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Function FOURIER
An alternative way to define a Fourier series is by using complex numbers as
follows:
where
Function FOURIER provides the coefficient c
n
of the complex-form of the Fourier
series given the function f(t) and the value of n. The function FOURIER requires
you to store the value of the period (T) of a T-periodic function into the CAS
variable PERIOD before calling the function. The function FOURIER is available
in the DERIV sub-menu within the CALC menu („Ö).
Fourier series for a quadratic function
Determine the coefficients c
0
, c
1
, and c
2
for the function f(t) = t
2
+t, with period
T = 2. (Note: Because the integral used by function FOURIER is calculated in
the interval [0,T], while the one defined earlier was calculated in the interval
[-T/2,T/2], we need to shift the function in the t-axis, by subtracting T/2 from t,
i.e., we will use g(t) = f(t-1) = (t-1)
2
+(t-1).)
Using the calculator in ALG mode, first we define functions f(t) and g(t):
∑
+∞
−∞=
⋅=
n
n
T
tin
ctf ),
2
exp()(
π
∫
∞−−−∞=⋅⋅
⋅⋅⋅
⋅=
T
n
ndtt
T
ni
tf
T
c
0
.,...2,1,0,1,2,...,,)
2
exp()(
1
π
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