LATAM Revista Latinoamericana de Ciencias Sociales y Humanidades, Asunción, Paraguay.
ISSN en línea: 2789-3855, noviembre, 2025, Volumen VI, Número 5 p 2415.

DOI: https://doi.org/10.56712/latam.v6i5.4749

Cardiac pulse detection by a pulse train using the
synchronous demodulation technique

Detección del pulso cardíaco mediante un tren de pulsos utilizando la
técnica de demodulación síncrona

Javier Yañez Mendiola1

jyanez@ciatec.mx
https://orcid.org/0000-0003-0772-5947

Ciatec A.C.
León Gto. – México

Roxana Zaricell Bautista López

thaleth0.0@gmail.com
https://orcid.org/0000-0002-3180-8825

Universidad Virtual de Guanajuato
León Gto. – México

José Martin López Vela

lopez2martin@aim.com
https://orcid.org/0009-0000-6261-2473

Investigador Independiente
León Gto. – México

Artículo recibido: 12 de julio de 2025. Aceptado para publicación: 11 de noviembre de 2025.

Conflictos de Interés: Ninguno que declarar.

Abstract
Photoplethysmography is a widely studied noninvasive optical technique with great potential for
application in clinical medicine. There is evidence that the PPG signal can provide information about
heart rate, oxygen saturation in arterial blood, respiratory rate among other cardiovascular signs. The
two-wavelength photoplethysmographic signal is generally used to determine oxygen saturation in
arterial blood under the principle that oxygenated and deoxygenated hemoglobin differentially absorb
red and near-infrared wavelengths. In this work it is proposed to use the same wavelengths that are
used in the pulse oximetry technique (660 nm and 940 nm) to calculate heart rate; Heart rate recovery
is done by analyzing the data using the synchronous demodulation technique. The sampled data was
generated from measurement carried out on two people. The heart rate obtained with the pulse
oximetry technique in conjunction with the synchronous demodulation technique was corroborated
with the heart rate obtained using the PPG signal at a single wavelength (940 nm).

Keywords: cardiac pulse, photoplethysmography, sensor, synchronous demodulation

Resumen
La fotopletismografía es una técnica óptica no invasiva ampliamente estudiada con gran potencial de
aplicación en la medicina clínica. Existe evidencia de que la señal PPG puede proporcionar
información sobre la frecuencia cardíaca, la saturación de oxígeno en sangre arterial y la frecuencia
respiratoria, entre otros signos cardiovasculares. La señal fotopletismográfica de dos longitudes de

1 Autor de correspondencia.

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ISSN en línea: 2789-3855, noviembre, 2025, Volumen VI, Número 5 p 2416.

onda se utiliza generalmente para determinar la saturación de oxígeno en sangre arterial, según el
principio de que la hemoglobina oxigenada y desoxigenada absorben de forma diferencial las
longitudes de onda del rojo y del infrarrojo cercano. En este trabajo, se propone utilizar las mismas
longitudes de onda que se emplean en la técnica de oximetría de pulso (660 nm y 940 nm) para
calcular la frecuencia cardíaca. La recuperación de la frecuencia cardíaca se realiza mediante el
análisis de los datos mediante la técnica de demodulación sincrónica. Los datos muestreados se
generaron a partir de mediciones realizadas en dos personas. La frecuencia cardíaca obtenida con la
técnica de oximetría de pulso junto con la técnica de demodulación sincrónica se corroboró con la
frecuencia cardíaca obtenida mediante la señal PPG a una sola longitud de onda (940 nm).

Palabras clave: pulso cardíaco, fotopletismografía, sensor, demodulación sincrónica

Todo el contenido de LATAM Revista Latinoamericana de Ciencias Sociales y Humanidades,
publicado en este sitio está disponibles bajo Licencia Creative Commons.

Cómo citar: Yañez Mendiola, J., Bautista López, R. Z., & López Vela, J. M. (2025). Cardiac pulse
detection by a pulse train using the synchronous demodulation technique. LATAM Revista
Latinoamericana de Ciencias Sociales y Humanidades 6 (5), 2415 – 2423.
https://doi.org/10.56712/latam.v6i5.4749

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ISSN en línea: 2789-3855, noviembre, 2025, Volumen VI, Número 5 p 2417.

INTRODUCTION

Photoplethysmography (PPG) is an optical measurement technique that is used to measure blood
volume changes in microvascular tissue (Challoner y Ramsay 1974) and has a wide range of clinical
applications, for example, pulse oximetry and cardiac pulse signals. PPG signals have great potential
for the non-invasive detection of a wide range of diseases with high performance; in a review of 43
studies that used photoplethysmography (PPG) signals for the detection and diagnosis of 25 health
conditions, Loh et al. (Loh et al. 2022) identified some limitations in the studies reviewed, such as the
lack of standardization in the collection of PPG signals, the lack of public access to PPG databases,
and the diversity of health conditions covered. This review also highlights the importance of noting that
PPG studies are still in an early stage of development and that more studies are needed to validate the
results obtained and to evaluate the performance of PPG techniques in real clinical settings.

