Time-frequency based Coherence and Phase Locking Value Analysis of

Human Locomotion Data using Generalized Morse Wavelets

Sopapun Suwansawang

1,2

and David M. Halliday

Department of Electronics, University of York, York, U.K.

Department of Electronics, Faculty of Science and Technology, Nakhon Pathom Rajabhat University,

Nakhon Pathom, Thailand

Keywords:

Analytic Wavelets, Phase Synchronization, Cone of Inﬂuence, Non-stationary Analysis.

Abstract:

Time-frequency analysis is a powerful and popular tool for studying time-varying properties of non-stationary

neurophysiological signals. In this study, time-frequency based coherence and phase locking value (PLV)

analysis using generalized Morse wavelets are presented. The methods are applied to pairs of surface EMG

signals recorded from leg muscles during treadmill walking in healthy human subjects. Time-frequency

based coherence and PLV analysis in this study detect similar patterns of 8-15 Hz and 15-20 Hz common

modulation of EMG during locomotion. Our results suggest that a combination of both methods would be

suitable for investigating and characterising non-stationary neurophysiological data. An understanding of the

basic principles of normal locomotion can further provide insight into pathological locomotion deﬁcits.

1 INTRODUCTION

Human locomotion can be characterised by rhythmic

activity that is governed by a series of complex

interactions between the human brain and the

spinal cord. These interactions can be analysed

by recording electromyograms (EMG) from human

muscles (Grosse et al., 2002; Halliday et al., 2003).

An analysis of human movement is a process

to investigate the characteristics of human body

movement that relates to both normal and abnormal

movement (Farmer et al., 2007; Tuncel et al., 2010).

Understanding human movement or how the brain

controls the muscles could help in recognising the

ﬁrst stages of many movement disorders, such as

Parkinson’s disease.

Analysis of the frequency content of

electrophysiological signals are useful ways to

examine neuronal synchrony (Grosse et al., 2002).

Time-frequency analysis has been used extensively

in studying time-varying properties of non-stationary

neurophysiological signals (Tuncel et al., 2010;

Allen and Mackinnon, 2010). Time-frequency

coherence analysis is one of the methods used

to represent signals whose frequency content is

varying with time (Zhan et al., 2006). This analysis

can be performed by mapping a one-dimensional

signal in the time domain into a two dimensional

representation in time-frequency product space.

Phase synchronisation is used to study phase

relationships between physiological signals (Quyen

et al., 2001; Lowet et al., 2016). Both time-frequency

coherence and phase synchronisation analysis can be

used to investigate and characterise non-stationary

neuronal coupling mechanisms, and provided

essentially the same information in frequency domain

(Mezeiov

a and s, 2012). However, coherence

analysis depends on two factors: phase consistency

and amplitude covariation of signals (Quyen et al.,

2001). Phase synchronisation analysis provides the

phase component that can be obtained separately

from the amplitude component for a given frequency

or frequency range (Quyen et al., 2001).

The wavelet transform is increasingly applied

in dynamic neurophysiological signal analysis in

both time and frequency domain (Tuncel et al.,

2010; Zhan et al., 2006; Quyen et al., 2001;

Hassan et al., 2010). There are a number of

wavelet families that are used in order to identify

the appearance of oscillations and other signal

properties. Currently, the continuous analytic wavelet

transform is more widely used for the analysis

of modulated oscillatory signals and discontinuities

(Lilly and Olhede, 2010). The generalized Morse

wavelets are exactly analytic wavelets that have been

used to estimate characteristics of non-stationary

Suwansawang S. and Halliday D.

Time-frequency based Coherence and Phase Locking Value Analysis of Human Locomotion Data using Generalized Morse Wavelets.

DOI: 10.5220/0006111800340041

In Proceedings of the 10th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2017), pages 34-41

ISBN: 978-989-758-212-7

neurophysiological signals (Brittain et al., 2007;

Nakhnikian et al., 2016). A particular subset

of the generalized Morse wavelets, Airy wavelets,

substantially outperforms the approximately analytic

Morlet wavelets (Lilly and Olhede, 2010).

In this study, generalized Morse wavelets are

applied to calculate time-frequency based coherence

and phase locking value for ten experimental data

sets: surface EMG during treadmill walking in

healthy subjects. Our aim is to compare results

from the two methods. The structure of the paper

is organised as follows. First, we introduce the

motivation and background of the study. Second,

we provide a brief review of methodologies, with

details about each of the required steps for their

implementation. Third, we provide the detail of

experiment data. Fourth, we illustrate the results of

the experiment data. Fifth, we discuss our results

in light of previous ﬁndings. The paper ends with

suggestions for future work.

