Reply by glen herrmannsfeldt●January 21, 20052005-01-21
Bob Cain wrote:
(I wrote)
>> Of all possible FIRs only a very small fraction have an
>> FIR as their inverse, but you might get lucky.
> OTOH, in world of audio impulse responses I have yet to see an inverse
> that isn't decaying to zero such that it eventually becomes finite just
> due to digital representation limits.
> Most inverses aren't much longer than the original for all practical
> purposes.
IIR, or more specifically recursive filters, have the advantage
in the number of terms required for some common filter designs,
but it would seem that in finite precision arithmetic (most
audio systems) FIR could do just as well.
-- glen
Reply by Jon Harris●January 20, 20052005-01-20
"Bob Cain" <arcane@arcanemethods.com> wrote in message
news:cspja301527@enews3.newsguy.com...
>
>
> glen herrmannsfeldt wrote:
>
> > Of all possible FIRs only a very small fraction have an
> > FIR as their inverse, but you might get lucky.
>
> OTOH, in world of audio impulse responses I have yet to see
> an inverse that isn't decaying to zero such that it
> eventually becomes finite just due to digital representation
> limits.
Worst case is probably something like an IIR reverb, which decays into the
digital noise floor typically after "seconds".
Reply by Bob Cain●January 20, 20052005-01-20
glen herrmannsfeldt wrote:
> Of all possible FIRs only a very small fraction have an
> FIR as their inverse, but you might get lucky.
OTOH, in world of audio impulse responses I have yet to see
an inverse that isn't decaying to zero such that it
eventually becomes finite just due to digital representation
limits.
Most inverses aren't much longer than the original for all
practical purposes.
Bob
--
"Things should be described as simply as possible, but no
simpler."
A. Einstein
Reply by robert bristow-johnson●January 20, 20052005-01-20
in article 35aphtF4j6ut4U1@individual.net, Jon Harris at
goldentully@hotmail.com wrote on 01/20/2005 17:27:
> "robert bristow-johnson" <rbj@audioimagination.com> wrote in message
> news:BE157E3C.3F3C%rbj@audioimagination.com...
>> in article 35abq6F4j58phU1@individual.net, Jon Harris at
>> goldentully@hotmail.com wrote on 01/20/2005 13:33:
>>
>>> it makes some sense that what we like to call FIR
>>> filters (zero only) are really a sub-set of a larger class of filters that
>>> we tend to call IIR filters (pole and zero).
>>
>> remember that FIR filters *do* have just as many poles as they have zeros.
>> it's just that all of the poles of an FIR filter are at z=0.
>
> You snipped the part where I said "non-trivial", which was my way of
> acknowledging that issue. I was considering the z=0 poles of an FIR filter to
> be "trivial poles".
ok, fine. i didn't know that's what you meant.
it's just that the kernal of the answer to the OP question is that when you
make the inverse of and FIR or IIR filter, the poles become zeros and the
zeros become poles which means that only minimum-phase filters can be
inverted to be a stable filter. whether that be FIR or IIR. those poles at
the origin become zeros.
--
r b-j rbj@audioimagination.com
"Imagination is more important than knowledge."
Reply by Jon Harris●January 20, 20052005-01-20
"Randy Yates" <randy.yates@sonyericsson.com> wrote in message
news:xxpsm4vzyq4.fsf@usrts005.corpusers.net...
> "Jon Harris" <goldentully@hotmail.com> writes:
>
> > "Randy Yates" <randy.yates@sonyericsson.com> wrote in message
> > news:xxp3bww2sop.fsf@usrts005.corpusers.net...
> > > glen herrmannsfeldt <gah@ugcs.caltech.edu> writes:
> > >
> > > >
> > > > Yes, but I also claimed that FIRs are a subset of IIRs.