The optical arrangement used is very simple: a light source illuminates the skin and after interacting
with the skin either by transmission or reflection, the results are collected for processing. The
interaction of light with living tissue is somewhat complex (reflection, transmission, absorption and
scattering) (Anderson y Parrish 1981) and many factors affect the amount of light received by the
sensor, for example the effect of pressure on the sensor (Hertzman 1938). Although the signal
processing technique through the plethysmography method is well known, where for the general case
of obtaining a cardiac pulse, a single light source is used; for pulse oximetry, a technique derived from
the application of photoplethysmography, two light sources at different wavelengths are used to
determine the percentage of oxygen between the proportions of hemoglobin and oxyhemoglobin. (de
Kock y Tarassenko 1993; Wukitsch et al. 1988; Chan, Chan, y Chan 2013). Leppänen et al. (Leppänen
et al. 2022) indicate that total absorption is lower with infrared light compared to red light, so the PPG
signal measured with the infrared wavelength is more stable and commonly used than red light.
However, measurements of both red and infrared light are required to estimate SpO2. The main
advantage of this device is that data collected from the two different wavelengths can be used to
estimate both heart rate and SpO2. Therefore, we propose that by using the pulse oximetry
configuration and synchronizing the activation of the light source (red and infrared LEDs) so that the
signal sent is a series of pulses, the cardiac pulse signal can be recovered by processing the data using
synchronous demodulation technique. Oximetry is a widely studied technique with clinical applications.
One of the main applications of pulse oximetry is the determination of oxygen saturation using different
signal processing techniques, however, blood oxygen saturation is not the only information that the
PPG signal can contain, but also signals of interest such as heart rate and respiratory rate (Chon, Dash,
y Ju 2009). It can be shown that it is possible to recover the respiratory rate from the
photoplethysmography signal because there is evidence that the respiratory rate modulates both the
frequency and the amplitude of the cardiac pulse signal (P. Leonard et al. 2003; Paul Leonard et al.
2004; P. A. Leonard et al. 2006; Shelley et al. 2006; Charlton et al. 2018). Chon et al. (Chon, Dash, y Ju
2009) proposed a method to estimate respiratory rate by pulse oximetry using the time-frequency
spectral estimation method: variable frequency complex demodulation (VCFDM) to identify the
frequency modulation (FM and AM) of the photoplethysmogram waveform.

The photoplethysmography technique is widely known and a wide range of technologies have been
developed around it (Kyriacou y Allen 2021). One of the main reasons for using this technique is to
avoid the use of additional equipment in monitoring vital signs such as heart rate or respiratory rate
(Addison y Watson 2004). It is important to know the range of beats per minute and breaths per minute
at rest and during exercise; for example, the respiratory rate range is between 10-20 breaths/minute
and can reach up to 45 breaths/minute for sports activities, and in the case of heart rate, it is between
38 and 110 beats/minute, including sports activities (Nakajima, Tamura, y Miike 1996). Knowledge of
these ranges allows us to design the electronic system, mainly the noise-reducing filters in the signal
to capture the cardiac pulse signal or respiratory rate signal that is in these ranges (Budidha y Kyriacou

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2022). Currently, existing technology makes possible the evolution of conventional PPG to image PPG
(IPPG) (Sun y Thakor 2016), algorithms based on four-layer deep neural networks (Biswas et al. 2019)
are also being applied, indicating that it is still a field with numerous research possibilities. Based on
the pulse oximetry setup and Ohmeda oximeter review by Wukitsch et al. (Wukitsch et al. 1988), we
propose to generate a train of pulses in such a way that for a time the red LED remains on and the
infrared LED off, and vice versa, synchronizing by a signal from a microcontroller. For the proposed
case, both light beams are used under the principle that the recovered signal is amplitude modulated
(AM) by the heart rate. The heart rate signal is recovered by applying the synchronous demodulation
technique to the signal from the photodetector.

The demodulation technique has been widely used since its origin in the field of communications
(Bruning et al. 1974), but it is also used in other research areas such as optics (Malacara 2007;
Rodríguez-Vera y Servín 1994; Servin, Malacara, y Rodriguez-Vera 1994). Instruments have been
developed specifically for its implementation (Zurich Instruments 2016). The synchronous detection
technique requires that the input signal to meet specific requirements: be purely sinusoidal and have a
duty cycle of at least 0.5 in order to determine the phase and amplitude of an input signal at a given
frequency (Warsza 2005). The signal can be analyzed by electronic or digital procedures; the
photoplethysmography technique allows the signal to be analyzed by a digital procedure, although
extensive instrumentation (technology) has already been developed (Kyriacou y Allen 2021). In the
synchronous detection section, the procedure used is discussed more extensively. A procedure for
applying synchronous detection in the detection of pulsed signals can be found in (Efthymiou y Ozanyan
2013), where they show us a periodic signal with a duty cycle close to 0.5, this signal is improved by
data processing using a Gated Quadrature Synchronous Demodulation (GQSD) algorithm to achieve
optimal pulse recovery conditions.

