# sampling below nyquist frequency

Can someone explain me that when we sample that sinusoid with a frequency below the Nyquist frequency (below half the sampling frequency), why we end up taking two samples per cycle of the sinusoid?

• "Below" the nyquist frequency means fewer than two samples per sinewave cycle. – Andy aka Apr 9 '16 at 9:44
• Nyquist states that you need to sample at at least twice the maximum frequency of the signal if you are to have any hope of reconstructing the original signal. Fix your question. – Transistor Apr 9 '16 at 9:47
• Since Nyquist states that you need to sample at a frequency bigger than twice the signal, for any signal that complies with this request, there will be at least THREE samples for each period. – Claudio Avi Chami Apr 9 '16 at 11:12
• @ClaudioAviChami It means there will be >= 2 samples, e.g. 2.x samples where x can be rather small. A CD can reproduce 20kHz with a sampling frequency if 44.1kHz. – user207421 Apr 9 '16 at 15:26
• You are correct, there will be > 2 samples, not necessarily 3... but for sure not two. – Claudio Avi Chami Apr 9 '16 at 15:31

## 1 Answer

Nyquist gives you the minimum sampling rate so that you can determine the frequency of a periodic wave.

If you sample a sine wave at 0.75 Nyquist, you get a false sine wave as shown in black dashes. This is called aliasing and it occurs at any frequency below Nyquist.

At Nyquist, you can determine frequency, but not amplitude, of a sinewave as shown by the black dashes.

Almost all images of Nyquist on the web show sampling at the peak, which is almost impossible. The following is a more appropriate representation.

Above Nyquist, it is possible to see frequency and amplitude of a periodic waveform by repeated samplings. At 1.25 Nyquist: