Function fourier, Fourier series for a quadratic function – HP 50g Graphing Calculator User Manual
Page 505
Page 16-28
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
t
in
c
t
f
),
2
exp(
)
(
π
∫
∞
−
−
−∞
=
⋅
⋅
⋅
⋅
⋅
⋅
=
T
n
n
dt
t
T
n
i
t
f
T
c
0
.
,...
2
,
1
,
0
,
1
,
2
,...,
,
)
2
exp(
)
(
1
π