This article is divided into the following sections. The introduction presents the state of the art,
theoretical framework and the proposal. In the development section, the operating principle is
presented, together with the mathematical demonstration of the theory on which the method for the
treatment and recovery of the heart rate signal is based. The results section shows the theory described
in the development applied to practice and the graphs (Fig. 6 and Fig. 7) show the signal before and
after applying the synchronous detection method to the collected data from the signal acquisition
system. In the conclusions, the final argument for the synchronous detection method and the possible
implementation in future works for recovering other signals immersed in the photoplethysmography
signal are presented.

METHODOLOGÝ

Methods and procedures

Participant Information: The initial trials of the technique were conducted with two participants to
establish its feasibility. More participants will be included in future studies. In total, 100 measurements
were collected from two subjects, each of whom was evaluated 50 times. The subject characteristics
are as described in the article by Fine et al. (Fine et al. 2021) they analyze the sources of noise in
photoplethysmography (PPG) and their impact on the development of PPG devices for health
monitoring. In their analysis, they discuss the reduced accuracy of PPG devices using green light (550
nm) in individuals with darker skin tones due to melanin absorption in the epidermis.

Red light and near-infrared light, with their ability to penetrate deeper into the skin, offer better
performance in such cases. Some of the subject characteristics are shown below.

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Subject 1

Age: Thirty-seven years old

Sex: Female

Physical condition: Active

Medications: None

Skin tone: Brown

Build: Thin

Measurement site: Index finger

Body temperature: 36.5 degrees Celsius

Subject 2

Age: Fifty-four years old

Sex: Male

Physical condition: Active

Medications: None

Skin tone: Brown

Build: Thin

Measurement site: Index finger

Body temperature: 36.5 degrees Celsius

Principle of Operation: Fig. 1 provides a basic flow diagram of the circuit designed for data collection.
The PIC16F1615 microprocessor, through the pulse width modulation (PWM) function, generated a
pulse train at a frequency of 122 Hz.

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Figure 1

Basic diagram of the circuit used for data collection

The same microprocessor controlled an on–and–off system of red and infrared LEDs (VSMD66694).
This control allowed one LED to remain on for a period of 8 pulses (data sampling period and its storage
in memory) while the other remained off, and vice versa (Fig. 2). The emission of the beams interacts
with the surface of human skin. The reflected light was collected and processed by the TEMD7000
photo-detector which is connected to a transimpedance circuit whose main component is the
ADA4505-2ARMZ amplifier, the output signal of the transimpedance circuit is amplified to become a
digital signal. The processor sends the data to the CY15V104QN 4 Mbit F-RAM memory. The time for
sending the signal (pulse train), collecting and storing data lasts 133 seconds (2.13 minutes). The
signal sampling frequency was 1950 Hz (t = 5.12x10−4 seconds). Once the data was stored, the circuit
was connected to a computer to extract the data through the USB port, the data was analyzed by the
synchronous demodulation algorithm which was programmed in the Python programming language.

The configuration of the analogue system used is shown in Fig. 2.

Figure 2

Basic connection diagram for the analogue data collection system, where ir is an infrared LED, r is a red
LED, R is the resistance, Op is the operational amplifier and GND is a ground line

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Signal processing method: The procedure for the implementation of the synchronous demodulation
algorithm is summarized next:

A train of pulses is sent to interact with the skin, Fig. 3.

The signal collected by the photodetector is taken, which has already gone through an analog and digital
conditioning process.

Apply a low-pass filter to the signal.

The frequency of the input signal is calculated.

With the frequency of the input signal, two signals are generated: sine and cosine.

A convolution is applied between the input signal and the sine and cosine signal respectively; this
generates two signals.

Apply a low-pass filter to the signal.

Feature scaling (normalization) is applied to the signal data generated in the previous step.

A low-pass filter is applied to the signals resulting from the previous step.

Finally, the magnitude of these two signals is calculated, which corresponds to the heart pulse rate.

Figure 3

Pulse train: on-and-off sequence for the LEDs. The pulse train frequency is 122 Hz. It is important to note
that there is a dead time in neither of the two LEDs are on to avoid data overlap, this time is 500 ns

The following equation describes a pulse train (Poularikas 2010):

�� = ��(�� (2��) ) = ��(�� (��) ) (1)

For this case, a pulse train is applied that is defined by the following form:

�� = ��(�� (2��) ) = �� + ��(�� (��) ) (2)

Where �� is the pulse train function, �� is time, �� is the fundamental frequency and �� is a constant.

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Photoplethysmography (Allen 2007; Mendelson y Ochs 1988; Nakajima, Tamura, y Miike 1996) is a
technique that allows visualizing the variation in blood volume changes as a result of flow variations,
thus allowing the detection and measurement of cardiac pulse, oxygen levels, and other biomedical
variables (Karlen et al. 2013). Herein, plethysmography is used to measure heart rate. The light beams
were applied in the form of a pulse train, as indicated by Equation (2). The signal was recovered by
reflection. If a convolution low-pass filter is applied to the sampled signal (Stearns y Hush 2011), the
following is obtained:

��(��) = [��(��)] ∗ �� = �� + �� (��) = �� + �� (2��)
(3)

where �� = 2��, where �� is the angular frequency of the carrier signal. From Equation (3) it can be
seen that there is a constant component �� that corresponds to an unchanged illumination beam and
that its magnitude is much greater than the amplitude of the oscillating signal |��| ≫ |��|. Fig. 4 shows
the signal recovered from the data acquisition system after applying a low-pass filter, as mentioned in
step 3 of the implementation of the synchronous demodulation algorithm, and Fig. 5 shows the Fourier
spectrum of the oscillation frequency of both light beams (122 Hz).

Graphic 1

Signal recovered by the sensor due to the light (red and infrared LEDs) reflected on the incident surface

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Graphic 2

Frequency of oscillation of red and infrared LEDs

Synchronous detection: The synchronous detection(Malacara 2007) method is based on the theory of
radio communication, where the phase or magnitude of an unknown signal is recovered by the
correlation of this signal with a sinusoidal signal of the same frequency (Rodríguez-Vera y Servín 1994).
If we consider that the signal derived from the heart rate, denoted as (|��(��)|), can modulate a train of
pulses according to Equation (2), with a carrier frequency (��, �� ∶ ��) much higher than the
frequency of heart rate (��, �� ∶ ℎ�� ) and we can consider this signal as a carrier signal.
Therefore:

�� ≪ �� (4)

A relationship can be considered as follows:

��(��) = ��(��)��(��) = ��(��)[�� + �� (2��) ] (5)

From Equation (5), we have the following:

��(��) = ��(��) + ��(��) �� (2��)

Knowing that |��| ≫ |��(��)| and also that |��(��)| will only modulate the �� (2��). If this signal ratio
shown in equation (5) is multiplied by 2 signals (sine and cosine) of frequency similar to the carrier
frequency, the following is obtained. If this signal ratio shown in equation (5) is multipliedby 2 signals
(sine and cosine) of frequency similar to the carrier frequency, the following is obtained.

��(��) �� (2��′��) = ��(��)[�� + �� (2��) ] �� (2��′��)

If the previous expression is developed, the Equation (6) is obtained:

��(��) �� (2��′��) = ��(��) �� (2��′��) + ��(��) �� (2��) �� (2��′��) (6)
A similar analysis is applied for the following relationship:

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��(��) �� (2��′��) = ��(��)[�� + �� (2��) ] �� (2��′��)

From the previous analysis we obtain Equation (7):

��(��) �� (2��′��) = ��(��) �� (2��′��) + ��(��) �� (2��) �� (2��′��) (7)

Equation (6) can be expressed as follows:

��(��) �� (2��′��) = ��
+ ��

= ��(��)�� (8)

Where:

��
= ��(��) �� (2��′��)

��
= ��(��) �� (2��) �� (2��′��)

Equation (7) is also expressed as follows:

��(��) �� (2��′��) = ��
+ ��

= ��(��)�� (9)
Where:

��
= ��(��) �� (2��′��)

��
= ��(��) �� (2��) �� (2��′��)

��
and ��

are the terms containing the information of interest, for cardiac pulse recovery. To apply
the synchronous demodulation technique, the term containing the constant A (��

and ��
) must

be removed from Equation (6) and (7) respectively to subsequently process the terms of interest (��

and ��
). For this purpose, we normalize y(t)c and y(t)s from Equations (8) and (9) as follows:

From the previous mathematical development, we obtain the signals of Equation (8) and (9), both
signals carry a DC component and we can rewrite the equations as shown:

��(��)�� = ��(��) �� (2��′��) = ��
+ ��

(10)

��(��)�� = ��(��) �� (2��′��) = ��
+ ��

(11)

Before applying feature scaling, both signals (��
) and ��

) of equations (10) and (11) are
processed by applying a low-pass filter; The DC signal is attenuated with the application of the low pass
filter, however, it is not completely removed, so the next step is to apply the following statistical
procedure known as feature scaling to remove by the DC signal. This normalization consists of
transforming the minimum value into 0 and the maximum value into 1 so that all other values remain
within that range (to meet the signal characteristics mentioned in Zygmunt L. Warsza’s publication in
the handbook of measuring system design manual (Warsza 2005), the formula is as follows:

��−�� =
�� − ��
− ��

(12)

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Where: �� = is the signal of ��(��)�� and ��(��)��, because both signals must be normalized.

