# Is phase and amplitude information necessarily lost when undersampling?

Is phase and amplitude information necessarily lost when undersampling if you have a constant periodic single frequency sinusoidal?

My second question is: How can one determine the undersampling frequency for such a case? And how to retrieve the amplitude and phase.

I want to know if this is possible for a sampling frequency much lower than the Nyquist rate.

• What exactly do you mean by undersmapling? – Phonon May 20 '14 at 0:51
• Do you have any other interfering signals (across the entire bandwidth visible to the sampler, even beyond its Nyquist rate), or are you observing only a single sinusoid and nothing else? If you don't, then undersampling should work just fine. Phase measurements are somewhat tricky in this case; you need to know the frequency a priori in order to reference its phase to anything meaningful. – Jason R May 20 '14 at 0:56
• @Phonon: Sampling below the Nyquist rate. – iQt May 20 '14 at 0:57
• @JasonR: Only one single sinusoid (ideally). There will be some noise ofcourse, but assume it is noise free. – iQt May 20 '14 at 0:58

If you sample a constant periodic signal of frequency f with a frequency less than twice the frequency (below Nyquist rate or Undersampling) you will lost the data due to aliasing. Lets say $f=100 Hz$ then by Nyquist rate we should sample the signal with a sampling rate higher than 200 Hz. If we under sample the signal (<200) by a sampling frequency say $f_s=180 Hz$. Then due to aliasing the reconstructed signal will be a periodic signal with a frequency less than the original signal. Here the reconstructed signal will be a 80 Hz signal instead of 100 HZ.