Page 16-45
Define this expression as a function by using function DEFINE (
„à
). Then,
plot the continuous spectrum, in the range 0 <
ω
< 10, as:
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
Inverse sine transform
Fourier cosine transform
Inverse cosine transform
Fourier transform (proper)
Inverse Fourier transform (proper)
Example 1 – Determine the Fourier transform of the function f(t) = exp(- t), for t
>0, and f(t) = 0, for t<0.
∫
∞
⋅
⋅
⋅
⋅
=
=
0
)
sin(
)
(
2
)
(
)}
(
{
dt
t
t
f
F
t
f
s
ω
π
ω
F
∫
∞
−
⋅
⋅
⋅
=
=
0
1
)
sin(
)
(
)
(
)}
(
{
dt
t
F
t
f
F
s
ω
ω
ω
F
∫
∞
⋅
⋅
⋅
⋅
=
=
0
)
cos(
)
(
2
)
(
)}
(
{
dt
t
t
f
F
t
f
c
ω
π
ω
F
∫
∞
−
⋅
⋅
⋅
=
=
0
1
)
cos(
)
(
)
(
)}
(
{
dt
t
F
t
f
F
c
ω
ω
ω
F
∫
∞
−∞
−
⋅
⋅
⋅
=
=
dt
e
t
f
F
t
f
t
i
ω
π
ω
)
(
2
1
)
(
)}
(
{
F
∫
∞
−∞
−
−
⋅
⋅
⋅
=
=
dt
e
F
t
f
F
t
i
ω
ω
π
ω
)
(
2
1
)
(
)}
(
{
1
F
Summary of Contents for 50G
Page 1: ...HP g graphing calculator user s guide H Edition 1 HP part number F2229AA 90006 ...
Page 130: ...Page 2 70 The CMDS CoMmanDS menu activated within the Equation Writer i e O L CMDS ...
Page 206: ...Page 5 29 LIN LNCOLLECT POWEREXPAND SIMPLIFY ...
Page 257: ...Page 7 20 ...
Page 383: ...Page 11 56 Function KER Function MKISOM ...
Page 715: ...Page 21 68 Whereas using RPL there is no problem when loading this program in algebraic mode ...
Page 858: ...Page L 5 ...