> > >
> > > That doesn't make sense to me, Glen. If the total class of digital
> > > filters can be partitioned into two sets, those with finite impulse
> > > response (i.e., "FIR" filters), and those with infinite impulse
> > > response (not including finite impulse responses), then including FIRs
> > > in the set of IIRs causes the set of IIRs to be equivalent to the
> > > total class of digital filters. If that is the case, then the original
> > > claim is trivially true, "I read that the inverse of a [digital] FIR
> > > filter is always a digital filter."
> >
> > Glen in I had a similar discussion recently in my little IIR puzzle thread.
The
> > terms FIR and IIR certainly do imply a nice neat distinction. However, if
you
> > consider IIR filters to be filters with both poles and zeros and FIR filters
to
> > be filters with only (non-trivial) zeros, then it makes more sense that one
is a
> > sub-set of the other.
>
> Essentially you're postulating that an IIR is a filter with a rational
transfer
> function, while an FIR is a filter with a polynomial transfer function with a
> possible exception of poles at z = 0.
>
> Yeah, I'll buy that Jon (i.e., that one is a subset of the other, defined this
> way).
Yes, and thanks for "rigourizing" it (taking my descriptive text and adding more
mathematical meat)!
Reply by Jon Harris●January 20, 20052005-01-20
"robert bristow-johnson" <rbj@audioimagination.com> wrote in message
news:BE157E3C.3F3C%rbj@audioimagination.com...
> in article 35abq6F4j58phU1@individual.net, Jon Harris at
> goldentully@hotmail.com wrote on 01/20/2005 13:33:
>
> > it makes some sense that what we like to call FIR
> > filters (zero only) are really a sub-set of a larger class of filters that
we
> > tend to call IIR filters (pole and zero).
>
> remember that FIR filters *do* have just as many poles as they have zeros.
> it's just that all of the poles of an FIR filter are at z=0.
You snipped the part where I said "non-trivial", which was my way of
acknowledging that issue. I was considering the z=0 poles of an FIR filter to
be "trivial poles".
Reply by Jerry Avins●January 20, 20052005-01-20
glen herrmannsfeldt wrote:
> Jerry Avins wrote:
>
>> Jon Harris wrote:
>
>
> (snip)
>
>>> Glen in I had a similar discussion recently in my little IIR puzzle
>>> thread. The
>>> terms FIR and IIR certainly do imply a nice neat distinction.
>>> However, if you
>>> consider IIR filters to be filters with both poles and zeros and FIR
>>> filters to
>>> be filters with only (non-trivial) zeros, then it makes more sense
>>> that one is a
>>> sub-set of the other. I know there are boundary cases that muddy the
>>> waters,
>>> but from that perspective, it makes some sense that what we like to
>>> call FIR
>>> filters (zero only) are really a sub-set of a larger class of filters
>>> that we
>>> tend to call IIR filters (pole and zero).
>
>
>> Poles-and-zeros vs. zeros-only is one dichotomy, but another -- closer
>> to the names -- is an impulse response that may decay but whose end
>> point depends only on the precision of the calculation vs. an impulse
>> response with a definite end. Integers are a subset of real numbers, but
>> integer vs. non-integer is a true dichotomy.
>
>
> Yes, that is the question. In the previous discussion we had:
>
> y(n) = A*y(n-1) + B*x(n) + C*x(n-1)
>
> As a first order IIR filter, or, as you say recursive.
>
> If you implement this filter in hardware or software you say that it is
> an implementation of an IIR filter. The hardware or software doesn't
> change if A happens to be zero. Every cycles y(n-1) is multiplied by
> zero.
>
> Consider a Fortran programmer: 2 is an integer, 2.0 is real.
>
> (In C, 2.0 is double, the analogy doesn't work.)
>
> Some might consider it the difference between theoretical science and
> experimental science. That is, whether you actually build it or just
> discuss it.
