# Sampling pure tone sine waves [closed]

What would happen if I am using the maximum frequency as the sample rate for sampling a pure tone sine wave?

For example, a $$10\ \rm kHz$$ sampling frequency for a $$10\ \rm kHz$$ monotone sine wave. What effect would aliasing produce at the output?

• Could you elaborate on what exactly it is that you don't understand? You sample a sine wave once per period, so what will the result be? – Matt L. Dec 3 '20 at 12:58
• yeah, what will be the result be? – Mark Steven Dec 4 '20 at 10:48

So, if you sample a sine wave $$x(t) = A \sin( 2 \pi f_0 t + \theta)$$ at a sampling frequency of $$F_s = f_0$$, (which is undersampled according to Nyquist-Shannon sampling theorem for bandlimited signals), then your samples will be $$x[n] = A \sin(\theta)$$ a constant signal! When reconstructed back into continuous waveform at the interpolator output, you will get a DC signal, $$x(t) = A \sin(\theta)$$, as opposed to the original sine wave.
The error is due to the false assumption at the interpolation stage that those samples $$x[n]$$ came from an original continuous-time signal which was band-limited to $$f_0/2$$, Nyquist frequency of sampling frequency $$f_0$$, which is not the case in reality.