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Smart Homes that Monitor Breathing and Heart Rate
Fadel Adib Hongzi Mao Zachary Kabelac Dina Katabi Robert C. Miller
Massachusetts Institute of Technology
32 Vassar Street, Cambridge, MA 02139
{
fadel,hongzi,zek,dk,rcm
}
@mit.edu
ABSTRACT
The evolution of ubiquitous sensing technologies has led to
intelligent environments that can monitor and react to our
daily activities, such as adapting our heating and cooling sys-
tems, responding to our gestures, and monitoring our elderly.
In this paper, we ask whether it is possible for smart en-
vironments to monitor our vital signs remotely, without in-
strumenting our bodies. We introduce Vital-Radio, a wire-
less sensing technology that monitors breathing and heart rate
without body contact. Vital-Radio exploits the fact that wire-
less signals are affected by motion in the environment, in-
cluding chest movements due to inhaling and exhaling and
skin vibrations due to heartbeats. We describe the operation
of Vital-Radio and demonstrate through a user study that it
can track users’ breathing and heart rates with a median ac-
curacy of 99%, even when users are 8 meters away from the
device, or in a different room. Furthermore, it can monitor the
vital signs of multiple people simultaneously. We envision
that Vital-Radio can enable smart homes that monitor peo-
ple’s vital signs without body instrumentation, and actively
contribute to their inhabitants’ well-being.
(a) Inhale Motion
(b) Exhale Motion
Figure 1—Chest Motion Changes the Signal Reflection Time.
(a)
shows that when the person inhales, his chest expands and becomes
closer to the antenna, hence decreasing the time it takes the signal
to reflect back to the device. (b) shows that when the person ex-
hales, his chest contracts and moves away from the antenna, hence
the distance between the chest and the antenna increases, causing an
increase in the reflection time.
Author Keywords
Wireless; Vital Signs; Breathing; Smart
Homes; Seeing Through Walls; Well-being
Categories and Subject Descriptors
H.5.2. Information
Interfaces and Presentation: User Interfaces - Input devices
and strategies. C.2.2. Network Architecture and Design:
Wireless Communication.
INTRODUCTION
heartbeats?” Furthermore, if non-intrusive in-home continu-
ous monitoring of breathing and heartbeats existed, it would
enable healthcare professionals to study how these signals
correlate with our stress level and evolve with time and age,
which could have a major impact on our healthcare system.
Unfortunately, typical technologies for tracking vital signals
require body contact, and most of them are intrusive. Specif-
ically, today’s breath monitoring sensors are inconvenient:
they require the person to attach a nasal probe [19], wear a
chest band [43], or lie on a special mattress [3]. Some heart-
rate monitoring technologies are equally cumbersome since
they require their users to wear a chest strap [18], or place
a pulse oximeter on their finger [21]. The more comfortable
technologies such as wristbands do not capture breathing and
have lower accuracy for heart rate monitoring [12]. Addition-
ally, there is a section of the population for whom wearable
sensors are undesirable. For example, the elderly typically
feel encumbered or ashamed by wearable devices [20, 37],
and those with dementia may forget to wear them. Children
may remove them and lose them, and infants may develop
skin irritation from wearable sensors [40].
In this paper, we ask whether it’s possible for smart homes
to monitor our vital signs remotely – i.e., without requiring
any physical contact with our bodies. While past research
has investigated the feasibility of sensing breathing and heart
rate without direct contact with the body [17, 16, 15, 34, 27,
48, 14], the proposed methods are more appropriate for con-
trolled settings but unsuitable for smart homes: They fail in
the presence of multiple users or extraneous motion. They
typically require the user to lie still on a bed facing the device.
Furthermore, they are accurate only when they are within
close proximity to the user’s chest.
The past few years have witnessed a surge of interest in ubiq-
uitous health monitoring [22, 25]. Today, we see smart homes
that continuously monitor temperature and air quality and
use this information to improve the comfort of their inhab-
itants [46, 32]. As health-monitoring technologies advance
further, we envision that future smart homes would not only
monitor our environment, but also monitor our vital signals,
like breathing and heartbeats. They may use this information
to enhance our health-awareness, answering questions like
“Do my breathing and heart rates reflect a healthy lifestyle?”
They may also help address some of our concerns by an-
swering questions like “Does my child breathe normally dur-
ing sleep?” or “Does my elderly parent experience irregular
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http://dx.doi.org/10.1145/2702123.2702200
We introduce Vital-Radio, a new input device for tracking
breathing and heartbeats without physical contact with the
person’s body. Vital-Radio works correctly in the presence
of multiple users in the environment and can track the vital
signs of the present users simultaneously. Also, Vital-Radio
does not require the user to face the device or be aware of
its presence. In fact, the user can be sleeping, watching TV,
typing on her laptop, or checking her phone. Furthermore,
Vital-Radio can accurately track a user’s breathing and heart
rate even if she is 8 meters away from the device, or in a dif-
ferent room.
Vital-Radio works by using wireless signals to monitor the
minute movements due to inhaling, exhaling, and heartbeats.
Specifically, it transmits a low-power wireless signal and
measures the time it takes for the signal to reflect back to
the device. The reflection time depends on the distance of the
reflector to the device, and changes as the reflector moves.
Fig. 1 illustrates the impact of breathing on the signal’s re-
flection time. When the person inhales, his chest expands
and moves forward, reducing the reflection time. In contrast,
when the person exhales, his chest contracts moving away
from the device, hence increasing the reflection time. Gener-
ally, even when the person is not directly facing our device,
the wireless signal traverses his body and his vital signs cause
periodic changes in the signal’s reflection time. Vital-Radio
measures these changes and analyzes them to extract breath-
ing and heartbeats.
A key feature of Vital-Radio is its ability to monitor the vital
signs of multiple people and operate robustly without requir-
ing the users to lie still. The main challenge in delivering this
feature is that any motion in the environment can affect the
wireless signal and hence interferes with tracking breathing
or heartbeats. Past work addresses this challenge by requir-
ing that only one person be present in front of the device and
that the person remains still. In contrast, Vital-Radio recog-
nizes that one can address this problem by building on recent
technologies that localize users using wireless signals [6].
Specifically, Vital-Radio first localizes each user in the envi-
ronment, then zooms in on the signal reflected from each user
and analyzes variations in his reflection to extract his breath-
ing and heart rate. By isolating a user’s reflection, Vital-Radio
also eliminates other sources of interference including noise
or extraneous motion in the environment, which may other-
wise mask the minute variations due to the user’s vital signs.
This enables Vital-Radio to monitor multiple users’ breathing
and heart rates, and to operate at distances up to 8 m from the
user or even from behind a wall.
We built a real-time prototype of Vital-Radio and validated
its capabilities by conducting experiments with 14 subjects.
For baselines, we use FDA-approved breathing and heart rate
monitors; these include chest straps for monitoring the inhale-
exhale motion and pulse oximeters placed on the subject’s
finger to monitor their heart rate. In our benchmark evalua-
tion, we ask the users to wear the baseline monitors, while
Vital-Radio monitors them remotely without any body con-
tact. We compare the output of Vital-Radio with the ground
truth from the FDA-approved baselines, demonstrating that
Vital-Radio accurately tracks breathing patterns and heart-
beats. Over more than 200 two-minute experiments, our re-
sults show that:
•
Vital-Radio can accurately track a person’s breathing and
heart rate without body contact, even when the user is up
to 8 meters away from the device, or behind a wall.
•
Vital-Radio’s median accuracy for breathing is 99.3% (er-
ror of 0.09 breath/minute) and for heart rate is 98.5% (0.95
beat/minute) when the person is 1 m away from the de-
vice. The accuracy decreases to 98.7% (error of 0.15
breath/minute) and 98.3% (1.1 beat/minute) when the per-
son is 8 m away from the device.
•
In an area that spans 8
m×5 m,
Vital-Radio can monitor the
vital signs of up to three individuals with the same accuracy
as for one person.
We also perform activity-focused experiments to explore
Vital-Radio’s monitoring capabilities.
Specifically, we
demonstrate that Vital-Radio can accurately measure users’
breathing and heart rates while they are typing on their com-
puter or using their cell phones. We also demonstrate that
Vital-Radio can track sharp changes in vital signs. Specifi-
cally, we perform experiments where users are asked to exer-
cise, and show how Vital-Radio accurately tracks the change
in breathing and heart rates after exercising.
We believe Vital-Radio takes a significant step toward en-
abling smart homes that allow people to monitor their vital
signals, and that its capabilities can have a significant impact
on our health awareness and our health-care system.
