IIR filter question

Steve Underwood <steveu@dis.org> writes:

> Adaptive IIRs seem to be widely used these days.

Why do you say that, Steve?
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Rick Lyons wrote:

> Hi Guys,
>    I was asked to review a potential article 
> for the IEEE Sig. Proc. magazine.  In that 
> article the author implies that IIR (recursive) 
> filters aren't as popular nowadays as they were in 
> the past (say 10-20 years ago).  
> 
> Now I'm no IIR filter designer, so I need your 
> opinions.  Aren't IIR filters still as popular 
> now for audio signal processing as they were 
> 10 years ago?
> 
> Thanks guys,
> [-Rick-]
> 
For general purpose signal processing -- I don't know.

For closing control loops?  Minimum phase filters are the only way to 
go, and you want filters with as few poles as possible.  So I think 
you'll see IIR filters there for decades to come.

-- 

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

Posting from Google?  See http://cfaj.freeshell.org/google/

Joerg wrote:

> I am no expert either but from what I have seen IIR is still
> used, often with some added measures to muffle their inherent
> instability upon signal loss.

What do you mean by "instability upon signal loss"?

> For narrowband applications wave digital filters (WDF) have made
> inroads and probably eaten away at IIR's "market share",
> especially in the telecom business.

Aren't WDF techically IIR too?


Martin

-- 
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Martin Eisenberg wrote:
> Joerg wrote:
...
> > For narrowband applications wave digital filters (WDF) have made
> > inroads and probably eaten away at IIR's "market share",
> > especially in the telecom business.
>
> Aren't WDF techically IIR too?

i think there is much more of a similarity to FIR.  sorta like an
analog, continuous-time delay line with discrete taps.  if the taps are
equally spaced you can do all of the FIR techniques such as
Parks-McClellan to design tap coefficients.

i suppose you can explicitly feed back to the input and it will be IIR.
 but you can do that with conventional FIRs, too.

r b-j

Hi Rick,

> Looking at your Item# 2, the author of the article
> that I'm reviewing states that IIR filters are "difficult,
> if not impossible" to use for adaptive filtering.

In my item #2, I was refering to the transitioning of filter
coefficients.  IIR filters have fewer coefficients which generally
makes them easier to adjust in real time.  (There are stability issues
to consider, but that is beyond the scope of this discussion.)  Also,
an IIR topology such as the Chamberlain topology has coefficients that
directly map to filter parameters, making it very easy to adjust in
real-time.

I have never tried to implement an adaptive IIR filter in the
traditional sense.  However, for many of the reasons already discussed
by others in the group, I would surmise that adaptive IIR filtering is
more difficult than adaptive FIR filtering although not "impossible."

Brian Neunaber

Hello Martin,

> 
>>I am no expert either but from what I have seen IIR is still
>>used, often with some added measures to muffle their inherent
>>instability upon signal loss.
> 
> What do you mean by "instability upon signal loss"?
> 

When the input signal is abruptly lost and comes back the output of the 
filter might keep on ringing for a long time, sometimes pretty much forever.

> 
>>For narrowband applications wave digital filters (WDF) have made
>>inroads and probably eaten away at IIR's "market share",
>>especially in the telecom business.
> 
> Aren't WDF techically IIR too?
> 

If done in the classical way they are usually stable. WDFs are a direct 
translation of analog components into the digital domain. Maybe there is 
another method these days but the only design methodology I know is to 
first design the analog filter and then proceed to translate to WDF. 
Suits me since I 'think analog' anyway ;-)

Regards, Joerg

http://www.analogconsultants.com

Martin Eisenberg wrote:

> Joerg wrote:
> 
> 
>>I am no expert either but from what I have seen IIR is still
>>used, often with some added measures to muffle their inherent
>>instability upon signal loss.
> 
> 
> What do you mean by "instability upon signal loss"?
> 
(snip)

It's a consequence of quantization, which is what you call the effect of 
rounding off the signal after multiplies and adds.

