Signal Analysis

Pablo Laso Mielgo

April 2020 - June 2020

Contents

1 Introduction 2

2 ElectroMyoGraphy 2

2.1 Anatomical and Physiological Background on Muscle Physiology 2

2.2 Reading an action potential . . . . . . . . . . . . . . . . . . . . . 3

2.3 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.3.1 Preparing the skin . . . . . . . . . . . . . . . . . . . . . . 4

2.3.2 Activities and Signal Acquisition . . . . . . . . . . . . . . 4

2.3.3 Signal Processing . . . . . . . . . . . . . . . . . . . . . . . 4

2.3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 Physiological Signals 7

3.1 Physiological variables . . . . . . . . . . . . . . . . . . . . . . . . 7

3.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.2.1 Signal Acquisition . . . . . . . . . . . . . . . . . . . . . . 8

3.2.2 Signal Processing . . . . . . . . . . . . . . . . . . . . . . . 8

3.2.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4 Anthropometry 11

4.1 Variables and parameters . . . . . . . . . . . . . . . . . . . . . . 12

4.2 Environment and theory . . . . . . . . . . . . . . . . . . . . . . . 12

4.3 Mathematical Analysis . . . . . . . . . . . . . . . . . . . . . . . . 13

4.3.1 Anthropometry experiment . . . . . . . . . . . . . . . . . 13

4.3.2 Center Of Mass . . . . . . . . . . . . . . . . . . . . . . . . 13

4.3.3 Total Center Of Mass . . . . . . . . . . . . . . . . . . . . 14

4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.5 MATLAB emulation . . . . . . . . . . . . . . . . . . . . . . . . . 15

5 Personal opinion and Motivation 17

1 Introduction

The scope of this paper is to descr i be -with the aim of allowing re-productivity-

the steps carried out to process signals obtained in three diﬀ er ent experiments

and topics, speciﬁcally, EMG (Section 2), psycho-physiology (Section 3) and

Anthropometry (Section 4). In each section is included a detailed description

of the experiment, the post-acquisition processing steps that were carried out

in order to achieve the purpose of each experiment, and a ﬁnal conclusion de-

rived from the analyze d and processed data, considerin g the theoretical points

explained in each introductory sub-section. These three experiments namely

were ElectrMyoGraphy (Section 2), robot-aided rehabilitation (Section 3) and

a bio-mechanics study (Section 4).

Some informative, theoretical sections may also be included in order to be-

stow the reader wit h a perspective and basic knowledge into the matter of study.

2 ElectroMyoGraphy

This section delves into the theory of Muscle Activity. Within this s ect i on ;

in the ﬁrst section, we provide some insight into what is really occurring at

a molecular level. Section 2 deals with th e science that underl ays reading an

action potential. Section 3 d es cr i bes the experiment, including the preparation,

tasks, signal processing and a ﬁnal conclusion inferred from all the former sub-

sections.

2.1 Anatomical and Physiological Background on Muscle

Physiology

Most skeletal muscle ﬁbers are inner vated by a single motor neuron. Since

there more muscle ﬁbers than motor neurons, individual motor axons branch

in order to synaps e diﬀerent ﬁbers within the muscle over a wide area. Thus,

we ensure the exertion of a contractile force is spread e venly. (6) Motor units

are the basic fun ct i on al unit of the neuromuscular system. (2) It is also worth

mentioning muscle ﬁbers, which cover muscle t i ss ue and the sarcolemma.

An action potential arrives at the terminal bottom of a neuromuscular junc-

tion, stimulating the release of acetylcholine, which diﬀuses across the cleft and

triggers an action potential in the muscle ﬁber. It arrives via the T tubules onto

the sarcoplasmic reticulum, triggering the release of Ca

into the cytosol.

