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Fourier series for a triangular wave
Consider the function
<
<
−
<
<
=
2
1
,
2
1
0
,
)
(
x
if
x
x
if
x
x
g
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:
