Re: [Discuss-gnuradio] USB2 <-> fast ADC & DAC

[Henrique Miranda]

On Wed, 28 May 2003, Joseph DiVerdi wrote:

> <snip>
> >In this case the minimum sample rate that can be used is
> >((10.7 + 1) / 2.5) = 4.68 Msps and the signal spectrum will be
> >placed in the fifth Nyquist region.
> <snip>
> 
> Dear Henrique,
> 
> Thanks for your comments.
> 
> If I understand your argument correctly in that you are saying
> that in a *practical sense* the full sampling domain isn't fully usable
> and that it is necessary to sample a bit "further out" than specified by
> the Nyquist condition, I agree completely.

If you want to sample a bandpass signal (of bandwidth B) two conditions
must be met in order to avoid aliasing:

1: fs >= 2*B
2: The occupied bandwidth must be in a single Nyquist region defined as
   the interval [(n-1)*fs/2 ; n*fs/2], being n an integer.

In this particular case, n=5 and fs=4.68 Msps. This defines the
smallest Nyquist region - [9.36; 11.7] MHz -  in which the signal spectrum
is fully contained. To minimize the proximity to the Nyquist
frontiers (thus minimizing possible aliasing problems) the 
IF signal frequency is usually placed at the center of the Nyquist
region. This happens if you increase slightly the sample rate to
4.756 MHz (10.7/((n-1)/2+1/4)). This would be the optimum sample rate
in the present case.

This works well if the analog bandwidth of your A/D converter is greater
than maximum frequency of the signal to be sampled (which is easily
achieved for 10.7 MHz IFs using mainstream ADCs)

Regards,

Henrique  

 
(there is a third condition 

> 
> Best regards,
> Joseph
> -- 
> Joseph A. DiVerdi, Ph.D., M.B.A.          
> http://xtrsystems.com/           970.980.5868 (voice) 
> PGP Key ID: 0xD50A9E33
> 
> 
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