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Message ID: 7052     Entry time: Mon Jul 30 16:05:36 2012
Author: Den 
Type: Update 
Category: digital noise 
Subject: filter checker 

 We decided to write a script that will check online filters for digital noise. One method can be implemented using the following algorithm:

  • calculate filter output using single precision
  • calculate filter output using double precision and assume that it is precise
  • find digital noise at the output of the filter when single precision is used
  • extrapolate the result to the double precision filter dividing by 2D-S ~ 107, D - number of bits used in double precision mantissa, S - in single precision

Restriction: Single precision filter internal variables must be checked for overflows.

I applied this method to filtering a 1 Hz sine wave with a notch filter. Precise output should also be a 1 Hz wave => at other frequencies we see noise => digital noise spectrum should coincide with filter output. The plot shows the method worked out for this example.

iir_psd_notch.png

Using this method I estimated digital noise of butter("LowPass", 2, 0.001) applied to white noise. Sampling frequency was 16 kHz. 

iir_psd_lp.png iir_time_lp.png

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