Wednesday, April 24, 2013

Nyquist criterion revisited (simplified)

The signal spectrum must be fully contained in a Nyquist zone, otherwise aliasing will occur!

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.

** Signals sampled in the even Nyquist zone have their spectra flipped while those in the odd Nyquist zone retain the spectra.

 More theoretical details can be found in "Understanding Digital Signal Processing" By Richard Lyons

An aweosme method (not by me) to find the optimum sampling rate using undersampling method :

1: The Nyquist region can be obtained using n = floor(fc/B + 1/2)
  where floor(x) rounds x towards minus infinity, fc is the
  IF center frequency and B the signal bandwidth.

2: The minimum fs can then be easily obtained by fs = (2*fc+B)/n
3: If the optimum fs is intended use fs = 4*fc/(2*n-1) instead.

Moreover, if (fc/B + 1/2) is an integer, then minimum fs equals
the optimum fs.

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