Equation (12) returns values between 0 and 1, which needs to be corrected as it requires a signal
centered on the x-axis or located between values above and below 0, with a minimum amplitude of 0.5
(Efthymiou y Ozanyan 2013), for this purpose Z – score normalization is used which is defined by the
following Equation (13):

��(��)�� =
��−�� − ��

��

(13)

Where:

��−��= Are the data obtained from Equation (12).

�� = It is the Arithmetic Average ��−��

�� = Is the Standard Deviation of ��−��

In Z - score normalization if a value is exactly equal to the mean of the data, this value is normalized to
0; if the value is below the mean, then it will be transformed to a negative number, and if the value is
above the mean, the value is transformed to a positive value. In Z - score normalization the amplitude
of the signal is determined by the standard deviation of the data. The data resulting from Z - score
normalization, are the signals ��(��)�� and ��(��)��:

��(��)�� = ��(��) �� (2��′��) + ��(��) �� (2��) �� (2��′��) (14)
��(��)�� = ��(��) �� (2��′��) + ��(��) �� (2��) �� (2��′��) (15)

From equation (14) and (15) note that the �� term is no longer present, since it is centered with respect
to the time axis.

If we develop the ��
part of Equation (14), we obtain the following:

��(��) �� (2��) �� (2��′��)

= ��(��) [
1
2

�� (2��(�� − ��′)��) +
1
2

�� (2��(�� + ��′)��) ]
= (2��(�� − ��′)��) + ��′��(��) �� (2��(�� + ��′)��)
= ��′��(��)[�� (2��(�� − ��′)��) +�� (2��(�� + ��′)��) ]

Developing the ��
part of Equation (15), we obtain the following:

��(��) �� (2��) �� (2��′��)
= ��(��) [

1
2

�� (2��(�� − ��′)��) +
1
2

Where ��′ =
��
2

Fig. 6 shows the signal coming from the data acquisition system after having applied a low-pass filter
according to Equation (3), it can be seen how the heart rate modulates the signal. Therefore, Equations
(14) and (15) can be rewritten as follows:

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��(��)�� = ��(��) �� (2��′��) + ��′��(��)[�� (2��(�� − ��′)��) +�� (2��(�� + ��′)��) ] (16)

��(��)�� = ��(��) �� (2��′��) + ��′��(��)[�� (2��(�� − ��′)��) +�� (2��(�� + ��′)��) ] (17)

The terms �� (2�� (��
��

− ��
��′

) ��) and �� (2�� (��
��

− ��
��′

) ��) corresponds to low frequency, and

the terms �� (2��
��′

��) , �� (2��
��′

��) , �� (2�� (��
��

+ ��
��′

) ��) and �� (2�� (��
��

��
��′

) ��) corresponds to high frequencies, if it is considered that �� ≪ ��.

By applying a low-pass filter (Butterworth type [33]) to the Equation (16) and (17), the following is
obtained:

�� = ��(��)�� ∗ �� = ��′��(��) �� (2��(�� − ��′)��) (18)

In addition, if ��′ ≈ �� , and after applying a low-pass filter, then:

�� = ��(��)�� ∗ �� = ��′��(��) �� (2��(�� − ��′)��) (19)

It is not interesting to recover the phase but rather the magnitude of (|��(��)|), because the signal from
the photodetector is amplitude modulated (AM) by the heart rate. From the previous Equations (18) and
(19), the following is obtained:

|��(��)| = √(′��(��) �� (2��(�� − ��′)��) )
2

+ (��′��(��) �� (2��(�� − ��′)��) )
2

Therefore, we have the following:

|��(��)| = √(��)2 + (��)2 (20)

From Equation (20), heart rate is calculated.

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Graphic 3

Recovered signal to which the low-pass filter has been applied according to Equation (3)

RESULTS

Applying the described procedure, the following results are obtained: Fig. 6 shows the processed signal
that is obtained from the signal acquisition system, that is, after Equation (3) is applied.

Applying the procedure according to Equations (18), (19) and (20), the result is shown in graphic 3 is
obtained.

Graphic 4

Pulse recovered from the synchronous detection method

Graphic 4 shows the signal of interest recovered with the pulse oximetry technique in conjunction with
the synchronous demodulation technique: heart rate. It is also observed that the pulse signal is
modulated by an additional signal. Applying the Fourier transform to the data obtained, the following
frequency spectrum is obtained (graphic 5).

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Graphic 5

Fourier spectrum of the data obtained by applying the synchronous detection method

The main peaks are at a frequency of 1.5p/s, which is corroborated by the signal in graphic 6,
14��

9��
=

1.5��/�� (pulses per second). Other important aspects to highlight are the peaks between the origin and
the heart rate, which were studied by Solange et al. (Akselrod et al. 1981).

