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A
16
FFT Definitions
■
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 frequency limitations. This phenomena occurs when
sampling occurs at a lower frequency 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:
f
s
= 2
f
max
......................................................................................... (10)
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 fs 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 indiscernible.
Portion Displayed on
Screen
Spectrum
Frequency
[kHz]
1
3
5
7
Time
Composite waveform of 1 kHz and 3 kHz components sampled at 10 kHz
Portion Displayed on
Screen
Spectrum
Frequency
[kHz]
1
3
5
7
Time
Composite waveform of 1 kHz and 7 kHz components sampled at 10 kHz
Summary of Contents for MR8827
Page 19: ...14 Operation Precautions ...
Page 81: ...76 Start and Stop Measurement ...
Page 111: ...106 Manage Files ...
Page 125: ...120 Miscellaneous Printing Functions ...
Page 143: ...138 View Block Waveforms ...
Page 191: ...186 Setting Output Waveform Parameters ...
Page 291: ...286 FFT Analysis Modes Measurable Ranges With Octave Analysis 1 1 OCT 1 3 OCT ...
Page 292: ...287 FFT Analysis Modes 1 1 OCT 1 3 OCT 13 FFT Function ...
Page 293: ...288 FFT Analysis Modes 1 1 OCT 1 3 OCT ...
Page 295: ...290 FFT Analysis Modes ...
Page 309: ...304 Editor Command Details ...
Page 387: ...382 Module Specifications ...
Page 405: ...400 Dispose of the Instrument Lithium Battery Removal ...
Page 431: ...A26 FFT Definitions ...
Page 436: ......