The molecules of Ca

binds on troponin thin ﬁlaments, which induces in it

a change of shape. Thus, the b i nd i ng sites of actin are uncovered for the myosin

cross bridges to attach. ATP molecules give the energy for this bridges to bend,

pulling the ﬁlament towards the center of the sarcomere. After such stroke, if

there is Ca

still pr e sent, the myosin cross bridges are created anew, repeating

the same process . (4)

Figure 1: Left: Motor Unit (6). Ri ght: Muscular Contraction at th e Molecular

Level

2.2 Reading an act io n po te ntial

The action potential that initiates all these afore-described, physiological pro-

cesses can be recorded by the proper positioning of the electrodes and enhanc es

by sub-sequential adequate manipulation (2). More speciﬁcally, we must con-

sider that the cellular membrane is negatively charged in the inside and pos-

itively in the outside (due to proteins and other intrinsic components, like he

Na/K pump ), having a potential diﬀerence ranging from -70mV up to -90mV.

In that case, the membrane is initially at rest, that is, polarized. As the impulse

arrives, the membrane depolarizes (if a threshold is achieved) and the poten-

tial diﬀerence increases (grows positive) -as Na

rushes in the inside of the

membrane- and repolarizes as K

. It may al s o happen that the cell membrane

is hyperpolarized, that is, it goes below th e resting potential (2). Generally,

however, this process is repeated and tran sm it t e d along the nerve,showinga

behaviour that resembles that of a dipole, at a speed of 2-3m/s. In Figure 2,

we can observe such transmission (le ft ) and the sum of diﬀerent signals(left)

which, depending on the distance t o the surface, will arrive weaker or stronger.

Therefore, since the electrodes are indeed in the surface of our skin, we should

not expect any pattern in the signal that reaches our electrodes.

2.3 Experiment

The experiment referred in the foll owing sub-sections was performed indepen-

dently of our work. We shall retake the work performed in other years by

students in UCBM as our data source, and use it in our project, which will deal

mainly with pro ce ss in g of such signals by means of MatLab s oftware.

Figure 2: Left: Electrical Dipole (7). Right: Distance and Signal received.

(8)

2.3.1 Preparing the skin

We do, nonethele ss , highlight some key aspects to bear in mind while repro-

ducing the experiment. Small elect rodes will have higher selectiv i ty and l ower

cross-talk, but also highe r impedance. A proper balance was attained with

electrodes having a diameter between 1 and 2cm, which can be adhesive (han-

dleable) or gel (lower imp ed an ce ) . For slow movements, alcohol is enough to

prepare the s ki n before the experiment, which should be properly cleansed to

enhance signal rece pt i on . Besides, elect r odes must always be parallel to the

muscle ﬁber and cannot be detached during muscle contraction.

2.3.2 Activities and Signal Acquisition

Several records were taken. Firstly, in or de r to later be able to norm al iz e all

our data, we took two MVC ( Max imum Voluntary Contraction), both from t he

biceps and the triceps, in which the patient was asked to exert all the f or ce

they could in three se qu ential occasions, during an overall 5s interval, b oth for

triceps and bice ps . After that, sixteen signal samples were obtained in diﬀerent

conditions, namely, half of them having the patient seated and half standing.

Each subset in turn halved in loaded or unloaded (depending whether the patient

held or not a weight). Each one of them was performed at a diﬀerent angle -

precisely, 45, 90 135, 180

- for a 15s interval. Figure 3 shows the positions that

the patient adopted during the experiment just described.

2.3.3 Signal Processing

The EM G signal that our receptor receives from our muscles ranges in frequency

from 6 to 500 HZ. However, from theory, we know that the frequency spectrum

in which our signal is strongest in the interval between 20 and 550 Hz (2) (4).

Therefore, if we take this interval only, we ensure a much higher SNR,whichis

easily achieved by a sim pl e but t e rworth pass-band ﬁlter between 20 and 350Hz,

as well as an order of 4 (steeper cut-oﬀ slope). Furthermore, we not i ce that the

network might have introduced a 50Hz noise signal, which is to be eliminated by

Figure 3: Positions adopted by pat i ent during EMG experiment for signal ac-

quisition.

a notch ﬁlter of such frequency and some units -say, 2- as mar gi n. Furthermore,

although our signal is not perfectly sym met r i cal , we just need one side of the

x axis to correctly interpret it. Such procedure is called rectiﬁcation. Finally,

we take the envelope of the resulting signal, that is, the ”shape” or ”outli n e” of

it. Similarly to the r eas oni n g in the previous step, this might yield a diﬀerent

signal but actually enhances human interpretability. We can see the results of

such procedure in Figure 4.

