HP 50g Graphing Calculator User Manual
Page 521
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Page 16-44
and
The continuous spectrum is given by
The functions C(
ω), S(ω), and A(ω) are continuous functions of a variable ω,
which becomes the transform variable for the Fourier transforms defined below.
Example 1 – Determine the coefficients C(
ω), S(ω), and the continuous spectrum
A(
ω), for the function f(x) = exp(-x), for x > 0, and f(x) = 0, x < 0.
In the calculator, set up and evaluate the following integrals to calculate C(
ω)
and S(
ω), respectively. CAS modes are set to Exact and Real.
Their results are, respectively:
The continuous spectrum, A(
ω) is calculated as:
.
)
sin(
)
(
2
1
)
(
∫
∞
−∞
⋅
⋅
⋅
⋅
=
dx
x
x
f
S
ω
π
ω
2
2
)]
(
[
)]
(
[
)
(
ω
ω
ω
S
C
A
+
=
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