[hpsdr] A/D

[Ben Hall]

Hi Henry and all!

Henry Vredegoor wrote:
> What this all comes down to, as I understand it, is that this guy (and 
> others) proved mathematically that EVEN WITH ONLY TWO samples per period 
> of the signal to be be digitized, it can be reconstructed correctly from 
> these two samples!

With the addition of an anti-aliasing low-pass filter to cutoff input 
below the 2X limit (IE: for a 60 MHz ADC, the filter is 30 MHz), you're 
absolutely correct.

However, Nyquist theory gives me some heartburn:

The 2X rule is true - you can use a 60 MHz ADC to capture a 30 MHz 
signal and reconstruct the signal.  But, you've got to assume a wave 
form shape, as sampling at 2X gives you no information as to the shape 
of the waveform, as you're only looking at two points per waveform 
period and don't have enough information to ascertain the waveform's 
shape.  At a 2X sample rate, you can't tell if the signal recorded is a 
sine wave, a square wave, a triangle wave, or what.

Tektronix has a great pamphlet, "The XZY's Of Oscillicopes" which goes 
into great detail on this, showing waveform shapes and what you'd get at 
various sample rates.  I used to have an even shorter, better 
explanation, but I can't find it.

A better rule and the rule I use at work for setting data acquisition 
rates on our turboshaft engine test cell is the 10X rule.  If I'm 
anticipating a 2 KHz signal, I'll set the data collection system at 20 
KHz to ensure that not only can I reconstruct the signal, but I can 
determine the shape of the waveform.

To me, the saving grace is that I believe we're looking not at direct 
sampling at 10 meters, but some sort of down-conversion of the 10 meter 
signal to something easily processed, correct?

thanks and 73,
ben
-- 
Thanks and 73,
Ben, KD5BYB


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