From: John Larkin
Subject: Re: Undersampling and its complement?
Date: Fri, 01 Nov 2002 17:30:46 -0800
Organization: Posted via Supernews, http://www.supernews.com
X-Newsreader: Forte Agent 1.91/32.564
On Sat, 02 Nov 2002 00:40:46 GMT, James Meyer
>My question is.... is there anything similar regarding generating an 8
yes, sort of. You were able to undersample the incoming signal under
the assumption that it was bandlimited, presumably by a 10 KHz wide
bandpass filter or its equivalent.
In the opposite direction, you could have a low DAC update rate but
feed an actual 10 KHz wide BPF centered at 8 MHz, and recreate the
narrowband signal. Just imagine applying the Sampling Theorem to the
Signal ==> bandpass filter ==> sampler ==> buffer ==> bandpass
filter ==> reconstructed signal
which reproduces the original signal. Now replace 'sampler' with 'adc'
and 'buffer' with 'dac' and there you are.
The only gotcha is that a DAC is a 'zero order hold' (ie, plateau or
level generator) whereas the Sampling Theorem assumes that the
reconstructing device is an impulse generator. Impulses are nice in
that they have infinite energy and endless harmonics.
The practical consequence of this is that there is frequency
distortion in using a real DAC, and the amplitude of the reconstructed
8 MHz signal components will be *very* small at such a high ratio of
sample frequency to filtered harmonic. So some sort of mixing scheme
would be more practical than directly plucking out the weak (roughly
400th!) harmonic with a filter.