Fourier Transforms - HP 50g User Manual

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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
F s
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-
f ( x )
written as
for n =1,2, ...
b
∫
) ( ) ,
t s f
a
∑
f ) ( t a
0
n
∑
a A cos(
0 n
n 1
2
A a
n n
) ( .
The function (s,t) is known as the
t dt
a cos x
n n
1
x ),
n n
2
b , tan
n n
b sin x ,
n n
where
⎛ ⎞
b
1 ⎜ ⎜ ⎟ ⎟
n
,
a
⎝ ⎠
n
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