User Manual

APPENDIX 17
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Appendix 3 Reference
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Appendix 3.9 FFT Function
Time domain
Frequency domain
F(
ω
)
|
F
(
ω
)
|
Real
Imaginal
FFT stands for Fast Fourier Transformation, which is a calculation method
used to decompose a time-domain waveform into frequency components.
By performing FFT calculation, various calculations can be performed.
 Concept of time domain and frequency domain
The signals measured by this memory recorder
have values which correspond to time, that is the
signals are functions of time.
Waveform in the figure on the left is an example
of such a signal.
Signals which are expressed as a function of
time are called time domain signals.
In reality, a signal consists of a number of sine-
waves of different frequencies, called frequency
components, which combine to create the final
shape of the waveform. Expressing waveform
the source signal, as a function of its frequency
components yields a frequency domain
representation.
Often, the characteristics of a signal which
cannot be easily analyzed in the time domain,
can be clearly revealed by the frequency domain
representation.
 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 2
f(t) =
-1
|F(ω)| = F(ω) exp(jωt)dω 3
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) 4
|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 (
4
). The
figure below shows F(
ω
) in vector form.