RELATED WORK
The desire for non-contact monitoring of vital signs has oc-
cupied researchers since the late 70’s [29]. Early work pre-
sented a proof of concept that the wireless signal is affected
by movements of the chest. In these experiments, the person
lies still on a bed and the sensor is placed only 3 cm away
from the apex of the heart. The results are qualitative with no
evaluation of accuracy.
Subsequently, military research explored the potential of
building radars that can detect human presence through walls
or under rubble by relying on the fact that breathing impacts
wireless signals [42, 47, 26, 45]. Specifically, because wire-
less signals traverse obstacles, they could be used to sense the
chest movements of a trapped victim through rubble or enable
SWAT teams to sense movement from behind an obstacle and
avoid being ambushed. However, since these systems target
the military, they typically transmit at excessive power and
use military-reserved spectrum bands [47, 45], which is not
feasible for consumer devices. More importantly, this line of
work generally focused on the detection of users by sensing
motion due to their vital signs rather than estimating or mon-
itoring the vital signs themselves.
Recently, the mounting interest in technologies for well-being
has led researchers to investigate non-contact methods for an-
alyzing vital signs. Current research on this topic can be di-
vided into two areas: vision-based techniques and wireless
systems. Specifically, advances in image processing allowed
researchers to amplify visual patterns in video feeds (such as
color changes due to blood flow) to detect breathing and heart
rate [8, 44]; however, such video-based techniques require the
user to face the camera and do not work when he/she turns
around or is outside the camera’s field of view.
Similarly, advances in wireless transmission systems and sig-
nal processing have enabled researchers to detect and analyze
human vital signs. Past proposals use one of the following
techniques: Doppler radar [17, 16, 15], WiFi [34, 27], or
ultra-wideband radar [48, 14, 7]. The key challenge in us-
ing wireless signals to extract vital signs is that any motion in
the environment affects the signal. Since breathing and heart-
beats are minute movements, they can be easily masked by
interference from any other source of movement in the envi-
ronment. Furthermore, the presence of multiple users – even
if none of them moves – prevents these systems from operat-
ing correctly since the wireless signal will be affected by the
combination of their vital signs, making it hard to disentangle
the vital signs of each individual. Past proposals deal with this
problem by ensuring that there is only one source of motion
in the environment: namely, the vital signs of the monitored
individual. Hence, their experimental setup has one person,
who typically lies still in close proximity to the device [17,
16, 15, 34, 27, 48, 14, 7, 4].
In contrast to these past systems, Vital-Radio has an intrin-
sic mechanism that enables it to separate different sources
of motion in the environment. To do so, Vital-Radio builds
on state-of-the-art wireless localization techniques [6], which
can identify the distance between the device and different
moving objects. Vital-Radio, however, uses these methods
to disentangle the incoming signals based on distance, rather
than estimate the actual location. This allows it to separate
signals reflected off different bodies and body parts. It then
analyzes their motion independently to estimate the breathing
and heart rate of potentially multiple individuals.
CONTEXT AND SCOPE
Bucket1*
Bucket*2*
Bucket*3*
Bucket*4*
Transmission*
Vital&Radio*
Reflec.ons*
Figure 2—Separating Reflectors into Different Buckets.
Vital-
Radio uses a radar technique called FMCW to separate the reflec-
tions arriving from objects into different buckets depending on the
distance between these objects and the device.
laptop, reading a newspaper, or sleeping. Vital-Radio can use
all of these intervals to monitor a user’s vital signs, and track
how they vary throughout the day.
THEORY OF OPERATION
Vital-Radio transmits a low power wireless signal and mea-
sures the time it takes its signal to travel to the human body
and reflect back to its antennas. Knowing that wireless sig-
nals travel at the speed of light, we can use the reflection time
to compute the distance from the device to the human body.
This distance varies slightly and periodically as the user in-
hales and exhales and his heart beats. Vital-Radio captures
these minute changes in distance and uses them to extract the
user’s vital signs.
However, natural environments have a large number of re-
flectors, such as walls and furniture as well as multiple users
whose bodies all reflect the wireless signal. To address these
issues, Vital-Radio’s operation consists of three steps:
1. Isolate reflections from different users and eliminate reflec-
tions off furniture and static objects.
