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 Tuesday, September 20, 2011 |
| Why is Nyquist important to A/D converters? |
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The problem of sampled systems keeps popping its head up. Remember what Nyquist said, that the maximum signal we can reconstruct is half of the sampling rate. If the signal we sample has components higher than 1/2 sampling rate then we get a phenomena called 'aliasing.' If I were to send an aliased signal back out of a computer to a D/A converter it would look like the signal was 'shifted' in frequency. This frequency shift would be equal to the sampling rate. Suppose a signal of Fs was put into an A/D converter and the sampling rate was Fs. It might appear on a D/A converter as a DC signal (because Fs - Fs = 0 ).
 As an everyday example of aliasing, have you ever seen a moving fan appear still under a strobe light? When the strobe is blinking at the same rpm's as the fans rotational speed, the fan will appear motionless.
The aliasing phenomena can occur if the sampled signal is at or above 1/2 the sampling rate OR IF IT HAS (Fourier) COMPONENTS AT OR ABOVE THIS RATE. In this case just those components above the Nyquist rate would be aliased, but the total signal if reconstructed will be distorted.
How do we deal with this issue? Typically we use an anti-aliasing filter on the front end of the A/D. It might be as simple as an RC or more complicated as a multi-pole active filter Chebychev or Buttworth configuration. The key is to understand how much attenuation we need at the stop band. Suppose our A/D is 12 bits. The ideal SNR is 72dB. Our filter should be designed to provide 72 db of attenuation at the stop band.
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damon at 8:29 PM |
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