2 METHODS

This section provides details of analytical methods

analysing non-stationary physiological signals.

Section 2.1 describes generalized Morse wavelets,

section 2.2 considers edge effects, section 2.3 gives a

summary on the time-frequency coherence estimates,

and section 2.4 presents the concepts of phase

synchronisation analysis.

2.1 The generalized Morse Wavelets

Generalized Morse wavelets are a promising class

of complex-valued exactly analytic wavelet transform

with vanishing support on negative frequency

axis, while the popular Morlet wavelet is only

approximately analytic wavelet for sufﬁciently large

radian frequency (Lilly and Olhede, 2009).

Generalized Morse wavelets are highly ﬂexible

and form a two-parameter family of wavelets. A

deﬁnition of zero-order (k = 0) generalized Morse

wavelets in the frequency domain form is provided

in (Olhede and Walden, 2003) as

β,γ

(ω) =

√

2H(ω)A

k;β,γ

−ω

(1)

where H(ω) is the Heaviside unit step function and

k;β,γ

is a normalising constant that can be expressed

k;β,γ

πγ2

Γ(k + 1/Γ(k + r)) (2)

where Γ(•) denotes the gamma function and r =

(2β + 1)/γ. The maximum amplitude occurs at the

peak frequency (Lilly and Olhede, 2009),

β,γ

≡





(3)

The rescaled second derivative of the

frequency-domain wavelets evaluated at its peak

frequency is P

β,γ

≡ βγ, and P

β,γ

is called the

dimensionless wavelet duration (Lilly and Olhede,

2010), deﬁned as

β,γ

≡

βγ (4)

The time domain form for the generalized Morse

wavelets may be expressed by the inverse Fourier

transform,

β,γ

(t) =

2π

∞

√

k;β,γ

−ω

iωt

dω (5)

β and γ are two parameters controlling

time-frequency localisation. The parameter β

controls the time-domain decay, and γ controls the

frequency-domain decay. Normally, β and γ are

greater than zero. An example of one member of the

generalized Morse wavelet family, the γ = 3 family

with β = 3, 9, and 27 is shown in Figure 1. The

γ = 3, called Airy wavelet, was found to have zero

asymmetry in time domain and is nearly symmetric

in the frequency domain. The Airy wavelets not only

preserve the spirit of the Morlet wavelet but also

substantially outperform the Morlet for high time

localisation while remaining analytic. More details

regarding the different roles of β and γ in controlling

wavelet properties can be found in (Lilly and Olhede,

2009), (Lilly and Olhede, 2012), and (Lilly and

Olhede, 2010).

0 0.5 1

β : 3, γ: 3, k: 0, P

β,γ

: 9, Energy: 1

−10 −5 0 5 10

−1

β : 3, γ: 3, k: 0, P

β,γ

: 9, Energy: 1

0 0.5 1

β : 9, γ: 3, k: 0, P

β,γ

: 27, Energy: 1

−10 −5 0 5 10

−1

β : 9, γ: 3, k: 0, P

β,γ

: 27, Energy: 1

0 0.5 1

β : 27, γ: 3, k: 0, P

β,γ

: 81, Energy: 1

Frequency (f)

−10 −5 0 5 10

−1

β : 27, γ: 3, k: 0, P

β,γ

: 81, Energy: 1

Time (t)

Figure 1: Examples of the generalized Morse wavelet for

γ = 3 and β = 3,9, and 27. , with time domain form ψ

β,γ

(t)

(left) and frequency domain form Ψ

β,γ

(ω) (right). In the

time domain, the solid line and the dashed line indicate the

real part and the imaginary part of the wavelet, respectively.

Frequency f is in cycles per second (Hz).

Time-frequency based Coherence and Phase Locking Value Analysis of Human Locomotion Data using Generalized Morse Wavelets

2.2 Cone of Inﬂuence

In practice, wavelet analysis is the convolution of

the signal and the wavelet function, therefore the

convolution will suffer edge effects. The region of

a wavelet transform affected by edge effects is called

the cone-of-inﬂuence (COI). Regions outside the COI

are neglected due to edge effects. In this paper, the

deﬁnition for identifying the COI is adapted from

(Torrence and Compo, 1998). The COI for the Morlet

wavelet is deﬁned by the e-folding time τ

√

which is chosen such that the wavelet power for a

discontinuity at the edge drops by factor e

−2

. To map

this approach to the generalized Morse wavelet, the

e-folding time at scale s can be deﬁned as

√

β,γ

(6)

where P

β,γ

and ω

β,γ

refer back to (4) and (3),

respectively. The e-folding time τ

will be used

to visualize the COI in time-frequency plots of the

wavelet power spectra, wavelet coherence and phase

locking value.

