HP F2226A - 48GII Graphic Calculator User Manual page 525

Graphing calculator
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F
{
(
)}
f
t
s
Inverse sine transform
1
F
{
(
F
s
Fourier cosine transform
F
{
(
)}
f
t
c
Inverse cosine transform
1
F
{
(
F
c
Fourier transform (proper)
F
{
(
f
t
Inverse Fourier transform (proper)
1
F
{
F
Example 1 – Determine the Fourier transform of the function f(t) = exp(- t), for t
>0, and f(t) = 0, for t<0.
The continuous spectrum, F(ω), is calculated with the integral:
1
2
π
1
lim
2
π
ε
This result can be rationalized by multiplying numerator and denominator by
the conjugate of the denominator, namely, 1-iω. The result is now:
2
(
ω
)
) (
F
f
t
π
0
ω
)}
) (
(
ω
)
f
t
F
0
2
(
ω
)
) (
F
f
t
π
0
ω
)}
=
) (
=
(
ω
)
f
t
F
0
1
)}
=
(
ω
)
=
F
f
2
π
ω
ω
(
)}
) (
(
f
t
F
1
1 (
i
ω
)
t
e
dt
=
lim
2
π
0
ε
1
exp(
1 (
i
ω
)
ε
)
1
i
ω
sin(
ω
)
t
dt
sin(
ω
)
t
dt
cos(
ω
)
t
dt
cos(
ω
)
t
dt
t
) (
t
e
dt
t
)
e
dt
ε
1 (
i
ω
)
t
e
dt
0
1
1
.
2
π
1
i
ω
Page 16-47

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