[hpsdr] how do you get 186 kHz display from 192 kHz sampling

[Raymond Mack]

This is one of those details of Nyquist that is not usually explained very well.

The Nyquist limit applies to "real sampled signals" which means there are evenly 
spaced samples in time and assumed to be sampled with the I of an I/Q but not 
the Q part.

The Nyquist criterion occurs because you can get amplitude, but not phase 
information at the Nyquist frequency.   Using "complex sampling" gives you a 
mechanism to go right up to the Nyquist limit because the I and Q samples give 
you both amplitude and phase.  In practical terms you can never really sample 
any useful data anywhere near the limit with real sampling because of the alias 
filter requirements.  It is only slightly better with complex sampling as 
evidenced by the 186 kHz display rather than all the way up to 192 kHz. The 
other practical effect is that you get better phase and amplitude information 
with I/Q sampling than you do with real sampling at twice the rate.  An I/Q 
sampling system at 192 ksps gives you the same number of samples as doing real 
sampling at 384 ksps, but the phase information is more robust with I/Q sampling 
because the two samples are not evenly spaced.

Said another way, you get both phase and amplitude information with every set of 
samples with I/Q basically right up to the limit.  With real sampling, it takes 
a large number of samples to get the phase information to show up when operating 
close to the limit.

Ray Mack
W5IFS
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***** High Performance Software Defined Radio Discussion List *****


  I'm trying to understand why and how the bandscope width (I'm not 
talking about the full spectrum bandscope on cuSDR) on cuSDR is twice as 
wide and the bandscope width on PowerSDR at the same sampling rate (192 
Khz).  PowerSDR provides a bandscope width that is roughly 1/2 the 
sampling rate.  This is what I have come to expect based on the fact 
that using a 192 Khz sampling rate the highest frequency that can be 
passed would be 96 Khz.  But then I noticed that cuSDR provides a 
roughly 192 Khz bandscope when using a 192 Khz sampling rate. At first I 
thought that was impossible, but after playing with it for a while I 
came to the conclusion that it was working properly.

So I'm trying to understand how that is possible.  Is it because 
PowerSDR has its heritage with I/Q sampling done in the analog domain 
with analog "real" aliasing filters so that for 192 Khz sampling the 
data contains frequencies from 0-96 Khz, whereas cuSDR is depending on 
the I/Q filtering being done in the digital domain with complex output 
and therefore the I/Q data can contain frequencies from -96 Khz to 96 
Khz? Or is it that the FPGA is not filtering at ~96 Khz but at ~192 Khz 
instead, so that the data contains aliased frequencies but somehow the 
aliases can be determined via the separate I and Q streams? I have 
severe doubts about the latter since I've always understood that once 
aliased always aliased.  Is there some other explanation?

How difficult would it be to "upgrade" PowerSDR to double the bandscope 
width?

Thanks,

John
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