Function Fourier; Fourier Series For A Quadratic Function - HP 50g User Manual

Function FOURIER

An alternative way to define a Fourier series is by using complex numbers as
follows:
where
1
T
∫
c f
n
0
T
Function FOURIER provides the coefficient c
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
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)
Using the calculator in ALG mode, first we define functions f(t) and g(t):
f ) ( t
2
i n
) ( exp(
t
T
, c , and c
0 1
2 in
∑
c exp(
n
n
) ,
t dt n
of the complex-form of the Fourier
n
for the function f(t) = t
2
2
+(t-1).)
t
),
T
,..., , 2 1
2
+t, with period
0 , 1 , 2 , ,... .
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