Hioki MR8740, Инструкция по эксплуатации

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Appendix 4 FFT Definitions
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Appe
ndix
What is FFT? __________________________________________________
FFT is the abbreviation for Fast Fourier Transform, an efficient method to calcu-
late the DFT (Discrete Fourier Transform) from a time-domain waveform. Also,
the reverse process of transforming frequency data obtained by the FFT back
into its original time-domain waveform is called the IFFT (Inverse FFT). The FFT
functions perform various types of analysis using FFT and IFFT.
Time and Frequency Domain Considerations _______________________
All signals are input to the instrument as a function of the time domain. This func-
tion can be considered as a combination of sine waves at various frequencies,
such as in the following diagram. The characteristics of a signal that may be diffi-
cult to analyze when viewed only as a waveform in the time domain can be eas-
ier to understand by transforming it into a spectrum (the frequency domain).
Discrete Fourier Transforms and Inverse FFT _______________________
For a discrete signal x ( n ), the DFT is X ( k ) and the number of Analysis points is N ,
which relate as follows:
X ( k ) is typically a complex number, so expression (1) can be transformed again
and written as follows:
Appendix 4 FFT Definitions
Amplitude
Frequency
Time
Time-Domain
Waveform
(1)
{ }
kn
N
N
n
W k X
N
k X IDFT n x
−
−
=
∑
= =
1
0
) (
1
) ( ) (
⎟
⎠
⎞
⎜
⎝
⎛
− =
N
j W
N
π
2
exp
(2)
(3)
(4)
(5)
{ }
) ( ) ( ) ( exp ) ( ) ( k k F k j k F k F
φ φ ∠ = =
{ }
{ }
) ( Re
) ( Im
tan ) (
1
k X
k X
k
−
=
φ
: Amplitude spectrum, : Phase spectrum
) ( k F
) ( k
φ