Figure 4: EMG signal from biceps (above) an d triceps (below) and the processed

envelope signal.

We also use the MCV that we mentioned before to normalize our data. To

do so, we use a software interface li ke MATLAB to extract the three intervals

in wh i ch the patient is exerting force. We plot all of them together in F igu r e

5. The dashed black line shows the mean of, in turn, the mean of the values

(biceps or triceps) that overcome a threshold of 0.7 times the maximum value.

2.3.4 Conclusions

We can see from Figure 5 that all contraction are more or less equal. We al so

note that it is precisely on the third biceps contraction that the patient performs

better and longer, which might be a sign of he al th , since he does not seemto

grow fatigue. Finally, since the patient is exerting maximal force, hemustbe

using both biceps and triceps muscles, so there is actually a correlation between

Figure 5: Left: MVC Biceps Estimation. Right: MVC Triceps Estimation.

them. In fact, albeit stronger in the bice ps , muscle activi ty is high in both,

unlike in the following exercises, whe r e the patient was told to lift a weight and,

depending on the degree that the arm holds it, would use one muscle more than

the other. For the sake visu al iz at ion , we plot Figure 6.

Figure 6: Biceps and triceps activity for all conﬁgurations that the patient did.

In Fig. 6 we can observe how subplots representing no load conﬁgurations

show no sign of force, since no load is heaved and therefore, muscles are relaxed.

However, sub-ﬁgures representing forces are diﬀerent dep e nd i n g not only on the

angle, but also on whether the patient is seated or standing. More precisely,

when the patient lifts a 5 Kg load and maintains an ar m position with a degree of

135

, the biceps must be highly active in order to sustain that weight. However,

when seated and when the degree is lower, that is, the patient brings the weight

closer to the bo dy, muscle activity diminished signiﬁcantly, even if loaded. This

is the case of 45

and 90

. In this case it is also interesting to notice that the

triceps is exerting, exception al ly, a larger force than the biceps is. This is due

to the fact t hat such position demands a larger eﬀort by the triceps, since the

weight is already close to the bo d y and contracting the biceps would not have

much sen se . It is i nteresting to note that the triceps, which usually serves as

an antagonist -that is, a muscle that produce an opposing joint torque to the

agonist muscle, the biceps- has actually a function other than retrieving the

arm to its original position. In some circumstances, like this one, the gravity

or the circumstances are not enough and the fore of the triceps is required. On

the contrary, if the patient must hold the weight at such angles when standing,

the force he must exert is much greater, as observable in the two right-most

columns of Figure 6. Similarly, in the case of a 180

degree posture, the force

will be much larger if the pat ie nt is seated (5L) than that when he is on hisfeet

(1L), since, in the former case, the with must be maintained perpendicular t o

gravity whereas, in the latter case, i t is parallel to the gravity vector and the

weight is sustained by the bone joint, rather than th e muscle.

Overall, we conclude that the force of the biceps is usually much greater

than that of the tr i cep s, but the function of the triceps as an antagonist i s not

to be disregarded and sometimes it can have more importance than the biceps,

like the case in which the patient was seated in a 45

position.

3 Physiological Signals

This section tackles the science of Physiology, and how it can be closely related

with Psychology. The ﬁrst section describes the variables and mention physi-

ological st at us related to them. Section 2 describes the experiment,including

signal acquisition, processing and, ﬁnally, an elaborated conclusion.

3.1 Physiological variables

Throughout the experiment, we will be using all types of physiological signals,

namely, Galvanic Skin Response (GSR), Heart Rate (HR), Heart Rate Variabil-

ity (HRV) and Respirat i on Rate (RR).

With these variables, we hope to accurately distinguish between moments of

stress, fatigue and attention in our patient.