When you have a signal going into the filter the effects of the 
quantization tends to appear to be white noise with a uniform 
distribution.  When the signal goes away, however, the quantization 
tends to look like little blocks of infinite gain because small input 
changes result in step changes at the output.  These little infinite 
gain blocks practically guarantee that any 2nd-order filter will 
oscillate.  Since the human ear (and no doubt other applications) are 
far more sensitive to single tones than they are to white noise this can 
cause problems with your system.

You can reduce this effect by increasing your filter precision and/or 
injecting an intentional noise signal into the filter input, but you 
can't make it go away.

-- 

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

Posting from Google?  See http://cfaj.freeshell.org/google/

Tim Wescott wrote:
> Martin Eisenberg wrote:
> 
>> Joerg wrote:
>>
>>
>>> I am no expert either but from what I have seen IIR is still
>>> used, often with some added measures to muffle their inherent
>>> instability upon signal loss.
>>
>>
>>
>> What do you mean by "instability upon signal loss"?
>>
> (snip)
> 
> It's a consequence of quantization, which is what you call the effect of 
> rounding off the signal after multiplies and adds.
> 
> When you have a signal going into the filter the effects of the 
> quantization tends to appear to be white noise with a uniform 
> distribution.  When the signal goes away, however, the quantization 
> tends to look like little blocks of infinite gain because small input 
> changes result in step changes at the output.  These little infinite 
> gain blocks practically guarantee that any 2nd-order filter will 
> oscillate.  Since the human ear (and no doubt other applications) are 
> far more sensitive to single tones than they are to white noise this can 
> cause problems with your system.
> 
> You can reduce this effect by increasing your filter precision and/or 
> injecting an intentional noise signal into the filter input, but you 
> can't make it go away.

The technique called fraction (or remainder) saving can reduce it 
greatly, sometimes eliminating any trace of a limit cycle. R.B-J. showed 
explicitly how to apply the technique to a DC blocker, but it works 
wherever division is done.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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Jerry Avins wrote:
> Tim Wescott wrote:
> > Martin Eisenberg wrote:
> >
> >> Joerg wrote:
> >>
> >>> I am no expert either but from what I have seen IIR is still
> >>> used, often with some added measures to muffle their inherent
> >>> instability upon signal loss.
> >>
> >> What do you mean by "instability upon signal loss"?
> >
> > It's a consequence of quantization, which is what you call the effect of
> > rounding off the signal after multiplies and adds.

the name for this is "limit cycling" and it is non-linear phenomena and
should not be confused with unstable IIR filters (because of pole
location).

> > When you have a signal going into the filter the effects of the
> > quantization tends to appear to be white noise with a uniform
> > distribution.

if the signal amplitude is a good deal larger than the quantization
step.  then where the pre-rounded signal lands within the step is
pretty random and the quantization error is pretty well
"pdeudo-independent" of the signal.

> > When the signal goes away, however, the quantization
> > tends to look like little blocks of infinite gain because small input
> > changes result in step changes at the output.  These little infinite
> > gain blocks practically guarantee that any 2nd-order filter will
> > oscillate.

that is not a bad way to look at it.

> >  Since the human ear (and no doubt other applications) are
> > far more sensitive to single tones than they are to white noise this can
> > cause problems with your system.
> >
> > You can reduce this effect by increasing your filter precision and/or
> > injecting an intentional noise signal into the filter input,

this noise is called "dither", and, strictly speaking, the place to
inject the dither is immediately before the quantization block, not
necessarily the input (you wouldn't want the dither to be in the input
feedforward states of the IIR or of an FIR).

