Fourier transforms, Fourier transforms ,16-42 – HP 50g Graphing Calculator User Manual
Page 519
Page 16-42
The solution is shown below:
Fourier Transforms
Before presenting the concept of Fourier transforms, we’ll discuss the general
definition of an integral transform. In general, an integral transform is a
transformation that relates a function f(t) to a new function F(s) by an integration
of the form
The function
κ(s,t) is known as the
kernel of the transformation.
The use of an integral transform allows us to resolve a function into a given
spectrum of components. To understand the concept of a spectrum, consider
the Fourier series
representing a periodic function with a period T. This Fourier series can be re-
written as
where
for n =1,2, …
∫
⋅
⋅
=
b
a
dt
t
f
t
s
s
F
.
)
(
)
,
(
)
(
κ
(
)
,
sin
cos
)
(
1
0
∑
∞
=
⋅
+
⋅
+
=
n
n
n
n
n
x
b
x
a
a
t
f
ω
ω
∑
∞
=
+
⋅
+
=
1
0
),
cos(
)
(
n
n
n
n
x
A
a
x
f
φ
ϖ
,
tan
,
1
2
2
⎟⎟⎠
⎞
⎜⎜⎝
⎛
=
+
=
−
n
n
n
n
n
n
a
b
b
a
A
φ