The GSR is obtained from the changes in conductance on the skin, due

to, for instance, the sweat. It can be distingu i sh ed (by the methods described

in sect i on 3.2.2) into SCL (baseline, tonic level) or SCR (skin response). The

former is a clear s i gn of stress while the latter might also mean attention. HR

is just the beats of the heart per mi nute and HRV its variability, inversely

proportional betwixt them. HR is a sign of stress and attention, whereas HRV

is unequivocally present in fatigue. RR refers to respirations perminute. Itis

highly present in st r es sf ul situation while it is less wont to appear in moments

of attention or fatigue.

3.2 Experiment

The e x periment was carried out upon a patient that presented back discomfort.

A robot (connected to the patient by a hand supp or t ) made him follow a series

of movement patterns, namely, an approaching movement t o take an object,

and that of returning to the original point. This dual pattern is repeated eighty

times (2).

3.2.1 Signal Acquisition

During the afore-described experiment, multiple sensors were recording diﬀerent

physiological activity from the patient, speciﬁcally, the Galvanic Skin Response

(GSR), Heart Rate (HR), Heart Rate Variability (HRV), Respirati on Rate (RR)

and Rob ot Motion (RM).

Amongst the data gathered during the experiment, we ﬁnd the Galvanic

Skin Response, Heart Rate, Heart Rate Variabili ty, Respiration Rate and Robot

Motion. If represented along time, as in Figure 7, we notice some changes at the

time that the robot is started (Robot Motion variable goes up to one), marked

with horizontal black lines in each graph (2).

Figure 7: Experimental parameters represented along time.

3.2.2 Signal Processing

As we can see in Figure 7, we have recorded th e GSR. The GSR signal was

low-pass ﬁltered at 5Hz using a butterworth ﬁlter (MatLab in-built function)

and ﬁltﬁlt() MatLab function. This allows us to remove motion artefacts (9).

The resulting ﬁltered signal, however, can give rise, in turn, to two more

meaningful variables if properly deri ved. Applying a Low-Pass Filterwitha

cutoﬀ frequency of 0.1Hz will yield the low-frequency component of the signal,

that is, the Skin Conductance Level (SCL). The SCL represents the baseline

or tonic level, given by the hydration or dryness of the skin. In p rac t ice, this

is done by means of a butterworth ﬁlter, which also dephases our signal, but

can also be recovered with the MatLab function ﬁltﬁlt. The result for both the

SCL and SCR is shown in Figure 8. It is noteworthy the fact that the SCR

component ﬂagrantly shows a higher-frequency behaviour than that of SCL.

Also, there is a correlation between frequency in SCR a and amplitude i n SCL,

due to the manner in which we derived both components. Therefore, ifwewere

to analyze the baselin e of our patient, we ought t o focus on the area where the

robot was still not active. Note, however, that it does take some time for the

SCR signal to arise and make noticeable changes from t he moment that the

robot was initially activated.

Figure 8: Experimental parameter s SCL and SCR (components of GSR), rep-

resented along time.

The next step is to compute the p hysiological response, that is, the response

from our body to a given stimuli. For such purpose, we cannot directly analyze

the active-robot area but rather compare it with the baseline, that is, study

those physiological changes that were recorded in a patient when he perceived

certain stimuli, compared with his tonic, res t in g stat e. In practice, what we did

was splitting our samples from the starting point to the last point before our

robot went active (value of 1, in graph). After that, we took the mean of each

parameter within the inactive-robot region and computed its baseline by means

of Eq. 1, where x

norm

is the normalized value of each sample in the active-robot

region x, with respect the mean or x

baseline

norm

x − x

baseline

(1)

Then, we divide th e ti me ax i s for each variable into minutes and take the

mean in each one, as shown in Figures 9 and 10.

After which, we can ﬁnd any signiﬁcant (10% of the maximal value) varia-

tions in our signal means, i. e. , we evaluate whether there exists an increase or

a decrease in our signal so as to later estimate which physiological indicator is

correspondent with such variations. Similarly, we take the peaks in ourSCR

signal, that is, those valu es with a minimum distance of 25 samples that are

able to reach a threshold of 0.03 µS.