> > but you can't make it go away.

yes, and no.  strictly speaking, you cannot with finite power dither
decouple *all* of the moments of the quantization error from the
signal, but with triangular PDF dither with amplitude of 2 LSBs, you
can decouple the first two moments, the mean and the variance, of the
quantization error from the signal getting quantized.  dunno about
other applications but no audio or aural experiment has ever shown that
human beings can here the correlation of the quantized signal to 3rd
and higher order statistical moments of the quantization noise.  with
that kind of dither you really *can* make it go away.  the quantizer
sounds like constant power white noise (if the dither was white and
there is no noise shaping) and the probabilistic mean of the quantized
output is precisely the value of the input to the quantizer.

> The technique called fraction (or remainder) saving can reduce it greatly,

at low frequencies, Jerry.  it makes it *worse* at Nyquist, but even at
Fs = 44.1 kHz, our ears don't give a rat's ass about increased noise at
Nyquist.

> sometimes eliminating any trace of a limit cycle.

only for DC.  there is no DC limit cycle if you do fraction saving.
other low frequencies the quantization noise is reduced and at some
frequency about an octave below Nyquist, there is the trade off.  above
that frequency, it gets worse but we don't really care.

> R.B-J. showed explicitly how to apply the technique to a DC blocker

Tim knows about that DC blocking trick and i remember Tim improved upon
it, making it 2 instructions per sample (with the right pipelining)
reducing it from 3 which i never thought could ever be done.  i'm still
impressed.  (i.e. Tim made a permanent impression on me with that, and
if Grant wants to, we should update the trick at dspguru.com .)

r b-j

R.Lyons@_BOGUS_ieee.org (Rick Lyons) wrote in news:44344259.337998187
@news.sf.sbcglobal.net:

> 
> Hi Guys,
>    I was asked to review a potential article 
> for the IEEE Sig. Proc. magazine.  In that 
> article the author implies that IIR (recursive) 
> filters aren't as popular nowadays as they were in 
> the past (say 10-20 years ago).  
> 
> Now I'm no IIR filter designer, so I need your 
> opinions.  Aren't IIR filters still as popular 
> now for audio signal processing as they were 
> 10 years ago?
> 
> Thanks guys,
> [-Rick-]
> 

I did my first DSP project with an NEC 7725 in the late 1980s. It was a 
first generation DSP chip.

In my application, I designed an FSK modem using IIR filters. FIR filters 
were not even an option since I din't have sufficient MIPS or memory.

IIRs do not necessarily need great precision math. It mostly depends on 
the filter requirements. High performance audio filters tend to be 
critical since the poles and zeros can get very close to the unit circle 
at low frequencies. A bandpass filter with a center at fs/4 might be 
fairly insensitive.

IIRs tend to take a lot less computation time and memory than a similar 
FIR.

My the early and mid 1990s, I was using a Analog Devices 21xx (2105 or 
2181) DSPs. The applications I did then used almost exclusively FIRs over 
IIRs. I think there were several reasons.

1. They are stable.
2. Memory was plentiful and MIPs were sufficient.
3. Linear Phase is often nice.
4. I was using 16 bit fixed point which can be a problem with IIR 
filters.

Mask charges have also been increasing over the years. This means that 
fewer custom silicon created. I.P. is more likely to be directed to a 
programmable part that a custom ASIC. I think this also will reduce the 
the IIR numbers a bit.

I am finding a new change in the last few years. Most of my applications 
have more than enough MIPS. I think that other features of devices have 
greater relative significance than in the past. You might decide that all 
candidates are fast but that processor A has better preripherals than B, 
or lower power, cost , etc. These might be the significant deciders.

IF MIPs and memory are abundant, its often easier to go FIR than IIR.

I do agree with Grant that with higher precision math IIR implementation 
is less of an issue. This is true whether you are looking a fixed point 
implementation or float.

So I guess, I agree that IIRs are probably a little less popular than say 
20 years ago. I think the change might have been about 15 years ago.

With modern programmable devices, I think you still should should pick 
type the works best for the situation at hand. I have many applications 
that use both.  


-- 
Al Clark
Danville Signal Processing, Inc.
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