平成19年度電気関係学会四国支部連合大会

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Linear and Nonlinear Analysis Methods
for Bio-Signal
Azian Azamimi(Tokushima University)

1 Introduction
Bio signal analysis becomes a hot research topic recently,
due to its importance demands for clinical and biomedical
application. Bio signal means a collective electrical signal
acquired from any organ that represents a physical variableof interest like EMG signals, EEG signals or ﬁnger pulse
signals. Bio signals are usually exhibit complex behaviour
with nonlinear dynamic properties and considering this,the nonlinear dynamics theory maybe a better approachthan traditional linear methods in characterizing the complex nature of bio signals [1].
In this study, we analyze the ﬁnger pulse signal using both linear and nonlinear characteristic measures like
Fourier transform (FFT) and Lyapunov spectrum. We
measure the ﬁnger pulse signal for 19 minutes with two
diﬀerent conditions (data for 1 person). Then, we compare
the characteristic extracted by both linear and nonlinear
methods.

2 FFT and Lyapunov Spectrum

Yoshifumi Nishio(Tokushima University)
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3 Simulation Results
Figure 1 shows the time series data of ﬁnger pulse signal
for 19 minutes with two diﬀerent situations. In the beginning of the experiment, the ﬁnger pulse is measured inrelax condition. Therefore, in the end of the experiment,
the ﬁnger pulse is measured in the condition where we haveto do some mathematics calculation. Figure 2 and ﬁgure
3 show the analysis result of FFT method and Lyapunov
method respectively.

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Figure 2: Result of FFT method.
(a) Relax. (b) Concentrate.
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0As you may know, a Fast Fourier transform (FFT) is aneﬃcient algorithm to compute the discrete Fourier transform (DFT) and its inverse. FFTs are of great importanceto a wide variety of applications, from digital signal processing and solving partial diﬀerential equations to algorithms for quickly multiplying large integers. In this case,
we use FFT method to carry out the signal processing ofﬁnger pulse signal as linear analysis method.
As for nonlinear analysis method, we use the Lyapunov
Spectrum instead. Lyapunov Exponent (λ) is a quantitative measure of the sensitive dependence on the initialconditions. It deﬁnes the average rate of divergence of
two neighbouring trajectories. Therefore, the existence ofa positive λ for almost all initial conditions in a bounded
dynamical system is widely used deﬁnition of deterministic chaos. To discriminate between chaotic dynamics andperiodic signals Lyapunov Exponent (λ) are often used.

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Figure 3: Result of Lyapunov Spectrum method.
(a) Relax. (b) Concentrate.
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Concentrate0.0331

Table 1 shows the ﬁnal value of Lyapunov exponent forrelax and concentrate conditions. We found that it is hard
to extract the diﬀerent characteristic of ﬁnger pulse signal
using the linear method. But on the other hand, we foundthe diﬀerent of lambda value of two diﬀerent conditions
by using the nonlinear methods. In the relax condition, λvalue is near to 0, showing that the orbits are on a stableattractor but in concentrate condition, λ value is a positive
exponent showing that the orbits are on a chaotic attractor.
This result show that the signal becomes less complex when
the person is in relax condition.

4 Conclusions
In this study, we had conﬁrmed that the nonlinear analysis approach is more suitable used in characterizing the biosignal. In the future, we will measure ﬁnger pulse signal ofmore persons with other diﬀerent situations and calculate
the average of numerical value. This is the ﬁrst step fordeveloping nonlinear analysis methods of bio-signal.

Time series data of pulse rate signal
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References

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[freq][1] K. Natarajan, R. Acharya, F. Alias et al., “Nonlinear analysis of EEG signals at diﬀerent mental states,”
BioMedical Engineering OnLine, 2004.

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Figure 1: Time series data of ﬁnger pulse signal.