Page 16-28
Thus, the first three terms of the function are:
f(t)
≈
1/3 – (4/
π
2
)
⋅
cos (
π⋅
t)+(2/
π
)
⋅
sin (
π⋅
t).
A graphical comparison of the original function with the Fourier expansion
using these three terms shows that the fitting is acceptable for t < 1, or
thereabouts. But, then, again, we stipulated that T/2 = 1. Therefore, the
fitting is valid only between –1 < t < 1.
Function FOURIER
An alternative way to define a Fourier series is by using complex numbers as
follows:
∑
+∞
−∞
=
⋅
=
n
n
T
t
in
c
t
f
),
2
exp(
)
(
π
where