From: Jerry Avins on
On 4/23/2010 4:33 PM, gretzteam wrote:

I wrote:
>> What Brent said. Keep in mind that you not only shift the carrier to
>> baseband, you also shift everything else down by a similar amount. Where
>> do the aliases of the out-of-band signals go?
> Ok this is the part I don't understand! Can you elaborate a bit more?

Rarely is a carrier to be demodulated sampled at more than twice the
carrier frequency; that would be a waste. The sampling theorem tells us
that we have to sample more than twice the frequency corresponding to
the bandwidth of interest. There are some practical restrictions (the
second edition of Understanding Digital Signal Processing by Rick Lyons
has an excellent analysis of them) but in general, sampling 20 KHz wide
signal on a 356 KHz carrier can be accomplished with a 50 KHz sample
rate. A bandpass filter assures that the AM signal is not contaminated
by adjacent channels. With bandpass sampling, we need to exclude signals
both above and below the band being sampled. Even if the signal were
sampled at 1 MHz, a low-pass filter would be needed to substantially
eliminate all signals above 500 KHz.

Incidentally, sampling at 1 MHz provides a little over 2 samples per
carrier cycle, with little chance that either of them will be near a
carrier peak and hence representative of the envelope. With bandpass
sampling at 50 KHz, there will be only one sample for every 9 or so
carrier cycles. There is then no hope of peak detection.

"It does me no injury for my neighbor to say there are 20 gods, or no
God. It neither picks my pocket nor breaks my leg."
Thomas Jefferson to the Virginia House of Delegates in 1776.