The data, which are obtained using the photoplethysmography technique, are shown in graphic 6.

Graphic 6

Data results from directly applying the photoplethysmography method

Their respective frequency spectrum can be seen in graphic 7.

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ISSN en línea: 2789-3855, noviembre, 2025, Volumen VI, Número 5 p 2417.

Graphic 7

Fourier spectrum of the photoplethysmography method data

The frequency corresponding to the data applying the synchronous detection method corresponds to
that of the data obtained directly applying the photoplethysmography technique �� = 1.5��/��.

From the data obtained with the proposed method (graphic 7), it can be seen that the pulse is
modulated; therefore, it is possible to apply techniques that can determine the respiratory rate (P.
Leonard et al. 2003; Paul Leonard et al. 2004; P. A. Leonard et al. 2006; Shelley et al. 2006; Charlton
et al. 2018) (graphic 8).

Graphic 8

Heart rate modulated by lung rate

The peaks of each spectrum and the measurement obtained with the MD300C23 CHOICEMED pulse
oximeter are shown in Table 1.

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ISSN en línea: 2789-3855, noviembre, 2025, Volumen VI, Número 5 p 2418.

Table 1

Mean squared error of the peaks in the heart rate frequency spectrum

number
of

observations

Subject 1 Subject 2
Estimated
spectrum
frequency

data

Observed
CHOICEMED

pulse
oximeter

data

Sum
of the

squared
errors

Estimated
spectrum
frequency

data

Observed
CHOICEMED

pulse
oximeter

data

Sum
of the

squared
errors

1 67 69 4 65 67 4
2 78 79 1 63 64 1
3 71 72 1 69 67 4
4 63 65 4 68 70 4
5 57 54 9 61 63 4
6 72 70 4 63 65 4
7 64 65 1 60 58 4
8 85 84 1 70 71 1
9 61 63 4 67 68 1

10 56 57 1 65 67 4
11 70 70 0 62 65 9
12 65 64 1 64 63 1
13 86 85 1 63 62 1
14 85 87 4 70 73 9
15 66 70 16 65 63 4
16 76 73 9 70 71 1
17 105 107 4 62 61 1
18 95 99 16 63 62 1
19 79 75 16 63 61 4
20 85 86 1 66 70 16
21 66 69 9 64 67 9
22 85 87 4 61 59 4
23 70 73 9 77 75 4
24 89 94 25 62 66 16
25 67 66 1 67 65 4
26 75 77 4 68 67 1
27 74 72 4 69 72 9
28 80 79 1 68 69 1
29 64 66 4 67 68 1
30 91 89 4 67 69 4
31 82 79 9 60 58 4
32 81 85 16 65 62 9
33 87 88 1 60 59 1
34 88 90 4 61 62 1
35 87 85 4 65 67 4
36 68 65 9 70 68 4
37 66 69 9 72 70 4
38 83 80 9 60 63 9
39 86 87 1 68 67 1
40 62 64 4 55 58 9
41 80 79 1 65 66 1
42 85 86 1 61 62 1
43 77 78 1 54 57 9
44 68 70 4 63 62 1
45 80 82 4 65 63 4
46 86 88 4 66 69 9

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ISSN en línea: 2789-3855, noviembre, 2025, Volumen VI, Número 5 p 2419.

47 85 84 1 67 65 4
48 83 84 1 65 62 9
49 58 60 4 60 64 16
50 87 89 4 54 57 9

average 76.52 77.16 5.08 64.5 64.98 4.8

CONCLUSION

Plethysmography is a technique that has a wide application in the clinical field. Its implementation has
allowed the development of a new technology, as well as a new technique in the treatment of data for
scrutinizing the additional information carried by the cardiac pulse signal. The application of the
synchronous detection method was presented as a technique to recover the cardiac pulse through the
configuration used in pulse oximetry. From the results obtained, the cardiac pulse recovered from the
set of information generated by the pulse oximeter configuration at two different wavelengths is shown.
In addition, cardiac pulse modulation can be achieved, which can guide the application of pulmonary
rate recovery techniques.

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REFERENCES

Addison, Paul S., y James N. Watson. 2004. «Secondary transform decoupling of shifted nonstationary
signal modulation components: application to photoplethysmography». International Journal of
Wavelets, Multiresolution and Information Processing 02 (01): 43-57.
https://doi.org/10.1142/S0219691304000329.

Akselrod, S., D. Gordon, F. A. Ubel, D. C. Shannon, A. C. Berger, y R. J. Cohen. 1981. «Power Spectrum
Analysis of Heart Rate Fluctuation: A Quantitative Probe of Beat-to-Beat Cardiovascular Control».
Science (New York, N.Y.) 213 (4504): 220-22. https://doi.org/10.1126/science.6166045.

