Page 95 - MATLAB Recipes for Earth Sciences

88 5 Time-Series Analysis

Periodic Signal
3
2

1 Amplitude A
y(t) 0

−1
−2
Period τ
−3
0 1 2 3 4 5 6 7 8 9 10
t
Periodic Signals
3
y 1 (t)
2
y 2 (t)
1
y(t) 0
−1

−2
Phase Shift ∆t
−3
0 1 2 3 4 5 6 7 8 9 10
t

Fig. 5.2 Two periodic signals y and y as a function of time t defined by the amplitudes A
1 2 1
and A , the period τ =τ , which is the inverse of the frequency f =f . Two signals y and y of
2 1 2 1 2 1 2
the same period are out of phase if the difference between ψ and ψ is not zero.
1 2
in the application of spectral analysis tools. Therefore we start with simple
data before we apply the methods to more complex time series.
The next example illustrates how to generate a basic synthetic data series
that is characteristic to earth sciences data. First we create a time axis t run-
ning from 0.01 to 100 in 0.01 intervals. Next we generate a strictly periodic
signal y(t), a sine wave with period 5 and amplitude 2 by typing
t = 0.01 : 0.01 : 100;
y = 2*sin(2*pi*t/5);
plot(t,y)