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 $f_s > 2 f_m$ ?
Although this is an old post, and it already has two answers, I felt that it could benefit from a graphical answer.
The image below shows a sine wave of a given frequency. The red dots represent one hypothetical possibility for samples taken at exactly twice that frequency. So we see that if $f_s = 2 f_m$, there is a chance that the sampled signal, although non-zero, may look like zero when sampled this way. This is guaranteed not to happen if $f_s > 2 f_m$, which is why the theorem is stated as a strict inequality.
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)
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..