2.3 The Estimation of Time-frequency

Coherence

The analysis of time-frequency coherence requires the

estimates for cross spectrum and auto spectra of two

non-stationary processes. Considering two signals

x(t) and y(t), the continuous wavelet transform

expressions of their time-frequency representations

are W

(τ, f ) and W

(τ, f ). The time-frequency cross

spectrum between x(t) and y(t) signals is deﬁned as

(τ, f ) = W

(τ, f )W

∗

(τ, f ) (7)

and the time-frequency auto spectra of x(t) and y(t)

signals are given as

(τ, f ) = |W

(τ, f )|

(8)

(τ, f ) = |W

(τ, f )|

(9)

The time-frequency coherence expression is obtained

from equations (7), (8) and (9), the squared coherence

can be calculated by the squared magnitude of the

cross spectrum normalised by the auto spectra of each

signal, is given by

(τ, f )|

(τ, f )S

(τ, f )

(10)

In real situations, the auto-and cross-spectra

can be estimated for a series of repeat trials that

is computed by averaging across trials without

smoothing within trials (Zhan et al., 2006). The

procedure for estimating the time-frequency

coherence is outlined in equations (11)-(14), see

(Zhan et al., 2006) for details. The time-frequency

coherence is estimated from the cross spectrum

(τ, f ) and the auto spectra

(τ, f ), and

(τ, f ) as

(τ, f )|

(τ, f )

(11)

where

(τ, f ) =

∑

n=1

(τ, f )|

(12)

(τ, f ) =

∑

n=1

(τ, f )|

(13)

(τ, f ) =

∑

n=1

(τ, f )W

y∗

(τ, f ) (14)

where N is number of trials. Some assumptions are

required of data in order to formulate a conﬁdence

interval for coherence estimates. This is essential for

determining which values of coherence are reliable.

The conﬁdence interval means that the obtained

coherence value can be viewed as signiﬁcant if the

estimated coherence value exceeds the conﬁdence

interval. If the two signals are independent and

have Gaussian distributions, the distribution of the

coherence estimates is given by (Gish and Cochran,

1988)

Pr(R

≤ r) = 1 −(1 −r)

(K−1)

,0 ≤ r ≤ 1 (15)

where Pr(.) denotes probability distribution function,

r is the detection threshold value and K is the

number of windows used to estimate the spectrum.

For the conﬁdence interval value of 95%, the

detection threshold value for this conﬁdence interval

is computed as r

95%

= 1 −0.05

1/(K−1)

(Zhan et al.,

2006).

2.4 Phase Synchronisation Analysis

Phase synchronisation measures can be used to

study the relationships between the phases of

physiological signals. Phase synchronisation refers to

the phases of two coupled oscillators that synchronise

even if the amplitude ﬂuctuations between the

oscillating signals are uncorrelated (Pereda et al.,

2005). Synchronisation of weakly coupled oscillating

system appears as some relation between their

phase and frequencies (Rosenblum and Kurths,

1998). A general framework for studying phase

synchronisation has three main steps (Quyen and

Bragin, 2007): ﬁrst, pre-ﬁltering of the raw signal

with a bandpass ﬁlter around a chosen frequency

value. Second, estimation of the phase. Third,

BIOSIGNALS 2017 - 10th International Conference on Bio-inspired Systems and Signal Processing

quantiﬁcation of the degree of phase-locking. There

are two methods of phase estimation, one using

complex wavelets (Quyen et al., 2001; Lachaux

et al., 1999) (refer back to (1) and another using the

Hilbert transform (HT) (Tass et al., 1998). The main

difference between these two methods is that the HT

is actually a ﬁlter with unit gain at every frequency. If

the signal is broadband, pre-ﬁltering in the frequency

band of interest is required before applying the HT, in

order to get an appropriate phase value (Pereda et al.,

2005). On the other hand, pre-ﬁltering is unnecessary

when using a complex wavelet because it can act

as a bandpass ﬁlter and, at the same time, provide

separate values for the instantaneous amplitude and

the phase (Hassan et al., 2010). In this study, phase

synchronisation is calculated using generalized Morse

wavelets.

