HP 50G, User Manual

Page: 505 / 887

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