User Manual

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21.3 Reference
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φ(ω)
Imagina
l
Rea
l
F(ω
)
｜F(ω)｜
Fourier transformation and the Inverse Fourier transformation
The following equations define the Fourier transformation and the Inverse
Fourier transformation.
F(ω)= |f(t)| = f(t)･exp(-jωt)dt
f(t) =
-1
|F(ω)| = F(ω)･exp(jωt)dω
The function F(ω)generally results in a complex number, and can be
expressed as follows.
F(ω) = |F(ω)|･exp(jφ(ω)) = |F(ω)|∠φ(ω)
|F(ω)|: Absolute value spectrum of f(t)
φ(ω): Unit spectrum of the phase of f(t)
When conversion is made from the time domain to the frequency domain, the
magnitude information and phase information are clearly expressed as
indicated in equation (
). The figure below shows F(ω) in vector form.