daestrom wrote:
So, if I have a signal with a 1000 hz carrier, with a bandwidth of 50 hz,
you think I can sample it at just 150 hz and get accurate reproduction?
That's just wrong.

It is the maximum frequency component in the signal that is important. The
bandwidth is not related unless the lower edge of the band is at 0 hz
(whereupon the upper side of the band is equal to the max frequency).

daestrom


No, it is correct. If you have a signal with a 1000 Hz carrier and a 50
Hz Bandwidth, you can indeed sample it at 150 Hz and get accurate
reproduction...provided the rest of the spectrum is clear. That
requirement is typically provided with an anti-alias filter. In this
case, the anti-alias filter has to be a BAND-PASS filter centered on
1000 Hz rather than the low pass filter associated with baseband
sampling. This works because sampling folds the spectrum (aliasing) so
that parts of the frequency band with higher frequency than the sampling
frequency get folded back onto baseband. As long as the full spectrum
only has energy in a bandwidth less than or equal to half the sample
rate, you get all of the information necessary to reconstruct the
original signal (assuming you know the characteristics of the fixed
anti-alias filter so that you know which image to select when you unfold
the spectrum). If there was signal energy outside of the Fs/2
bandwidth, it adds to signal inside the bandwidth during the folding
that sampling causes, and then you lose information since there is no
way to separate the energy if it has been added with other energy by
folding.