HP 50g User Manual page 523

The continuous spectrum, F( ), is calculated with the integral:
lim
This result can be rationalized by multiplying numerator and denominator by
the conjugate of the denominator, namely, 1-i . The result is now:
F
which is a complex function.
The absolute value of the real and imaginary parts of the function can be
plotted as shown below
Notes:
The magnitude, or absolute value, of the Fourier transform, |F( )|, is the
frequency spectrum of the original function f(t). For the example shown above,
|F( )| = 1/[2 (1+
Some functions, such as constant values, sin x, exp(x), x
Fourier transform. Functions that go to zero sufficiently fast as x goes to infinity
do have Fourier transforms.
1
∫
1 ( i ) t
e
2
0
1 1 exp(
⎡
⎢
1
2 ⎣
1 1
( )
2 1 i
1
⎛
⎜
2 1
⎝
2 1/2
)] . The plot of |F( )| vs.
1
∫
lim
dt
2
1 ( i ) ) t
⎤
⎥
i
⎦
1 1
⎛
⎜
2 1 i
⎝
1
i
2
1
1 ( i ) t
e dt
0
1 1
.
1 i
2
1 i
⎞ ⎛ ⎞
⎟ ⎜ ⎟
1 i
⎠ ⎝ ⎠
⎞
⎟
2
⎠
was shown earlier.
2
, etc., do not have
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