The Nyquist-Shannon Sampling Theorem estabilishes that a sampling process of a continuous-time signal is perfectally reversible if the sampling frequency is at least the Nyquist rate (the double of the sampled signal bandwidth). However, I’ve been realizing some really experienced engineers have a lightly distorced interpretation of the theorem: to believe that the quality of a reconstructed signal increases with the sampling frequency and the frequencies much higher than Nyquist rate are needed to perform a satisfatory reconstruction.
A strongly possible reason to this erroneous understanding is the thought that the signal reconstruction is made by a linear interpolation of the samples. From that perspective, a higher rate sampling really makes the reconstructed signal closer to its original shape. But, the point is that the signal is not simply reconstructed by an interpolation. Instead, the process is compose by two stages:
- A train of impulses is generated, which one multiplicated by it respective sample value;
- Then, the resulting signal passes into a low-pass filter to discard all frequencies above the original signal bandwidth.
It is important to know that in practical terms, the reconstruction is not perfect because the theorem is only valid for bandlimited signals – requiring the signal to be prefiltered what makes a distortion on it and the low-pass filter is unrealizable because it’s response is not causal. So, although the mathematical behavior of the theorem is not achived phisically, the constraint is not the sampling rate, since the Nyquist rate be respected.