2.4.1 Phase Locking Value

Phase locking value (PLV) is an important measure

for investigating synchronisation of neural activity,

including the muscle activities detected by EMG.

In particular, (Tass et al., 1998) found that the

phase locking between the activity of primary

and secondary motor areas can be related to the

coordination of antagonistic muscles.

Analytically, the interaction between two

oscillating systems essentially affects the evolution

of their phases if the frequency ω

and ω

are in

resonance for some integers p, q, indicating the

ratios of possible frequency locking (for details

see (Wacker and Witte, 2011) and (Tass et al.,

1998)). The existence of locking or entrainment

between frequencies are close to rational relation,

pω

≈ qω

(Pereda et al., 2005). The generalised

phase difference of two series is given by

p,q

(t) = pφ

(t) −qφ

(t) (16)

where φ

(t) and φ

(t) are the unwrapped phases of

the signals. The principle of phase synchronisation

of periodic self-oscillatory systems corresponds to a

phase locking between two systems deﬁned as

p,q

(t) = |pφ

(t) −qφ

(t)| ≤ constant (17)

Here, as the aim is to detect functional connectivity

between two signals from the same physiological

system. The m:n synchronisation index mostly

considers the simplest case of p = q = 1. This

is used here. The local phase of the generalized

Morse wavelet transform for trial n at time τ and

frequency f is quantiﬁed from the ratio between

the imaginary part (ℑ) and the real part (ℜ) of the

wavelet transform,

(τ, f ) = tan

−1

ℑ(W

(τ, f ))

ℜ(W

(τ, f ))

(18)

The phase of a given time-series x(t) can be deﬁned

such that it is parameterized in the range φ

(τ, f ) ∈

[−π,π], with similar expressions for the phase of

time-series y, φ

(τ, f ). The phases are used to

calculate the phase difference between x(t) and y(t)

at time t. A representation of time-frequency phase

locking values over N trials between the signals

(Lachaux et al., 2000) is deﬁned as

PLV (τ, f ) =



∑

n=1

i(φ

(τ, f )−φ

(τ, f ))



(19)

PLV is a normalised measure that varies between

0 and 1, where a value of 1 means perfect phase

synchrony.

2.4.2 The Statistical Signiﬁcance Level of PLV

The statistical signiﬁcance of phase locking values is

determined by using surrogate series. These surrogate

series are created by shifting the trials of signal y

(see (Lachaux et al., 2000), (Pereda et al., 2005),

and (Gupta and James, 2007) for details). In this

study, the signiﬁcance level for PLV is considered if

the PLV is greater than the 95% conﬁdence interval

of the von Mises distribution of the mean of PLV

calculated from surrogate data. The percentage of

the linear Normal distribution (z=1.96) is used to give

the 95% conﬁdence interval for the mean direction in

Von Mises distribution. The value of conﬁdence limit

depends on the number of trials. A small number

of trials will result in a large conﬁdence limit. In

this study, for 380 trials, a PLV above 0.0538 is

statistically signiﬁcant at P < 0.05. For comparison

the 95% signiﬁcance level for coherence with 380

trials is 0.0079.

3 EXPERIMENTAL DATA

3.1 Data

Ten datasets were taken from the study of (Halliday

et al., 2003), using experiments to investigate the

functional coupling of motor units during treadmill

walking in healthy subjects. All subjects were made

to walk on a treadmill at normal speed. Paired surface

EMG electrodes were placed over two sides from the

ankle ﬂexor TA. Surface EMG was used to record the

aggregate muscle potentials (Mima et al., 2001). The

two EMG signals over the ankle ﬂexor can be used as

a substitute for pairs of motor unit recordings that can

identify any modulation in the functional coupling

during walking, and provide a basis for investigating

Time-frequency based Coherence and Phase Locking Value Analysis of Human Locomotion Data using Generalized Morse Wavelets

the highly adaptive nature of human gait patterns

(Halliday et al., 2003). Recordings were made over

a period of 500 seconds. A contact switch identiﬁed

heel strike. Thresholding of the heel strike record

provides a sequence of trigger times. These trigger

times provide a reference point within each step cycle

which is used to segment the data for undertaking

time-frequency analysis, where time is deﬁned with

respect to heel contact. Further details of experiments

are given in (Halliday et al., 2003). Examples of EMG

signals obtained from one subject during treadmill

walking are in Figure 2.

