I was told in my electronics course that "to reproduce a wave, we need to sample it at least twice every period."
If I take this to be literally true, then a sine wave with only 2-3 samples per period looks very ugly even though it obeys this rule. It looks more like a triangle wave.
I'm currently working with an FPGA and I need to synthesize and then sample the same high frequency sine wave (rf domain).
- If I use a 50Mhz clock to synthesize a 12Mhz sine wave I get something pretty ugly even though it obeys "Nyquist's theorem".
- After running simulations, I've found my clock needs to be ~20X faster to reproduce a "nice" sine wave of frequency $f$.
- This leads me to believe I can't simply use an ADC which is 50Mhz to sample a 12Mhz sine wave because it will be as ugly as the sine wave I would create using such a sampling rate (it's not even five samples per period).
This would mean I either need expensive hardware or must build something myself.
Why does Nyquist's theorem seem woefully inadequate? It seems that a sample rate of 2-3 times higher is merely sufficient to tell me what the period of the signal is, not reproduce the signal with any resemblance of the original signal. Am I misapplying or misunderstanding Nyquist's theorem?