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periodicity in the graph of the series. This periodicity is easy to visualize by
expanding the horizontal range of the plot to (-0.5,4):
Fourier series for a triangular wave
Consider the function
which we assume to be periodic with period T = 2. This function can be
defined in the calculator, in ALG mode, by the expression
DEFINE(‘g(X) = IFTE(X<1,X,2-X)’)
If you started this example after finishing example 1 you already have a value
of 2 stored in CAS variable PERIOD. If you are not sure, check the value of this
variable, and store a 2 in it if needed. The coefficient c
0
for the Fourier series
is calculated as follows:
The calculator will request a change to Approx mode because of the integration
of the function IFTE() included in the integrand. Accepting, the change to
Approx produces c
0
= 0.5. If we now want to obtain a generic expression for
the coefficient c
n
use:
⎩
⎨
⎧
<<−
<<
=
21,2
10,
)(
xifx
xifx
xg