# HP 48gII User Manual Page 522

Graphing calculator.

integration of the form
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
f
) (
t
representing a periodic function with a period T. This Fourier series can be
f
(
x
)
=
a
re-written as
0
A
n
for n =1,2, ...
The amplitudes A
will be referred to as the spectrum of the function and will
n
be a measure of the magnitude of the component of f(x) with frequency f
n/T. The basic or fundamental frequency in the Fourier series is f
all other frequencies are multiples of this basic frequency, i.e., f
we can define an angular frequency, ω
where ω
is the basic or fundamental angular frequency of the Fourier series.
0
Using the angular frequency notation, the Fourier series expansion is written
as
f
(
a
0
b
(
)
κ
(
) ,
) (
F
s
t s
f
a
a
a
cos
ω
x
0
n
n
n
1
+
A
cos(
ϖ
x
+
φ
n
n
n
n
=
1
2
2
=
a
+
b
,
φ
=
tan
n
n
n
= 2nπ/T = 2π⋅f
n
x
)
a
A
cos(
ω
0
n
n
1
a
cos
ω
x
b
n
n
n
1
.
The function κ(s,t) is
t
dt
b
sin
ω
x
,
n
n
),
where
b
1
 
 
n
,
a
n
= 1/T, thus,
0
= n⋅f
. Also,
n
0
= 2π⋅ n⋅f
= n⋅ω
n
0
x
φ
).
n
n
sin
ω
x
n
n
Page 16-44
=
n
,
0