"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 thatwe> > 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".
inverse of an FIR filter
Started by ●January 18, 2005
Reply by ●January 20, 20052005-01-20
Reply by ●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, ifyou> > consider IIR filters to be filters with both poles and zeros and FIR filtersto> > be filters with only (non-trivial) zeros, then it makes more sense that oneis a> > sub-set of the other. > > Essentially you're postulating that an IIR is a filter with a rationaltransfer> 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 ●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 ●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 ●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 ●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
