corner. Peripheral pulse waveform can be seen in the top panel in the window. One can scan through the whole file with the help of “Pan” buttons (left and right; provided near right top corner). The facility is provided for changing the sampling rate, if required, from the combo-box near the top right corner. A click on the PROCESS button displays the PSD of the data in two windows provided in the middle of the screen. The small window on the left displays PSD up to a frequency of 0.5 Hz and that on the right displays PSD up to 10 Hz, called ANS spectrum and power spectrum, respectively. To obtain a smooth spectrum, the average value of all the input samples is first subtracted from the individual sample values in the entire data and then routed through a Hanning window. Fourier coefficients corresponding to 0.0 Hz are forced to zero for meaningful display. From the spectral data, peaks pertaining to first and other harmonics are detected and parameters (frequency of the peak [Freq], the amplitude of the peak [Peak], normalized amplitude of the peak [nPeak], power of the peak [Power], normalized power of the peak [nPower], and width of the peak [Width]) are computed and displayed in the Harmonic Table (bottom left corner of the GUI). Very low frequency (VLF), low frequency (LF), and HF pertaining to ANS spectrum[10] have usual ranges of frequencies, that is, 0.005–0.04 Hz, 0.041–0.15 Hz, and 0.151–0.5 Hz, respectively; their parameters are also displayed in the Harmonic Table. Few values namely Blood Flow Mean, MI Mean, Total Power, and Total Variability are displayed in the mid-bottom of GUI. Peak amplitude and power are in arbitrary units since their absolute values are very low (empirically multiplied by 10,000). The analysis can be saved in an Excel sheet by a click on SAVE button.
Figure 3: Graphical user interface (GUI) panel for the pulse harmonic analyzer system. The top row shows the raw peripheral pulse and PAN buttons provided by its side. The middle row shows the ANS spectrum and power spectrum of the peripheral pulse. The bottom row shows a computed harmonic table, mean parameters and function select buttons (at right corner). One can load the prerecorded DAT FILE or BATCH of files by clicking on respective buttons, process a loaded file, and save the output data in an excel sheet.

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This software has been used to perform pulse harmonic analysis of prerecorded PPA data[3] from control subjects, hypertensive patients, and offspring of patients with type II diabetes. The latter, being the progeny of diabetic parents, were considered at high risk of acquiring diabetes[11] and were called as diabetes susceptible (DS) subjects. These subjects did not have any notable cardiovascular or endocrinological complaints and were as good as control subjects except for parental history of type II diabetes. [Table 2] gives the mean and SD values computed from the average value in each subject for 15 of the PHA parameters. In addition to mean and standard deviation (SD) values, Student’s t and deviation in units of SD (of controls) are given for the two target groups in the same table. As can be seen from the table, 12 and 11 parameters are significantly different at a 5% significance level by Student’s t for hypertensive and DS group, respectively. Of these, four parameters in hypertensive group (1H_nPeak, 1H_nPower, 2H_nPeak, and 5H_Width) and one parameter in the DS group (1H_nPeak) have shown that the mean value in the target group is at least 2 SD away from the control mean. Statistically, the significance of these parameters is higher in the target groups with respect to the control group due to the lower value of type-II error β.
Table 2: PHA parameters in control and diseased subjects

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As described above, 13 parameters in the hypertensive group and 11 of 15 in the DS group are significantly different (α< 0.05 and β < 27%) as compared to those in control subjects. However, mean values are two or more SD away from the control mean in four and one parameters in hypertensive in DS group, respectively, yielding a negligible value of type-II error β. The sensitivity of PHA parameters is thus evident from results. 1H_npeak can thus be used to screen subjects prone to diabetes due to parental history of type II diabetes, provided other PHA parameters are within 2 SD of control value.

In the past, Chang et al.[12] have described the development of noninvasive harmonic wave analyzers for blood pressure pulses and established inter and intraobserver reliability of harmonic analysis. Although the majority[4],[6-8] of the work reported on pulse harmonic analysis is on the determination of aging effect and cardiovascular risk, some researchers have shown pulse harmonic analysis to be useful in the determination of arterial elasticity caused by arteriosclerosis or diabetes[13] and also for monitoring benefits derived from corrective therapy.

The main difference between the studies of Sherebrin and Sherebrin[4] and Jindal et al.[3] is that the former shows decrease in power of second harmonic due to aging and the latter shows increase in peak/power of first harmonic in hypertensive and DS subjects. This difference is probably caused by the fact that Sherebrin and Sherebrin[4] have normalized PSD with respect to the power of first harmonic and Jindal et al.[9] have normalized PSD with respect to total power. This may require standardization for consistency in pulse harmonic analysis in a manner similar to that introduced for heart rate variability.


