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camsr
KVRAF
 
6805 posts since 16 Feb, 2005

Postby camsr; Tue Jun 12, 2018 6:14 pm Re: Practical concerns when implementing “dynamically recalculable” filters in audio/musical equalizers?

Delay orders above 1 are invalid with respect to (direct, naive) modulation. To modify the higher order delays requires calculating their modification via the instant 0 order delay state and the 1st. The basis of this behavior is like simulating a transmission line, versus simulating an in-phase feedback circuit. A transmission line has elements that are not present at the calculation and are still traveling through the system.
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Z1202
KVRian
 
938 posts since 11 Apr, 2002

Postby Z1202; Tue Jun 12, 2018 10:28 pm Re: Practical concerns when implementing “dynamically recalculable” filters in audio/musical equalizers?

@camsr: is this a reply to my previous post?

mystran just mentioned that he's not sure how to formalize the requirement for smooth parameter modulation. My reply was that for the cutoff the problem can be formalized by looking at it as time axis warping (this is an, I believe, commonly known fact, and is particularly covered in the latest revision of my book). For other modulation types there is a spontaneous idea to require that the modulation should preserve the energy contained in a filter. However as there are probably infinitely many ways to define the contained energy, I was thinking of how to make it unequivocally defined (for the purpose). The eigenvectors, Jordan cells etc are a part of the state-space analysis.
camsr
KVRAF
 
6805 posts since 16 Feb, 2005

Postby camsr; Wed Jun 13, 2018 12:19 am Re: Practical concerns when implementing “dynamically recalculable” filters in audio/musical equalizers?

Z1202 wrote:@camsr: is this a reply to my previous post?


No, just waxing on second order equations and their delays. Changing a second order delay state via the instantaneous parameter is invalid. It's delayed so it's obvious that the current input state has nothing to do with it. Unfortunately this isnt true with the first order delay state, it forms the basis of the differentiation necessary to provide the filtering function, yet has it's own dilemmas regarding the fixed time step accuracy (even if time-warping attempts to mitigate that).
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