Hioki Memory HiCorder MR6000, Инструкция по эксплуатации, Страница: 379 / 392

373
FFT Definitions
Aliasing
When a measured signal oscillates at a higher frequency compared to the sampling rate you have
chosen, the instrument may plot a false waveform oscillating lower than the actual signal with
respect to a frequency once the signal frequency reaches a certain level. This phenomena, which
occurs when a signal is sampled at a lower frequency than that defined by the Nyquist-Shannon
sampling theorem, is called aliasing.
Let
f
max
denote the highest frequency component of an input signal, and
f
s
denote a sampling
frequency. The following expression have to stand.
f
s
= 2 f
max
.........................................................................................(10)
Thus, if the input includes frequency components higher than f
s
/ 2 , a lower frequency component
folds higher frequency components, resulting in an occurrence of false frequency components.
The following figures show the results of spectrum analysis of composite waveforms that have
components of 1 kHz and 3 kHz, and of 1 kHz and 7 kHz.
If the instrument samples a signal that has frequency components of above 5 kHz (in this case,
7 kHz) at the sampling frequency f
s
of 10 kHz, folded spectral components of 5 kHz or lower are
observed.
This example demonstrates that the difference between the 3 kHz and 7 kHz components is
indistinguishable from one anther.
1 3 5 7
Composite waveform of 1 kHz and 3 kHz waveforms sampled at 10 kHz
Waveform shown on the
screen
Time
Frequency
(kHz)
Spectrum waveform
1 3 5 7
Composite waveform of 1 kHz and 7 kHz waveforms sampled at 10 kHz
Waveform shown on
the screen
Time
Frequency
(kHz)
Spectrum waveform
Appendix
HIOKI MR6000A966-03