Appendix 5 FFT Definitions
A
18
Aliasing ______________________________________________________
When the frequency of a signal to be measured is higher than the sampling rate,
the observed frequency is lower than that of the actual signal, with certain fre-
quency limitations. This phenomena occurs when sampling occurs at a lower fre-
quency than that defined by the Nyquist-Shannon sampling theorem, and is
called aliasing.
If the highest frequency component of the input signal is
f
max
and the sampling
frequency is
f
s
, the following expression must be satisfied:
Therefore, if the input includes a frequency component higher than
f
s
/2, it is
observed as a lower frequency (alias) that does not really exist.
The following diagrams show the results of spectrum analysis of composite
waveforms having components of 1 kHz and 3 kHz, and of 1 kHz and 7 kHz.
If sampling frequency
f
s
is 10 kHz, the spectral component of an input frequency
above 5 kHz (in this case, 7 kHz) is observed as an alias at 5 kHz or below.
In this example the difference between the 3 and 7 kHz components is indiscern-
ible.
max
2 f
f
s
=
(10)
Composite waveform of 1 kHz and 3 kHz components sampled at 10 kHz
Time
Portion Displayed on
Screen
Spectrum
1
3
5
7
Frequency
[kHz]
Composite waveform of 1 kHz and 7 kHz components sampled at 10 kHz
Time
Spectrum
Frequency
[kHz]
1
3
5
7
Portion Displayed on
Screen
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: ......