2. For each user, identify the signal variations that are due to
breathing and heartbeats, and separate them from variations
due to body or limb motion.
3. Analyze signal variations to extract breathing and heart
rates.
In what follows, we describe how these steps enable us to
monitor users’ vital signs using Vital-Radio.
Step 1: Isolate Reflections from Different Users and Elim-
inate Reflections off Furniture and Walls
We envision that Vital-Radio can be deployed in a smart home
to monitor its inhabitants’ breathing and heart rates, without
body instrumentation. The device can monitor multiple users’
vital signs simultaneously, even if some of them are occluded
from the device by a wall or a piece of furniture. A single de-
vice can monitor users’ vital signs at distances up to 8 meters,
and hence may be used to cover a studio or a small apart-
ment. One can cover a larger home by deploying multiple
Vital-Radio devices in the environment.
Vital-Radio’s algorithms run continuously, separating signals
from different users, then analyzing the signal from each user
independently to measure his/her vital signs. However, when
a user walks (or performs a large body motion), the chest mo-
tion is mainly impacted by the walk and no longer represen-
tative of the breathing and heart rate.
1
At home, there are
typically sufficient intervals when a user is quasi-static; these
include scenarios where the user is watching TV, typing on a
The vast majority of vital signs monitors, including chest bands
that monitor breathing and pulse oximeters that monitor heart rate,
cannot provide accurate estimates when the user walks or moves
a major limb [35, 28, 11]. To prevent such motion from causing
errors in its vital-signs estimates, Vital-Radio automatically detects
periods during which the user is quasi-static and computes estimates
only during such intervals.
1
To understand the operation of Vital-Radio, let us consider
the scenario in Fig. 2, where the device is placed behind the
wall of a room that has two humans and a table. When Vital-
Radio transmits a wireless signal, part of that signal reflects
off the wall; the other part traverses the wall, reflects off the
humans and the table inside the room, and then traverses the
wall back to the device.
To isolate signals reflected off different objects, Vital-Radio
uses a radar technique called FMCW (Frequency Modulated
Carrier Waves). We refer the reader to [6] for a detailed de-
scription of how FMCW works. A key property of FMCW
that we exploit in this paper is that it enables separating the
reflections from different objects into buckets based on their
Phase (in radians)
reflection times. Since wireless signals travel at the speed of
light, signals reflected off objects at different distances would
fall into different buckets.
However, in contrast to past work on localization, which uses
FMCW to sense the amount of power arriving from different
distances to localize the users, Vital-Radio uses the FMCW
technique as a filter –i.e., it uses it to isolate the reflected sig-
nals arriving from different distances in the environment into
different buckets, before it proceeds to analyze the signals in
each of these buckets to extract the vital signs (step 2 below).
Our implementation of FMCW follows the system in [6],
where the resolution of FMCW buckets is about 8 cm. This
has two implications:
•
Reflections from two objects that are separated by at least
8 cm would fall into different buckets. Hence, two users
that are few feet apart would naturally fall into different
buckets. For example, in Fig. 2, the wall, Bob, the table,
and Alice are at different distances from our device, and
hence FMCW isolates the signals reflected from each of
these entities into different buckets, allowing us to focus
on each of them separately.
•
Using FMCW as a filter also allows us to isolate some of
the limb motion from chest movements due to breathing
and heartbeats. For example, the signal reflected off the
user’s feet will be in a different bucket from that reflected
off the user’s chest. Thus, having the user move his feet
(in place) does not interfere with Vital-Radio’s ability to
extract the breathing and heart rate.
After bucketing the reflections based on the reflector’s dis-
tance, Vital-Radio eliminates reflections off static objects like
walls and furniture. Specifically, since static objects don’t
move, their reflections don’t change over time, and hence can
be eliminated by subtracting consecutive time measurements.
At the end of this step, Vital-Radio would have eliminated
all signal reflections from static objects (e.g., walls and furni-
ture), and is left with reflections off moving objects separated
into buckets.
2
Step 2: Identifying Reflections Involving Breathing and
Heart Rate
Heartbeats'
1.5
1
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.9
Phase (in radians)
Exhale'
0.95
1
1.05
1.1
1.15
1.2
1.25
Time (in minutes)
1.3
1.35
1.4
0.5
0
-0.5
-1
-1.5
0
0.2
0.4
0.6
Inhale'
0.8 1 1.2 1.4
Time (in minutes)
1.6
1.8
2
Figure 3—Phase variation due to vital signs.
