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 2^{DS} ~ 10^{7}, 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.
Using this method I estimated digital noise of butter("LowPass", 2, 0.001) applied to white noise. Sampling frequency was 16 kHz.