Now that we kn ow how the diﬀerent variables vary over time (increase or

decrease wit h respect to previous values), we use this as a way of comparison

Figure 9: The mean of each paramet e r per minute of si gnal acquisition, plotted

over the s ign al .

Figure 10: The mean of each parameter per minute of signal acquisition, as

bars.

with the expected values of each physiological status that we are studying, i.e.,

stress, attention and fatigue. In practice we just assign 1 or -1 depending on

whether the r e is an increase or decrease. We stor e these vectors as columns in a

matrix and confront them one by one with our expected values. With the aim

of setting a threshold for properly selecting the status, as well as overcoming

possible noise or un ex pected events that can happen in experimental, real-life

situations, we require at least three (out of ﬁve) conditions to hold true for a

decision to be deemed true. Thus, we can plot the diﬀerent results and analyze

the variation of each state per minute, as shown in Figure 11.

3.2.3 Conclusions

We note in Fig. 11 that the patient seems to have normal or low values in

all status, at the beginning of the test. Soon, we can observe an i n cr eas e in

stress, usually followed by an increase in attention, which makes, indeed, much

sense, since some stress may help the patient maintain the attention needed

to perform the required task. As those variables increase, the physiological

Figure 11: The physiological status of a p e r son per minute; below, the rest of

variables.

parameters ind ic at in g energy seem to r i se at ﬁrst, maintain a constant,medium

level afterwards, and ﬁnally start decaying, probably due to the continuous eﬀort

that the patient is exerting.

In Fig. 10, we can readily see how the HR is constantly increasin g, be it due

to stress, attention or both, and re aches maximum values at the last minutes of

the test. However, the RR is not always kept at high levels. RR seems to increase

at ﬁrst, which suggests, along with a high HR, that our patient might be stressed

but then decreases, while RR simultaneously increases, as well as SCL, which

can be a clear sign of at t ention, since the patie nt might be focusing harder on

the task. Just after that, especially in the last mi nutes as we approach the end

of the test, HR decreases and both components of GSR decr eas e, as opposed to

what would be expected from attention moments. This might be an indication

of fatigue, which is also observable in Fig. 11 by a decrease in energy levels.

4 Anthropometry

Anthropometry refers to the measurement of the human individual. In Section

4.1, we present the variables and parameters used. In Section 4.2, we describe

the theory from what could be real-life case. We will be studying, within Section

4.3, the mathematical analysis to implement these parameters. In Section 4. 4

we study the COM path for diﬀerent velocities and derive an inference from the

diﬀerent p att e rn s that appear. In Section 4.5, we show t he motion of a person

-that is simpl y walking- through the theoretical concepts derived from the afore-

mentioned sections. Furthermore, we will be emulating the body motion in the

MATLAB environment.

4.1 Variables and parameters

There are a set of variables or parameters that must be deﬁned in the MATLAB

script and are obtained from the table st u di ed in Anthropometry theory (2).

In order to carry out the mathematical comp ut at i ons in Section 4.3, we will

need the variables from the table in the Anthrop omet r y theory (2). Speciﬁcally,

we will need α

=0.061, from which we wil l be able to obtain the mass M

M · α

, used in later secti on s. Also note that the gravity is commonly expressed

as g =9.81 and the length of the table as l = 2.

4.2 Environment and theory

A man is seated in a ﬁxed spot, his legs hanging in the air. A sensor is aboveits

ankle, recording motion i n the x direction, and a mass is att ached to its ankle

by a system of pulleys. Θ is the angle of i t s leg; x, the displacement.

Patient’s initial position is as illustrated in Figure 14. The weight attached

to the patient’s ankle by a system of pulleys is pulling his leg forward. The leg

is, at ﬁrst, pushed backwards and, then, left free.

As shown in Figure 14 (Right), we compute all parameters in the leg system

from the values shown in the left-hand side of the equations, namely b, l

, l

and l

Figure 12: Patient’s initial position ( Le ft ) and the schematic representation of

the leg as a s y s t em (Right).

In a second experiment, a man is laying down on a 2m table, as shown in

Fig. 13.