>
> -- glen
If one equates IIR to recursive, then he must accept your categories. I
prefer to think that y(n) = A*y(n-1) + B*x(n) + C*x(n-1) is recursive,
but that for some values of A, B, and C, it is FIR.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by robert bristow-johnson●January 20, 20052005-01-20
in article 35abq6F4j58phU1@individual.net, Jon Harris at
goldentully@hotmail.com wrote on 01/20/2005 13:33:
> it makes some sense that what we like to call FIR
> filters (zero only) are really a sub-set of a larger class of filters that we
> tend to call IIR filters (pole and zero).
remember that FIR filters *do* have just as many poles as they have zeros.
it's just that all of the poles of an FIR filter are at z=0.
--
r b-j rbj@audioimagination.com
"Imagination is more important than knowledge."
Reply by glen herrmannsfeldt●January 20, 20052005-01-20
Jerry Avins wrote:
> Jon Harris wrote:
(snip)
>>Glen in I had a similar discussion recently in my little IIR puzzle thread. The
>>terms FIR and IIR certainly do imply a nice neat distinction. However, if you
>>consider IIR filters to be filters with both poles and zeros and FIR filters to
>>be filters with only (non-trivial) zeros, then it makes more sense that one is a
>>sub-set of the other. I know there are boundary cases that muddy the waters,
>>but from that perspective, it makes some sense that what we like to call FIR
>>filters (zero only) are really a sub-set of a larger class of filters that we
>>tend to call IIR filters (pole and zero).
> Poles-and-zeros vs. zeros-only is one dichotomy, but another -- closer
> to the names -- is an impulse response that may decay but whose end
> point depends only on the precision of the calculation vs. an impulse
> response with a definite end. Integers are a subset of real numbers, but
> integer vs. non-integer is a true dichotomy.
Yes, that is the question. In the previous discussion we had:
y(n) = A*y(n-1) + B*x(n) + C*x(n-1)
As a first order IIR filter, or, as you say recursive.
If you implement this filter in hardware or software you say
that it is an implementation of an IIR filter. The hardware or
software doesn't change if A happens to be zero. Every cycles
y(n-1) is multiplied by zero.
Consider a Fortran programmer: 2 is an integer, 2.0 is real.
(In C, 2.0 is double, the analogy doesn't work.)
Some might consider it the difference between theoretical
science and experimental science. That is, whether you actually
build it or just discuss it.
-- glen
Reply by ●January 20, 20052005-01-20
"Jon Harris" <goldentully@hotmail.com> writes:
> "Randy Yates" <randy.yates@sonyericsson.com> wrote in message
> news:xxp3bww2sop.fsf@usrts005.corpusers.net...
> > glen herrmannsfeldt <gah@ugcs.caltech.edu> writes:
> >
> > > Jerry Avins wrote:
> > > (someone wrote)
> > >
> > > >>>>I read that the inverse of an FIR filter is always an IIR filter. I
> > > >>>> have no idea how to prove this mathematically.
> > >
> > >
> > > (snip)
> > >
> > > > Glen's H(z) = 1 is a counterexample. Are there others?
> > >
> > > Yes, but I also claimed that FIRs are a subset of IIRs.
> >
> > That doesn't make sense to me, Glen. If the total class of digital
> > filters can be partitioned into two sets, those with finite impulse
> > response (i.e., "FIR" filters), and those with infinite impulse
> > response (not including finite impulse responses), then including FIRs
> > in the set of IIRs causes the set of IIRs to be equivalent to the
> > total class of digital filters. If that is the case, then the original
> > claim is trivially true, "I read that the inverse of a [digital] FIR
> > filter is always a digital filter."
>
> Glen in I had a similar discussion recently in my little IIR puzzle thread. The
> terms FIR and IIR certainly do imply a nice neat distinction. However, if you
> consider IIR filters to be filters with both poles and zeros and FIR filters to
> be filters with only (non-trivial) zeros, then it makes more sense that one is a
> sub-set of the other.
Essentially you're postulating that an IIR is a filter with a rational transfer
function, while an FIR is a filter with a polynomial transfer function with a
possible exception of poles at z = 0.
Yeah, I'll buy that Jon (i.e., that one is a subset of the other, defined this
way).
--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
randy.yates@sonyericsson.com, 919-472-1124