IIR filter stability issues

Srikar wrote:
> Thanks Tim, and ya.. its for the second reason that I have to check the
> filter stability. I hav already checked them in theory and the problem
> has been that some of these filters turned up with noise when tested
> practically. Hence the effort to check them before I implement them in
> hardware.
> Srikar
>
> PS: Mark could you please elucidate further, the issue of limit cycle
> testingand also  With a large step function what should i look for in
> the output?

You want to apply large signals at frequencies that are equal to the
resonant frequency of poles  to check for overflow that may occur at
intermediate parts of the filter, i.e.  not necessarily the output but
at some stage in the middle.  The overflow can cause non-linearities
and also can sometimes cause a steady state oscillation that continues
even after the input is removed.  (This can happen in hardware also).
So you want to look for clipping anywhere in the filter.

Limit cycle oscillations are small low level oscillations that can
occur due to roundoff errors in an IIR filter.  These oscillations also
can continue after the input is removed.   I'm not sure what is the
best way to stimulate these to test for them.

I think FIR filters, because their structure lacks feedback,  are
immune to both of these problems.

Mark wrote:

> 
> Srikar wrote:
> 
>>Thanks Tim, and ya.. its for the second reason that I have to check the
>>filter stability. I hav already checked them in theory and the problem
>>has been that some of these filters turned up with noise when tested
>>practically. Hence the effort to check them before I implement them in
>>hardware.
>>Srikar
>>
>>PS: Mark could you please elucidate further, the issue of limit cycle
>>testingand also  With a large step function what should i look for in
>>the output?
> 
> 
> You want to apply large signals at frequencies that are equal to the
> resonant frequency of poles  to check for overflow that may occur at
> intermediate parts of the filter, i.e.  not necessarily the output but
> at some stage in the middle.  The overflow can cause non-linearities
> and also can sometimes cause a steady state oscillation that continues
> even after the input is removed.  (This can happen in hardware also).
> So you want to look for clipping anywhere in the filter.
> 
> Limit cycle oscillations are small low level oscillations that can
> occur due to roundoff errors in an IIR filter.  These oscillations also
> can continue after the input is removed.   I'm not sure what is the
> best way to stimulate these to test for them.

In general non-linear systems theory a limit cycle is any path through 
the phase space of the system that loops back on itself, i.e. any 
oscillation that reaches a steady amplitude, frequency and shape -- it 
doesn't even have to be a stable limit cycle; you can have unstable 
limit cycles where any small divergence will cause the system state 
vector to go someplace else.

In DSP the term has come to mean the small limit cycle as a result of 
quantization.  In practice any excitation that will get the states to 
nonzero values will probably excite a limit cycle.
> 
> I think FIR filters, because their structure lacks feedback,  are
> immune to both of these problems.
> 
Yes, they are.

-- 
-------------------------------------------
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Thanks for your help Tim, Mark. I was able to finish the project in
time.