Allen, John. 2007. «Photoplethysmography and Its Application in Clinical Physiological Measurement».
Physiological Measurement 28 (3): R1-39. https://doi.org/10.1088/0967-3334/28/3/R01.

Anderson, R. Rox, y John A. Parrish. 1981. «The Optics of Human Skin». Journal of Investigative
Dermatology 77 (1): 13-19. https://doi.org/10.1111/1523-1747.ep12479191.

Biswas, Dwaipayan, Luke Everson, Muqing Liu, Madhuri Panwar, Bram-Ernst Verhoef, Shrishail Patki,
Chris H. Kim, et al. 2019. «CorNET: Deep Learning Framework for PPG-Based Heart Rate Estimation and
Biometric Identification in Ambulant Environment». IEEE Transactions on Biomedical Circuits and
Systems 13 (2): 282-91. https://doi.org/10.1109/TBCAS.2019.2892297.

Bruning, J. H., D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, y D. J. Brangaccio. 1974. «Digital
Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses». Applied Optics 13 (11):
2693-2703. https://doi.org/10.1364/AO.13.002693.

Budidha, Karthik, y Panicos Kyriacou. 2022. «Photoplethysmography technology». En , 43-68.
https://doi.org/10.1016/B978-0-12-823374-0.00002-5.

Challoner, A. V., y C. A. Ramsay. 1974. «A Photoelectric Plethysmograph for the Measurement of
Cutaneous Blood Flow». Physics in Medicine and Biology 19 (3): 317-28. https://doi.org/10.1088/0031-
9155/19/3/003.

Chan, Edward D., Michael M. Chan, y Mallory M. Chan. 2013. «Pulse Oximetry: Understanding Its Basic
Principles Facilitates Appreciation of Its Limitations». Respiratory Medicine 107 (6): 789-99.
https://doi.org/10.1016/j.rmed.2013.02.004.

Charlton, Peter H., Drew A. Birrenkott, Timothy Bonnici, Marco A. F. Pimentel, Alistair E. W. Johnson,
Jordi Alastruey, Lionel Tarassenko, Peter J. Watkinson, Richard Beale, y David A. Clifton. 2018.
«Breathing Rate Estimation From the Electrocardiogram and Photoplethysmogram: A Review». IEEE
Reviews in Biomedical Engineering 11: 2-20. https://doi.org/10.1109/RBME.2017.2763681.

Chon, Ki H., Shishir Dash, y Kihwan Ju. 2009. «Estimation of Respiratory Rate from
Photoplethysmogram Data Using Time-Frequency Spectral Estimation». IEEE Transactions on Bio-
Medical Engineering 56 (8): 2054-63. https://doi.org/10.1109/TBME.2009.2019766.

Efthymiou, Spyros, y Krikor B. Ozanyan. 2013. «Pulse Detection by Gated Synchronous Demodulation».
IEEE Sensors Journal 13 (9): 3349-60. https://doi.org/10.1109/JSEN.2013.2263496.

Fine, Jesse, Kimberly L. Branan, Andres J. Rodriguez, Tananant Boonya-ananta, Ajmal, Jessica C.
Ramella-Roman, Michael J. McShane, y Gerard L. Coté. 2021. «Sources of Inaccuracy in
Photoplethysmography for Continuous Cardiovascular Monitoring». Biosensors 11 (4): 126.
https://doi.org/10.3390/bios11040126.

LATAM Revista Latinoamericana de Ciencias Sociales y Humanidades, Asunción, Paraguay.
ISSN en línea: 2789-3855, noviembre, 2025, Volumen VI, Número 5 p 2421.

Hertzman, Alrick B. 1938. «The blood supply of various skin areas as estimated by the photoelectric
plethysmograph». American Journal of Physiology-Legacy Content 124 (2): 328-40.
https://doi.org/10.1152/ajplegacy.1938.124.2.328.

Karlen, Walter, Srinivas Raman, J. Mark Ansermino, y Guy A. Dumont. 2013. «Multiparameter
Respiratory Rate Estimation from the Photoplethysmogram». IEEE Transactions on Bio-Medical
Engineering 60 (7): 1946-53. https://doi.org/10.1109/TBME.2013.2246160.

Kock, J. P. de, y L. Tarassenko. 1993. «Pulse Oximetry: Theoretical and Experimental Models». Medical
and Biological Engineering and Computing 31 (3): 291-300. https://doi.org/10.1007/BF02458049.

Kyriacou, Panicos, y John Allen. 2021. Photoplethysmography - Technology, Signal Analysis and
Applications. 1st Edition. © Academic Press 2021.
https://www.elsevier.com/books/photoplethysmography/kyriacou/978-0-12-823374-0.

