[hpsdr] sampling

[Bob McGwier]

Jason A. Beens wrote:
> ***** High Performance Software Defined Radio Discussion List *****
>
> You would get no information in the case you mentioned, but strictly
> speaking the Nyquist theorem is violated because the sampling frequency
> is equal to 2x, instead of greater than 2x the bandwidth of interest.
> Sampling at exactly 2x would cause an alias to DC.  In this case the DC
> value would be zero because we are sampling on zero crossings.    
>   
You will get some information even if imperfect.  If the phase of the 
signal is not zero or pi radians,  then one or both will be non-zero.

> I think, but am not certain, that the 192 kHz rate is simply being used
> to over sample the audio frequency range (20-20,000 Hz).  I don't think
> the high sample rate is being used to reproduce audio up to 86 kHz,
> because dogs can't even hear that.  :) 
>   
The sample rate is being used because it is

a) supported by high end sound devices and Winblows, Linux, etc.
b) it provides nearly 200 kHz of IF (I/Q sampling) to look at.
> The over sampling provides extra dynamic range.  If you wanted the
> performance a 192 kHz sample rate gives you but you only wished to
> sample at the CD sample rate of 44 kHz, then you would have to sample
> the audio data with a higher resolution ADC.  There is a limitation on
> the practical bit-width of ADC's, and one solution is to sample with
> less resolution more often.  
>   
This is indeed true BUT only if you downsample and filter.  It is 
commonly called processing gain  and can be intuitively thought about as 
follows:  you are filtering off the noise power that is outside the 
bandwidth of interest and with significantly non-zero probability,  the 
signal of interest will "wiggle the voltage" on those samples where the 
noise and other signals "come near zero in amplitude" in the I or Q 
channel.  This will not happen often and that is because the signal is 
weak.  But it does not have to do it often if you filter and decimate to 
rise out of the noise.


> Hopefully someone knows definitively why the 192 kHz rate was chosen,
> and then speak up on the list.  You have me curious now... I will have
> to goo do some research.
>
> Jason Beens
> KB0CDN
>   


-- 
Robert W. McGwier, Ph.D.
Center for Communications Research
805 Bunn Drive
Princeton, NJ 08540
(609)-924-4600
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