[sdiy] Do digital filters still explode?

[karl dalen]

Thanks Richie and Eric to, most interesting read!
I will keep this in mind when it's time for me to
start to fiddle around with filters!

KD

>Richie Burnett <rburnett at richieburnett.co.uk>:

> 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, 
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