0 0.5 1 1.5 2 2.5 3 3.5

−2

−1.5

−1

−0.5

0.5

1.5

2.5

TA − EMG Channel 1

Time (s)

Voltage (V)

0 0.5 1 1.5 2 2.5 3 3.5

−2

−1

TA − EMG Channel 2

Time (s)

Voltage (V)

0 0.5 1 1.5 2 2.5 3 3.5

0.5

1.5

2.5

rectified TA − EMG Channel 1

Time (s)

Voltage (V)

Wind ow

0 0.5 1 1.5 2 2.5 3 3.5

0.5

1.5

2.5

rectified TA − EMG Channel 2

Voltage (V)

Time (s)

Wind ow

Figure 2: An example of paired surface EMG signals

obtained from one subject during treadmill walking, with

(top) the EMG signal before rectiﬁcation and (bottom)

rectiﬁed EMG signal showing analysis window.

3.2 Data Analysis

In this paper, the power spectrum, coherence and PLV

were computed using generalized Morse wavelets

with γ = 3 and β = 9. The aim is to investigate the

functional coupling between paired EMG signals in

the time-frequency domain. The standard practice

of rectiﬁcation of surface EMG signals has been a

commonly used pre-processing procedure that allows

detection of signiﬁcant coherence (Farmer et al.,

2007). EMG-EMG spectral and PLV analysis were

calculated using averages over 380-step cycles. All

steps were segmented into 1040 ms segments with

820 ms before heel trigger and 220 ms after heel

trigger. The time scale on time-frequency plots is

labelled as 0-1040 ms, heel triggers are at 820 ms in

these plots (Figure 3). Thus, each coherence and PLV

plot covers swing phase including early, mid, and

late swing for each step cycle. Examples of rectiﬁed

EMG signal and analysis window are provided in

Figure 2. The EMG-EMG coherence and PLV was

considered signiﬁcant if above the 95% conﬁdence

limits, calculated using (15) for coherence and in

section 2.4.2 for PLV. Signiﬁcant coherence and PLV

were observed at frequencies ≤ 50 Hz. All analyses

were implemented using MATLAB (The MathWorks,

Natick, MA).

4 RESULTS

Examples of time-frequency power spectra,

coherence and PLV from two subjects walking

at 4 km/h are shown in Figure 3. Figure 3A and B

illustrate estimates of spectra for each EMG channel.

Figure 3C and D illustrate time-frequency coherence

and PLV estimates between the EMG signals. Figure

3E and F illustrate line plots of the 8-to 15- and

15- to 20-Hz rhythmic components in coherence

and PLV estimates averaged over these frequency

ranges, respectively. Spectra are plotted as Log

values. Only coherence and PLV inside the COI are

represented on the line plots. The 95% conﬁdence

limit for coherence estimate in this study is 0.0079,

and 0.0538 for PLV based on analysis of 380 step

cycles. The black line indicates the COI in Figure

3A-D (see section 2.2).

Table 1: Summary of mean coherence and PLV from

380-step cycles for 10 subjects at frequency 2-50 Hz in

beginning, middle and end swing of the step cycle.

No. Coherence PLV

Begin / Mid / End Begin / Mid / End

1 0.28 / 0.24 / 0.44 0.54 / 0.46 / 0.60

2 0.34 / 0.41 / 0.44 0.46 / 0.52 / 0.57

3 0.34 / 0.40 / 0.43 0.45 / 0.52 / 0.55

4 0.40 / 0.33 / 0.43 0.54 / 0.46 / 0.56

5 0.42 / 0.36 / 0.45 0.55 / 0.48 / 0.57

6 0.45 / 0.43 / 0.62 0.57 / 0.55 / 0.77

7 0.41 / 0.39 / 0.47 0.57 / 0.55 / 0.61

8 0.46 / 0.42 / 0.57 0.60 / 0.54 / 0.65

9 0.48 / 0.43 / 0.57 0.61 / 0.53 / 0.64

10 0.50 / 0.41 / 0.50 0.64 / 0.53 / 0.64

The results suggest that the wavelet spectra of

EMG signals are similar over all subjects. There is

an increase in power in early, with a reduction in the

middle and then increase in late swing of the step

cycle (Figure 3A and B). Strongest coherence is at

frequency<5 Hz. In some subjects this low frequency

component persists across the swing phase (Figure

3D), in other subjects it is prominent in the early

and late phases of swing (Figure 3C). Note that some

of the low frequency coherence is outside the COI,

therefore potential edge effects should be taken into

account. In addition, weaker coherence between 8

BIOSIGNALS 2017 - 10th International Conference on Bio-inspired Systems and Signal Processing

