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

[Joseph DiVerdi]

Dear Henrique,

Aha, thank you for your patient explanation. I now understand your point.

<snip>
>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.
<snip>

To help me understand the point more clearly I created a little table showing 
the Nyquist borders as a function of sampling frequency and order:

               F sample ---->
    +-------------------------------------------+
    |   |  4.00    4.50    4.60    4.70    4.80 |
 o  +-------------------------------------------+
 r  | 0 |  0.00    0.00    0.00    0.00    0.00 |
 d  | 1 |  2.00    2.25    2.30    2.35    2.40 |
 e  | 2 |  4.00    4.50    4.60    4.70    4.80 |
 r  | 3 |  6.00    6.75    6.90    7.05    7.20 |
 |  | 4 |  8.00    9.00    9.20    9.40    9.60 |
 |  | 5 | 10.00   11.25   11.50   11.75   12.00 |
 |  | 6 | 12.00   13.50   13.80   14.10   14.40 |
 v  | 7 | 14.00   15.75   16.10   16.45   16.80 |
    +-------------------------------------------+

As you have noted, 4.68Msample/second is the lowest sample frequency which 
fully contains our target signal band.

Is there a analytic relationship which provides a minimum sample frequency, 
orders, and interval limits? such as:

F(fcenter, fbandwidth/2) = { fsample, n-1, n }

Or must it be determined by trial and error in each case?

Best regards,
Joseph
-- 
Joseph A. DiVerdi, Ph.D., M.B.A.         
http://xtrsystems.com/           970.980.5868 (voice)
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