While describing sampling theorem, is it $f_s \ge 2 f_m$ or $f_s > 2 f_m$?

Question

I have a doubt regarding sampling theorem.

Sampling theorem states that if a band limited signal has to be recovered after sampling, then the sampling frequency $f_s$ should obey $f_s \ge 2 f_m$ where $f_m$ is the maximum frequency content in the signal.

But is it $f_s \ge 2 f_m$ or $f_s > 2 f_m$ ?

Answer 1

So here is the answer from my friend Prasanna Hegde.

Sampling creates repeated band of frequencies, which is the replication of signal spectrum.

with $fs = 2 fm$ these repeated bands are non-overlapping but there is no separation between them. It requires infinite order filter(transition band of zero width) to separate them and to recover the signal without aliasing.

with $fs > 2 fm$ the bands will have non-zero separation and this separation increases with increase in fs. So with a wide enough separation any lower order filter with non-zero transition band can recover the signal.

So $fs > 2 fm$ is a practical limitation(not theoretical)

Answer 2

Theoretical definition is fs >= 2fm. Ofcourse its not possible in practical, but the question is not clearly stating for what purpose its going to be used.. If its for ur studies keep it fs>= 2fm.. thats it.. U will be able to reconstruct back the signal if u come up with an ideal filter..