Another important observation pulse harmonic analysis has shown is the presence of low-frequency subharmonics[3] in the frequency range from 0.005 to 0.5 Hz. These small peaks are in the frequency band of physiological variability and are therefore displayed separately on an amplified scale termed as ANS spectrum on the left side of the power spectrum. Their values are also derived with respect to the total power in this frequency band. Age, gender, and disease (hypertension) stratified PPA data with significant observations[14],[15] (shown in the second column of [Table 3]) have been reanalyzed using PHA software. Significantly different parameters by analysis of variance (ANOVA) and Tukey’s test are shown in the third column of [Table 3]. As can be seen from the table, very low frequency peak and power of PHA match with those of peripheral blood flow variability (PBFV). Similarly, high frequency peak of PHA matches with that of PBFV. Thus, PBFV has direct relevance with VLF, LF, and HF peak/power of PHA. It is significant to mention that none of the PPA parameters could differentiate between male controls and hypertensives in the higher age group (>30); HF peak of PHA has shown a significant difference; this gives an edge to PHA sub-harmonic analysis.
Table 3: Significantly different PPA and PHA parameters in controls and hypertensive groups excluding those showing age and gender dependency

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This close relationship between PPA and PHA offers new avenues of research and applications. Presently for PPA analysis, considerable manual time is to be spent during processing as the peaks detected by the system have to be screened for their correctness. If peaks are wrongly detected, they need to be edited manually by an experienced person as per task force recommendation.[10] Subharmonics observed in PHA, which is a truly automatic process without human intervention can be correlated to PPA parameters. It is expected that the correlation coefficient may not be very high as the PPA processing removes unnecessary noise from the data, whereas PHA data are not processed for noise. In such a case, peripheral pulse raw signal can be denoised using wavelet transformation before PHA analysis. Higher values of correlation coefficients, thus obtained, can do away with PPA manual processing and allow PHA subharmonics to be used in place. This will lead to the use of PPA and PHA for continuous monitoring in intensive care units.


Authors are grateful to Board of Research in Nuclear Sciences, Department of Atomic Energy, Government of India for their support to various research projects related to this subject, to Shri Rajesh Kumar Jain and Shri Vineet Sinha from Electronics Division, Bhabha Atomic Research Centre (BARC), for being Principal Collaborators to these research projects and to Dr. Geeta Lathkar, Director, MGM College of Engineering and Technology (MGMCET), Navi Mumbai, India for her encouragement and support. The authors thank all their colleagues from Electronics Division, BARC, and Department of Biomedical Engineering, MGMCET, Mumbai, India for all kinds of help.

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.

  References Top

Jindal GD, Sawant MS, Jain RK, Sinha V, Bhat SN, Deshpande AK Seventy five years of impedance plethysmography in physiological data acquisition and medical diagnostics. MGM J Med Sci 2016;3: 84-90.  Back to cited text no. 1
Jindal GD, Lakhe AS, Jethe JV, Mandlik SA, Jain RK, Sinha V, Deshpande AK: Photoplethysmography and its clinical applications. MGM J Med Sci 2017;4:89-96.  Back to cited text no. 2
Jindal GD, Jain RK, Bhat SN, Pande JA, Sawant MS, Jindal SK, et al. Harmonic analysis of peripheral pulse for screening subjects at high risk of diabetes. J Med Eng Technol 2017;41:437-43.  Back to cited text no. 3
Sherebrin MH, Sherebrin RZ Frequency analysis of the peripheral pulse wave detected in the finger with a photoplethysmograph. IEEE Trans Biomed Eng 1990;37:313-7.  Back to cited text no. 4
Jindal GD, Jain RK, Sinha V, Mandlik SA, Sarade B, Tanawade P, et al. Early detection of coronary heart disease using peripheral pulse analyzer. BARC Newslett 2012;326:15-21.  Back to cited text no. 5
O’Rourke M, Winter D Characterisation of aging effect and cardiovascular risk. Patent No. US 8 2013;435:184B2.  Back to cited text no. 6
Wang Y-YL, Hsu T-L, Jan M-Y, Wang W-K Theory and applications of the harmonic analysis of arterial pressure pulse waves. J Med Biol Eng 2010;30:125-31.  Back to cited text no. 7
Wan-An L Pulse spectrum analysis in primary hypertension patients. Taipei City Med J 2006;3:859-68.  Back to cited text no. 8
Jindal GD, Dube A, Bhat SN, Jain RK Development of software for harmonic analysis of peripheral pulse. Proceedings of the International Conference on Computing, Communication & Control Technology, held at Lucknow, 2016:58-61.  Back to cited text no. 9
Camm AJ, Malik M, Bigger JT Jr, Breithardt G, Cerutti S, Cohen RJ, et al. Heart rate variability: Standards of measurement, physiological interpretation and clinical use. Circulation 1996;93:1043-65.  Back to cited text no. 10
Meigs JB, Cupples LA, Wilson PW Parental transmission of type 2 diabetes: The Framingham offspring study. Diabetes 2000;49:2201-7.  Back to cited text no. 11
Chang CW, Chen JM, Wang WK Development of a standard protocol for the harmonic analysis of radial pulse wave and assessing its reliability in healthy humans. IEEE J Transl Eng Health Med 2015;3:2900206.  Back to cited text no. 12
Korpas D, Hálek J, Dolezal L Parameters describing the pulse wave. Physiol Res 2009;58:473-9.  Back to cited text no. 13
Sawant M, Jindal GD, Agarwal S, Deshpande AK Variability in peripheral blood flow and morphology index in controls and hypertensive subjects. Int JSci Res 2018;7:45-8.  Back to cited text no. 14
Sawant M, Jindal GD, Agarwal S, Deshpande AK Study of heart rate variability in control and hypertensive subjects. Indian J Physiol Pharmacol 2019;63:113-21.  Back to cited text no. 15


  [Figure 1], [Figure 3]

  [Table 1], [Table 2], [Table 3]


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