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Dan Boschen
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If you note on the upper left corner of the upper plot, the scale of the magnitude is $10E4$close to 40,000. An error of 15 is not very significant. The reason we decompose (factor) the higher order filter into 2nd order sections is to decouple the poles which significantly reduces numerical precision errors (compare an error raised to the 8th power vs an error squared and added 4 times which is essentially what happens when the smaller filters are cascaded). Due to this, the “ideal” filter as described in the plot is likely the less ideal of the two and the we are seeing the limits of the floating point precision that is used (and ultimately rounding of the coefficients from their ideal values).

If you note on the upper left corner of the upper plot, the scale of the magnitude is $10E4$. An error of 15 is not very significant. The reason we decompose (factor) the higher order filter into 2nd order sections is to decouple the poles which significantly reduces numerical precision errors (compare an error raised to the 8th power vs an error squared and added 4 times which is essentially what happens when the smaller filters are cascaded). Due to this, the “ideal” filter as described in the plot is likely the less ideal of the two and the we are seeing the limits of the floating point precision that is used (and ultimately rounding of the coefficients from their ideal values).

If you note on the upper left corner of the upper plot, the magnitude is close to 40,000. An error of 15 is not very significant. The reason we decompose (factor) the higher order filter into 2nd order sections is to decouple the poles which significantly reduces numerical precision errors (compare an error raised to the 8th power vs an error squared and added 4 times which is essentially what happens when the smaller filters are cascaded). Due to this, the “ideal” filter as described in the plot is likely the less ideal of the two and the we are seeing the limits of the floating point precision that is used (and ultimately rounding of the coefficients from their ideal values).

Source Link
Dan Boschen
  • 55k
  • 2
  • 59
  • 143

If you note on the upper left corner of the upper plot, the scale of the magnitude is $10E4$. An error of 15 is not very significant. The reason we decompose (factor) the higher order filter into 2nd order sections is to decouple the poles which significantly reduces numerical precision errors (compare an error raised to the 8th power vs an error squared and added 4 times which is essentially what happens when the smaller filters are cascaded). Due to this, the “ideal” filter as described in the plot is likely the less ideal of the two and the we are seeing the limits of the floating point precision that is used (and ultimately rounding of the coefficients from their ideal values).