The figure shows
the variations in phase due to breathing and heartbeats, where peaks
and valleys in the phase correspond to exhale and inhale motions
respectively; also, zooming in on the signal allows us to observe the
heartbeats modulated on top of the breathing motion.
where
λ
is the wavelength of the transmitted signal, and
d(t)
is the traveled distance from the device to the reflector and
back to the device. The above equation shows that one can
identify variations in
d(t)
due to inhaling, exhaling, and heart-
beats, by measuring the resulting variations in the phase of the
reflected signal.
To illustrate how the phase varies with vital signs, let us con-
sider the example in Fig. 1, where a user sits facing the device.
When the person inhales, his chest expands and gets closer to
the device; and when he exhales, his chest contracts and gets
further away from the device. Because the phase and the dis-
tance to a reflector are linearly related, Vital-Radio can track a
person’s breathing. Fig. 3 shows the phase of the captured re-
flection as a function of time. Specifically, a peak in the phase
corresponds to an exhale (highest distance from the device),
and a valley in the phase corresponds to an inhale (smallest
distance from the device). We note that our implementation
uses a wavelength
λ
around 4.5 cm. According to the above
equation, sub-centimeter variations in the chest distance due
to breathing cause sub-radian variations in the phase, which
is what we observe in the figure.
Similarly, a person’s heartbeats cause minute movements of
different parts of his body. Specifically, the physiological
phenomenon that allows Vital-Radio to extract heart rate from
signal reflections is ballistocardiography (BCG). BCG refers
to movements of the body synchronous with the heartbeat due
to ventricular pump activity [36]. Past work has documented
BCG jitters from the head, torso, buttock, etc. [5, 8]. Periodic
jitters cause periodic variations in the wireless signal allow-
ing us to capture the heart rate. These movements translate
to smaller fluctuations on top of the breathing motion in the
wireless reflection as we can see from local peaks in Fig. 3.
Note that the periodicity of breathing and heartbeats is inde-
pendent of the user’s orientation. For example, if the user
has his back to the device, the valleys become peaks and vice
versa, but the same periodicity persists.
Still, an important question to answer is: what happens when
a person moves around or moves a limb, and how can Vital-
Radio distinguish such motions from breathing and heart-
After Vital-Radio isolates reflections from different moving
users into separate buckets, it proceeds by analyzing each of
these buckets to identify breathing and heart rate. For exam-
ple, in Fig. 2, we would like to identify whether the user in
bucket 2 is quasi-static and his motion is dominated by his vi-
tal signs, or whether he is walking around or moving a limb.
To do that, Vital-Radio zooms in on the signal reflection
which it isolated in the corresponding bucket. This wireless
reflection is a wave; the phase of the wave is related to the
distance traveled by the signal as follows [39]:
d(t)
φ(t)
=
2π
,
(1)
λ
While unlikely, it is possible that multiple users are at the same
distance from the device and hence fall into the same bucket. To
deal with such cases, one may deploy multiple devices so that if two
users are at the same distance with respect to one device, they are at
different distances with respect to another device.
2
3
2
1
0
-1
-2
-3
0.4
Phase (in radians)
300
FFT Magnitude
200
100
0
Peak at
Breathing Rate
Breathing
Limb Motion
0.5
0.6
0.7
0.8
0.9
Time (in minutes)
1
1.1
1.2
0
10
20
30
40
50
Breathing Rate (breaths per minute)
60
Figure 4—Limb motion affects vital sign monitoring.
The figure
shows the subject breathing until right before the 1 minute mark
where he waves his hand. The device eliminates time intervals when
such motion happens.
Figure 5—Output of Fourier Transform for Breathing.
The fig-
ure shows the output of the FFT performed on the phase of the signal
of Fig. 3. The FFT exhibits a peak around 10 breaths/minute, pro-
viding a coarse estimate of the breathing rate.
Step 3: Extracting Breathing and Heart Rate
Breathing Rate Extraction
beats? To help answer this question, we show in Fig. 4 a
scenario where the user waves his hand before the one minute
mark resulting in aperiodic phase variations of the signal.
