Appendix 5 FFT Definitions
A
15
Appendi
x
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 5 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
Summary of Contents for 8847
Page 1: ...MEMORY HiCORDER Instruction Manual 8847 December 2010 Revised edition 4 8847A981 04 10 12H ...
Page 2: ......
Page 18: ...Operating Precautions 8 ...
Page 26: ...1 4 Basic Key Operations 16 ...
Page 74: ...4 4 Waveform Observation 64 ...
Page 98: ...5 5 Managing Files 88 ...
Page 110: ...6 6 Miscellaneous Printing Functions 100 ...
Page 126: ...7 8 Seeing Block Waveforms 116 ...
Page 160: ...8 10 Making Detailed Settings for Input Modules 150 ...
Page 198: ...10 6 Numerical Calculation Type and Description 188 ...
Page 296: ...15 7 Controlling the Instrument with Command Communications LAN USB 286 ...
Page 304: ...16 2 External I O 294 ...
Page 362: ...Appendix 5 FFT Definitions A28 ...
Page 368: ...Index Index 6 ...
Page 369: ......
Page 370: ......
Page 371: ......