A B

C D

E F

Figure 3: EMG-EMG wavelet coherence and PLV analysed from 380-step cycles, which segmented into 1040 ms non

overlapping epochs from two subjects, subject 1 (left column) and subject 10 (right column). A and B: estimates of spectra

for each EMG channel, C and D time-frequency coherence and PLV plots, E and F: line-plot of coherence and PLV estimates

at f = 8-15 Hz, and f = 15-20 Hz. Two horizontal dashed lines in E and F are the 95% conﬁdent limit for coherence estimates

(black) and PLV estimates (red).

and 20 Hz occurs in early and late swing. PLV has

signiﬁcant features in both time and frequency which

are similar to those seen in coherence estimates; see

Figure 3C-F.

Some aspects are common across all the

experiments as illustrated in Table 1. The magnitude

of the correlation between paired EMG signals is not

constant over the step cycle. For 8 of the 10 subjects,

the magnitude of the coherence and the PLV reduce

during the mid swing of the step cycle. Two of the

subjects (subjects 2 and 3) have magnitude in the

early swing that is smaller when compared to mid

and end swing. A signiﬁcant low-frequency (< 8 Hz)

component is present throughout the step cycle, but

some of these features are outside the COI so many

reﬂect edge effects in wavelet transform. A distinct 8-

to 15- and 15- to 20-Hz correlation are present during

early and late swing as illustrated clearly in Figure 3E

and F. Analysis of this locomotion data using wavelet

coherence and wavelet PLV gives similar results.

5 DISCUSSION

This study presents time-frequency coherence and

PLV analysis using generalized Morse wavelets with

β = 9 and γ = 3. The methods are used to

characterise the correlation structure in experimental

data consisting of paired surface EMG signals during

treadmill walking. The main ﬁnding of the study

is that both methods are able to detect localised

correlation in the time-frequency plane. The results

obtained in this study are similar to Fourier based

Time-frequency based Coherence and Phase Locking Value Analysis of Human Locomotion Data using Generalized Morse Wavelets

time-frequency estimates in (Halliday et al., 2003),

functional coupling of motor unit during locomotion

was investigated. This demonstrated the presence

of 8-15 Hz and 15-20 Hz, frequency components of

motor unit correlation. These frequency components

are prominent around heel contact, which reﬂect

rhythmic neural activity associate with a particular

phase of locomotion. Traditional spectral analysis

method based on Fourier transform contains no

temporal information. (Halliday et al., 2003) applied

coherence function and estimates of the cumulant

density function to characterise the correlation

between the EMG signals in the frequency domain

and the time domain, respectively. By analysing

data, each step cycle was divided into three different

non-overlapping segments each lasting 200 ms

corresponding to early, mid, and end swing.

The generalized Morse wavelet based coherence

and PLV estimates in this study provide a similar

description of the data. The PLV estimates have larger

magnitudes than the coherence estimates. The PLV

appears noisier than the coherence despite the same

number of trials (Figure 3C-D). The conﬁdence limit

derived from surrogate data is larger for the PLV

estimate than for the coherence estimate for the same

number of trials. The wavelet edge effects should not

be a problem if the window length is made sufﬁciently

large. For example, for a frequency of 10 Hz the edge

effect has duration around 120 ms for the generalized

Morse wavelets used here. Changes in parameters

β and γ relate to temporal and spectral resolution in

the time-frequency plane. Adjustment of these will

alter the resolution in time and frequency (Lilly and

Olhede, 2009).

Our results suggest both methods give useful

information and are suitable for investigation of

non-stationary neuronal coupling mechanisms

underlying human treadmill locomotion. Although

this study is constrained to EMG acquired during

walking, this approach could be applied to other

physiological data.

6 FUTURE WORK

The methods in this study will be used to identify

modulations in the functional coupling of motor units

during overground walking in normal and Parkinson’s

disease subjects. This will provide insight into the

organisation of the neural pathways involved in gait

patterns in health and disease.

ACKNOWLEDGEMENTS

Financial support is provided by the Royal Thai

government science and technology scholarships.

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