Figure 13: Patient’s initial position (Left), laying face-down on a table, and

same patient lifting their feet (Right).

4.3 Mathematical Analysis

In this section, we describe all the mathematical procedures for both the anthro-

pometry study (ﬁrst sub-section), and software emulation (later sub-sections).

4.3.1 Anthropometry experiment

We use our theory knowledge f rom Reference (2) to compute the unknown

parameters, sp ec iﬁ cal l y ρ. Note that, in order to ﬁnd such parameter, we must

ﬁrst carry out the following operations to ﬁ nd the require d variables that will

lead us towards ρ.

= m · l

.· (2)

(3)

From Eq. 2 we can ﬁnd ρ

in Eq. 3. Then we ﬁnd the regression line for l

and ρ

. Similarly, we use equation 5 to ﬁnd l

, aided by Eqs. 4 and 6.

b =(s − s

) ·

(4)

= l

− M

· b

(5)

(6)

Once again, we ﬁnd, in the same manner as before, Eq. 7 with the help of

Eq. 8, for the distal components.

= l

+ M

· (l

− b)

(7)

(8)

Finally, we compute the regre ssi on be tween I

and the diﬀerent ρ values,

namely, ρ

, ρ

, as shown in Fig. 15.

4.3.2 Center Of Mass

Throughout the experiment, we must compute the center of mass between sev-

eral parts of our body, where our markers are placed, for instance, feet at the

bottom, or trochanters in the femur. We can do so by means of E q. 9.

marker

· (1 − b)+marker

· b (9)

Figure 14: Patient’s data used in mathematical step in Section 4.3. S on the

right and Mass on the Right.

Figure 15: Linear regression models for each ρ value.

Also note th at we might need to hypothesize to ﬁnd some in-between mark-

ers. For example, the pelvis will be in the middle of each throcanter, but L4

(lumbar region, 4th vertebrae) will be found between C7 (cervical region, 7th

vertebrae) and the pelvis.

4.3.3 Total Center Of Mass

The total center of mass is computed by multiplying each center of mass by the

mass corresponding to such se gme nt. It must be divided by the mass of the

patient. Note that each leg must be consi d er ed twice, while pelvis or thorax,

just once. Such equation is d esc r ibed in Eq. 10.

A = com

· m.T + com

· m.S + com

· m.F + com

· m.T

B = com

· m.S + com

· m.F + com

· m.T A + com

· m.P

A + B

2 · m.T +2· m.S +2· m.F + m.T A + m.P

(10)

Figure 16: COM paths for diﬀerent speeds.

4.4 Conclusions

Regarding the last experiment, conduc t ed on MatLab, we can study the Center

of mass (COM) path in coronal pl ane (X-Z) across range of walking speeds.

With such aim, we shall plot the diﬀerent COM paths for the diﬀerent speeds,

as shown in Fig. 16. It is observable that the COM path seems to foll ow an

inﬁnite-shaped (∞) pattern, especially for v03. We can also appreciate from the

same ﬁgure that, as the speed increases, so does the pattern b ec ome more U-

shaped, more ﬂagrantly in v06 (10). Mathematically, the values in which theZ

axis ranges is (-686.9, -596.8), (-677.6, -631.5), (-662.8, -626.1), for v03, v05 and

v06, respectively. Clearly, the range of values reduces as the speed i n cr eas es. In

the Y axis, however, repeat i ng analogously the mathematical steps, we obtain

(583.3, 605.3), (585.2, 599.9), (586.9, 605.6). In this case we can deduce that

increasing the speed does not signiﬁcantly reduce the range of values on the Y

axis. Thus, reducing the values on the Z axis but maintaining constant those in

the Y axis, the COM path patt er goes from a inﬁnite shape to a U-ish shape.

4.5 MATLAB emulation

In this section, we present some of the photo-frames of our MATLAB-based

software emulation. The script was built from the theoretical concepts described

above but, obviously, a skilled software implementation is req ui r ed to take it to

practice, as shown in Figure 17.

1 2 3

4 5 6

Figure 17: Several ordered, r an dom photo-frames from the MATLAB software

emulation.

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