Geoscience Reference
In-Depth Information
a
b
Fig. 5.2 a
Periodic signal
x
a function of time
t
dei ned by the amplitude
A
, and the period
˄ which is the inverse of the frequency
f
.
b
Two signals
x
and
y
of the same period are out of
phase if the dif erence between ˈ
x
and ˈ
y
is not equal to zero.
disks (CDs) are sampled at frequencies of 44,100 Hz (Hertz, where 1 Hz=1
cycle per second), but the corresponding Nyquist frequency is 22,050 Hz,
which is the highest frequency a CD player can theoretically produce. h e
performance limitations of anti-alias i lters used by CD players further
reduce the frequency band and result in a cutof frequency of around 20,050
Hz, which is the true upper frequency limit of a CD player.
We can now generate synthetic signals to illustrate the use of time-series
analysis tools. When using synthetic data we know in advance which features
the time series contains, such as periodic or random components, and we can
introduce a linear trend or gaps in the time series. h e user will encounter
plenty of examples of the possible ef ects of varying the parameter settings,
as well as potential artifacts and errors that can result from the application
of spectral analysis tools. We will start with simple data and then apply the
