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I am currently reviewing the Nyquist criterion which says I need to sample the signal at 2 times the maximum frequency in order to avoid aliasing in the reconstructed signal.

My question is that in all the applications I've done, I rarely ever remember having to reconstruct the signal after sampling it.

For example, in controlling a digital controller, all I have to do is to sample the signal and send the sampled signal to the controller. End of story, no reconstruction required.

In other applications, I sample the signal to analyze its frequency content. After looking at the frequency distribution, the signal is completely discarded. No reconstruction required.

Can someone make it clear why do we need to respect the Nyquist criterion if no reconstruction is needed (so no worry about aliasing effect)?

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The concept of reconstruction has nothing to do with the application, rather it has to do with the question: did I get the same signal that is really there. If you cannot recreate the signal back, that means the conversion process is loosing/modifying underlying information, which in most cases you do not want to happen.

So the confidence on the Fourier Transform, or to use the digitized data in the controller, comes from the fact that the loss of information is within the tolerance limits of your application. You can measure the quality of your digitized signal, by actually re-synthesizing the signal and comparing it to the original signal.

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  • $\begingroup$ So reconstructing the signal is good to check whether you have sampled it correctly or not. neat $\endgroup$ – Carlos - the Mongoose - Danger Feb 1 '15 at 17:54
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You may not need to explicitly reconstruct. But if you did reconstruct a waveform using the samples that you have, and end up with something different from the actual input, your controller is controlling as if that new different reconstructed waveform was really the input. Depending on what your controller is doing, you may have wanted it to do something different given those two different (before sampling) input waveforms. If so, you need to sample in a such way as to retain enough information in the samples so that the reconstructed waveform is close enough to the real input to meet your controller processes needs or requirements.

Also, if aliasing occurs, any high frequency (around or above half the sample rate) spectrum present in the waveform before sampling will distort your low frequency distribution measurements and thus reduce their accuracy (due to added noise), which may or may not meet your requirements.

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You may find a function that reconstrucs the signal from the break down of diferent frequencies. If you inverse the function, you may need to reconstruct the signal if you denoise the signal or if you want to extract specific frequencies and remain with the signal post frequency extraction (like you want to extract the noise only)

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