To deal with such scenarios, Vital-Radio exploits that mo-
tion due to vital signs is periodic, while body or limb mo-
tion is aperiodic. It uses this property to identify intervals
of time where a user’s whole body moves or where she per-
forms large limb movements and discards them so that they
do not create errors in estimating vital signs. To achieve this,
Vital-Radio operates on time windows (30 seconds in our im-
plementation). For each window, it measures the periodic-
ity of the signal. If the periodicity is above a threshold, it
determines that the dominant motion is breathing and heart
rate; otherwise, it discards the window. A typical approach to
measure a signal’s periodicity is evaluating the sharpness of
its
Fourier transform
(or FFT) [10]. Hence, we perform an
FFT on each window, choose the FFT’s peak frequency, and
determine whether the peak’s value is sufficiently higher than
the average power in the remaining frequencies.
3
This metric allows us to maintain intervals where a user
does not perform large limb movements, including scenarios
where the user types on her laptop or checks her phone. This
is because, while these movements are indeed aperiodic, they
do not mask the breathing or the heart rate since their power
does not overwhelm the repetitive movements due to our vi-
tal signs.
4
Additionally, in some of these scenarios, the user’s
hands are stretched out to the laptop and away from his chest
as he is typing. As a result, the major part of his typing mo-
tion falls into a separate FMCW bucket than the user’s chest.
Naturally, because the human body is connected, hand move-
ments would still result in muscle stretches and minor shoul-
der jitters that are close to the user’s chest; however, because
such movements are weak and aperiodic, they are diluted at
the output of the FFT. In contrast, periodic movements due to
vital signs are enforced in the FFT operation, which results in
maintaining intervals of such quasi-static scenarios.
The above steps allow us to filter out extraneous motion and
focus on time windows where the dominant motion for each
user is the breathing and heart rate. In the following section,
we show how Vital-Radio extracts breathing and heart rate
from these intervals.
In our implementation, we choose this peak to be at least 5× above
the average power of the remaining frequencies.
4
Mathematically, these signals would appear as “white noise” in low
frequencies, and are filtered out in Step 3 of Vital-Radio’s operation.
3
Because breathing is a periodic motion, we can extract the
frequency (rate) of breathing by performing a Fourier trans-
form (an FFT). The peak at the output of the FFT will cor-
respond to the dominant frequency, which in our case is the
breathing rate. Specifically, we perform an FFT of the phase
signal in Fig. 3 over a 30 second window and plot the output
in Fig. 5. The peak of this signal gives us an initial estimate
of the person’s breathing rate.
However, simply taking the peak of the FFT does not provide
an accurate estimate of breathing rate. Specifically, the fre-
quency resolution of an FFT is 1/window
size.
For a window
size of 30 seconds, the resolution of our breath rate estimate is
≈
0.033Hz, i.e., 2 breaths/minute. Note that a larger window
size provides better resolution, but is less capable of tracking
changes in breathing rate. To obtain a more precise measure-
ment, we exploit a well-known property in signal processing
which states that: if the signal contains a single dominant fre-
quency, then that frequency can be accurately measured by
performing a linear regression on the phase of the complex
time-domain signal [33]. Hence, we perform an additional
optimization step, whereby we filter the output of the FFT,
keeping only the peak and its two adjacent bins; this filtering
allows us to eliminate noise caused by extraneous and non-
periodic movements. Then, we perform an inverse FFT to
obtain a complex time-domain signal
s
(t).
The phase of
s
(t)
will be linear and its slope will correspond to the breathing
frequency, i.e., the breathing rate. Mathematically, we can
compute an accurate estimate of the breathing rate (in terms
of breaths per minute) from the following equation:
slope{∠s
(t)}
Estimate
=
60
×
,
(2)
2π
where the factor of 60 transforms this frequency from
Hz
(i.e.,
1/second) to breaths/minute.
Heart Rate Extraction
Similar to breathing, the heartbeat signal is periodic, and is
modulated on top of the breathing signal, as shown in Fig. 3.
However, the breathing signal is orders of magnitude stronger
than the heartbeat. This leads to a classical problem in FFT’s,
where a strong signal at a given frequency leaks into other
frequencies (i.e., leaks into nearby bins at the output of the
FFT) and could mask a weaker signal at a nearby frequency.
To mitigate this leakage, we filter the frequency domain sig-
nal around [40-200] beats per minute; this allows us to filter

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