[hpsdr] A/D

[John Kolb]

At 07:45 AM 4/21/2007, Henry Vredegoor wrote:
>***** High Performance Software Defined Radio Discussion List *****
>
>Hi Ben, All,
>
><
>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.
> >
>
>Assumed there IS significant content above 30 MHz....... ;-)
>
><
>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.
> >
>
>Is this true? I thought it would be possible to reconstruct it to a 100 % ?
>I didn't know this, I am still studying the sample theory in more detail as
>I get along.
>But I get frustrated by the mathematics....... :-0
>I will have to study this more.

I can't follow higher math, but can follow simple examples.

Take a 3 kHz sine wave, sample it at a 60 MHz rate, and graph the result
drawing a straight line between each sample - a nice picture of a sine wave.
Change the waveform to a triangle, then a square wave - nice pictures
of triangles and square waves.

Now take a 30 MHz sine wave, 2V peak to peak. Sample at 60 MHz, fortunately
sampling at the 90 and 270 degree times of the 30 MHz signal.  A/D samples
will measure +1, -1, +1, -1, +1, -1 ...
Graph these, drawing a straight line between each sample - looks like
a triangel \/\/\
Change the waveform to a triangle, then a square, still samples read 
+1, -1, +1, -1, +1 ...
and graph still looks like a triangle.
Change the waveform back to a sine, and sample now at the 0 and 180 
degree times
on the waveform.  A/D readings are now 0, 0, 0, 0 ...   can't do much trying
to graph that.

Input a 59.999 MHz signal, and sample at a 60 MHz rate.  A graph of 
the A/D readings
will look like the input waveform, sine, triangle or square, but at 1 
kHz.  Sample aliasing.
Change the input to 50 MHz and a 10 MHz alias is created.  Change the input
to 30.5 MHz and a 29.5 MHz alias is created.

Thus if we want to receive 29.5 MHz signals, we do not want to also 
hear 30.5 MHz signals
at the same time.  We can't have a brick wall filter which will pass 
0 to 30 MHz signals,
and provide 100 db or more rejectection to 30.001 MHz signals and above.

We can, however, create a decent 30 MHz low pass filter, which will 
attenuate singals 40 MHz
and above.  If we then use a 80 MHz sample rate instead of 60 MHz, no 
aliasing problem.

The figure I've most often seen is that we can operate up to 40% of 
the sample rate, not up
to 50% as predicted by Nyquist theory.

John



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