Abstract: Nyquist theorem is the basis for continuous signal discretization. In many cases, we simply think that as long as the sampling frequency of the ADC is greater than 2 times the highest frequency in the signal, the signal waveform seen will not be seriously distorted. Is that true?
First look at the two waveforms, Figure 1, Figure 2, the sampling frequency of the signal discretization in these two figures is much larger than the frequency of the signal itself.
Figure 1 200ms time window waveform
Figure 2 1ms time window waveform
Under the condition that the above description satisfies the Nyquist sampling theorem, we simply analyze: the screen in Figure 1 is 200ms, containing 10 cycles, and it is common sense to infer that the signal period is about 200ms/10=20ms, that is, the signal frequency is about 50Hz; In this way, the signal period of Figure 2 is about 1ms/10=0.1ms, or 10kHz.
First, the problem
The fact is that both figures are the waveforms of the PA5000 power analyzer when measuring 10.05 kHz signal in the normal mode 2MHz sampling frequency. As shown in Figure 3 and Figure 4, the Urms and the frequency of the waveform are also equal in the measurement results. . Why does the waveform reflect such a big difference?
Figure 3 200ms measurement information
Figure 4 1ms measurement information
A simple review of the Nyquist sampling theorem: If the signal is band-limited and the sampling frequency Fs is more than twice the maximum frequency Fmax of the signal, the information in the original signal is completely preserved in the sampled sample. If the frequency component is higher than or equal to half of the sampling frequency, it will lead to aliasing. As shown in Figure 5, the sampling frequency is too small, the number of samples per signal period is too small, and the reconstructed waveform frequency component falls below the sampling. The frequency range of the frequency is quite different from the original signal.
Figure 5 frequency confusion
It is obvious that the waveforms in Figure 1 and Figure 3 are aliased, but the 2MHz sampling frequency is definitely sufficient for the 10.05kHz signal. What is the problem? Since the measurement results are correct, the ADC sampling part is no problem, the target is turned to the waveform display, and the PA5000 waveform display menu is viewed. It is found that there are waveform selection methods, such as equal interval extraction and peak extraction. It makes people realize that the equal interval extraction is actually subsampling the signal, and the screen resolution is 1280*800, which means that the horizontal axis points are no more than 1280 at most. When the 200ms waveform signal is displayed by equal interval extraction, the display is displayed. The actual sampling rate of the waveform does not exceed 1280pts/200ms=6400pts/s, and the signal frequency less than 10.05kHz naturally produces aliasing. The above phenomenon is not surprising.
The PA5000 power analyzer can be used as an oscilloscope to support a time window of 1ms (about 500kHz signal frequency). The time window of the waveform display can be adjusted to the appropriate range to see the true equally spaced waveforms.
The sampling theorem is familiar to us, but it will be subconsciously applied to the hardware circuit only. It is easy to ignore other processes that are not familiar with the professional direction. The beginners are more susceptible to the definition of the sampling theorem on the online part, so that the application range is in the simulation. In the process of changing the digital signal, the essential cause or even the misjudgment can not be found. It can be seen that the ear is virtual, and the waveforms that are seen are not necessarily true. Professional instruments and eye discrimination are required.
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