Leonard, P., T. F. Beattie, P. S. Addison, y J. N. Watson. 2003. «Standard Pulse Oximeters Can Be Used
to Monitor Respiratory Rate». Emergency Medicine Journal: EMJ 20 (6): 524-25.
https://doi.org/10.1136/emj.20.6.524.

Leonard, Paul A., David Clifton, Paul S. Addison, James N. Watson, y Tom Beattie. 2006. «An Automated
Algorithm for Determining Respiratory Rate by Photoplethysmogram in Children». Acta Paediatrica
(Oslo, Norway: 1992) 95 (9): 1124-28. https://doi.org/10.1080/08035250600612280.

Leonard, Paul, Neil R. Grubb, Paul S. Addison, David Clifton, y James N. Watson. 2004. «An Algorithm
for the Detection of Individual Breaths from the Pulse Oximeter Waveform». Journal of Clinical
Monitoring and Computing 18 (5-6): 309-12. https://doi.org/10.1007/s10877-005-2697-z.

Leppänen, Timo, Samu Kainulainen, Henri Korkalainen, Saara Sillanmäki, Antti Kulkas, Juha Töyräs, y
Sami Nikkonen. 2022. «Pulse Oximetry: The Working Principle, Signal Formation, and Applications». En
Advances in the Diagnosis and Treatment of Sleep Apnea : Filling the Gap Between Physicians and
Engineers, editado por Thomas Penzel y Roberto Hornero, 205-18. Cham: Springer International
Publishing. https://doi.org/10.1007/978-3-031-06413-5_12.

Loh, H. W., S. Xu, O. Faust, C. P. Ooi, P. D. Barua, S. Chakraborty, R.-S. Tan, F. Molinari, y U. R. Acharya.
2022. «Application of Photoplethysmography Signals for Healthcare Systems: An in-Depth Review.»,
abril. https://opus.lib.uts.edu.au/handle/10453/167716.

Malacara, Daniel, ed. 2007. Optical Shop Testing. 3rd ed. Wiley Series in Pure and Applied Optics.
Hoboken, N.J: Wiley-Interscience.

Mendelson, Yitzhak, y B.D. Ochs. 1988. «Noninvasive pulse oximetry utilizing skin reflectance
photoplethysmography». IEEE Transactions on Biomedical Engineering 35 (10): 798-805.
https://doi.org/10.1109/10.7286.

Nakajima, K., T. Tamura, y H. Miike. 1996. «Monitoring of Heart and Respiratory Rates by
Photoplethysmography Using a Digital Filtering Technique». Medical Engineering & Physics 18 (5): 365-
72. https://doi.org/10.1016/1350-4533(95)00066-6.

Poularikas, Alexander D., ed. 2010. Transforms and Applications Handbook. 3rd ed. Electrical
Engineering Handbook ; 43. Boca Raton, Fla: CRC Press.

Rodríguez-Vera, R., y M. Servín. 1994. «Phase Locked Loop Profilometry». Optics & Laser Technology
26 (6): 393-98. https://doi.org/10.1016/0030-3992(94)90050-7.

LATAM Revista Latinoamericana de Ciencias Sociales y Humanidades, Asunción, Paraguay.
ISSN en línea: 2789-3855, noviembre, 2025, Volumen VI, Número 5 p 2422.

Servin, M., D. Malacara, y R. Rodriguez-Vera. 1994. «Phase-Locked-Loop Interferometry Applied to
Aspheric Testing with a Computer-Stored Compensator». Applied Optics 33 (13): 2589-95.
https://doi.org/10.1364/AO.33.002589.

Shelley, Kirk H., Aymen A. Awad, Robert G. Stout, y David G. Silverman. 2006. «The Use of Joint Time
Frequency Analysis to Quantify the Effect of Ventilation on the Pulse Oximeter Waveform». Journal of
Clinical Monitoring and Computing 20 (2): 81-87. https://doi.org/10.1007/s10877-006-9010-7.

Stearns, Samuel D., y Donald R. Hush. 2011. Digital Signal Processing with Examples in MATLAB(R).
2nd ed. Boca Raton, FL.

Sun, Yu, y Nitish Thakor. 2016. «Photoplethysmography revisited: from contact to noncontact, from
point to imaging». IEEE transactions on bio-medical engineering 63 (3): 463-77.
https://doi.org/10.1109/TBME.2015.2476337.

Warsza, Zygmunt. 2005. Handbook of Measuring System Design, 3 Volume Set | Wiley. Vol. 3.

Wukitsch, Michael W., Michael T. Petterson, David R. Tobler, y Jonas A. Pologe. 1988. «Pulse Oximetry:
Analysis of Theory, Technology, and Practice». Journal of Clinical Monitoring 4 (4): 290-301.
https://doi.org/10.1007/BF01617328.

Zurich Instruments. 2016. «Principles of Lock-in Detection and the State of the Art». Zurich Instruments.
noviembre de 2016. https://www.zhinst.com/americas/en.

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