Definition Of Fourier Transforms - HP 50g User Manual
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Define this expression as a function by using function DEFINE („à). Then,
plot the continuous spectrum, in the range 0 <
Definition of Fourier transforms
Different types of Fourier transforms can be defined. The following are the
definitions of the sine, cosine, and full Fourier transforms and their inverses used
in this Chapter.
Fourier sine transform
s F
Inverse sine transform
Fourier cosine transform
F
Inverse cosine transform
F
Fourier transform (proper)
Inverse Fourier transform (proper)
F
Example 1 – Determine the Fourier transform of the function f(t) = exp(- t), for t
>0, and f(t) = 0, for t<0.
{
(
)}
(
f
t
F
1
F
{
(
)}
F
f
s
{
(
)}
(
c
f
t
F
1
{
(
)}
F
f
c
F
{
(
)}
(
f
t
F
1
{
(
)}
F
f
2
∫
)
) (
f
t
0
∫
) (
(
)
t
F
0
2
∫
)
) (
f
t
0
∫
) (
(
)
t
F
0
1
∫
)
2
1
∫
) (
t
2
< 10, as:
sin(
)
t
dt
sin(
)
t
dt
cos(
)
t
dt
cos(
)
t
dt
i
t
) (
f
t
e
dt
i
t
(
)
F
e
dt
Page 16-45
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