HP 49g+ - Manual (Page 503)

Page 16-29
∫ ∞ − − −∞ = ⋅ ⋅
⋅ ⋅ ⋅
− ⋅ =
T
n
n dt t
T
n i
t f
T
c
0
. ,... 2 , 1 , 0 , 1 , 2 ,..., , )
2
exp( ) (
1 π
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):
Next, we move to the CASDIR sub-directory under HOME to change the value
of variable PERIOD, e.g.,
„ (hold) §`J @)CASDI `2 K
@PERIOD `
Return to the sub-directory where you defined functions f and g, and calculate
the coefficients (Accept change to Complex mode when requested):