[sdiy] Do digital filters still explode?

[Paul Perry]

For that matter, some analog filters explode when modulated (or adjusted by 
pots) rapidly.
At least, the amplitude can swing out of range, clipping.
Behaviour while varying paramaters is something usually neglected in filter 
design.
(Not that *I* could do the calculations myself.. but I know there is a 
potential problem!)

paul perry Melbourne Australia

----- Original Message ----- 
From: "Richie Burnett" <rburnett at richieburnett.co.uk>
To: <synth-diy at dropmix.xs4all.nl>
Sent: Monday, February 07, 2011 8:53 AM
Subject: [sdiy] Do digital filters still explode?


> Yes, if they're not programmed well !
>
> Some filter realisations like the direct-form IIR biquad take particularly
> badly to rapid modulation of the cutoff frequency.  There are a number of
> things that can happen when you start changing the filter coefficients on
> the fly:
>
> As Eric said a digital filter can go unstable if the trajectory taken by 
> the
> poles takes them outside the unit circle in the z-domain, even for just a
> short time.  So you need to give some thought to the order in which you
> update denominator coefficients if they are not to even temporarily
> factorise to give poles outside the unit-circle!   This is more an issue 
> of
> poor implementation of the coefficient modification though than the choice
> of filter itself.
>
> However, there is a more fundamental problem with the direct-form IIR
> realisation when it comes to modulating its coefficients.  Each output
> sample is effectively defined by previous output samples and input 
> samples.
> So in the case of a highly resonant filter which now has a silent input, 
> the
> only thing that keeps the output ringing is the information contained in 
> the
> last two output samples.  The filter's states are essentially the last two
> output samples.  (i.e. What the previous output is, and what the 
> difference
> between the previous output and the one before is.)  _BUT_  if you 
> suddenly
> change the IIR filter coefficients to modify the cutoff frequency or Q,
> these two state variables may now not be at all appropriate for the new
> filter design!
>
> Imagine switching suddenly from a high-Q response with high cutoff 
> frequency
> where consecutive output samples are radically different, to a new high-Q
> response with a very low resonant frequency where the output varies very
> little between consecutive samples.  Suddenly switching filter 
> coefficients
> without modifying the history stored in the previous states is likely to
> make the output of a direct-form IIR go ape.  The low Fc filter kernel
> ultimately expects the last two output states to be quite close together,
> but if they are far apart because they apply to a filter with much higher
> resonant frequency, the output of the filter is likely to blow up.  If the
> arithmetic isn't programmed properly this can then cause the accumulator 
> to
> overflow.  Now, consecutive output samples are even less appropriate if 
> some
> are overflowed, triggering violent bursts of noise, limit cycles etc.
>
> Alternative digital filter realisations that store the filter states
> differently like the coupled-form designs, and Chamberlain 
> (state-variable)
> filter tolerate coefficient modulation much better.  This is because the
> current filter conditions are stored as two orthogonal states at the same
> point in time which are far more applicable after the filter coefficients
> have been modified.
>
> -Richie,
>
> _______________________________________________
> Synth-diy mailing list
> Synth-diy at dropmix.xs4all.nl
> http://dropmix.xs4all.nl/mailman/listinfo/synth-diy


--------------------------------------------------------------------------------



No virus found in this incoming message.
Checked by AVG - www.avg.com
Version: 9.0.872 / Virus Database: 271.1.1/3425 - Release Date: 02/06/11 
06:33:00