Hello All,
As we all know that the brickwall filters h(n) response
extends from -inf to inf.
It is also non-causal system.
The filter has infinite taps and coefficients are symmetric.
so linear phase and constant group delay is gauranteed.
Now since the impulse response extends all the way to +/- inf
can this system be classified as IIR?
Though i understand that it might be physically possible to
implement it.
So my question is can an ideal LPF be called as Linear Phase
IIR?
Regards
Bharat Pathak
Arithos Designs
www.Arithos.com
ideal filter impulse response
Started by ●August 2, 2008
Reply by ●August 2, 20082008-08-02
bharat pathak wrote:> Hello All, > > As we all know that the brickwall filters h(n) response > extends from -inf to inf. > > It is also non-causal system. > > The filter has infinite taps and coefficients are symmetric. > so linear phase and constant group delay is gauranteed. > > Now since the impulse response extends all the way to +/- inf > can this system be classified as IIR? > > Though i understand that it might be physically possible to > implement it. > > So my question is can an ideal LPF be called as Linear Phase > IIR?For what my opinion is worth, no. Perhaps yes, but only as a matter of courtesy. Filters normally classified FIR or IIR are causal or quasi-causal (have responses that don't extend very far back in time). It is easy to fabricate a paradox by misapplying a dichotomy. If I call a snail's shell a house, are all snails domesticated by virtue of living in houses? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●August 2, 20082008-08-02
On Aug 2, 10:35 am, "bharat pathak" <bha...@arithos.com> wrote:> Hello All, > > As we all know that the brickwall filters h(n) response > extends from -inf to inf. > > It is also non-causal system. > > The filter has infinite taps and coefficients are symmetric. > so linear phase and constant group delay is gauranteed. > > Now since the impulse response extends all the way to +/- inf > can this system be classified as IIR? > > Though i understand that it might be physically possible to > implement it. > > So my question is can an ideal LPF be called as Linear Phase > IIR? > > Regards > Bharat Pathak > > Arithos Designswww.Arithos.comYou can call it the Arithos Filter (TM) if you want. You won't get much argument from the practitioner about what to call something that can't be realized in practice. John
Reply by ●August 2, 20082008-08-02
On 2 Aug, 16:35, "bharat pathak" <bha...@arithos.com> wrote:> Hello All, > > � � � As we all know that the brickwall filters h(n) response > � � � extends from -inf to inf.I would agree with the proviso that we talk about the impulse response and not the frequency response...> � � � It is also non-causal system. > > � � � The filter has infinite taps and coefficients are symmetric. > � � � so linear phase and constant group delay is gauranteed.With the usual definitions, it is a zero-phase filter and a zero-delay filter.> � � � Now since the impulse response extends all the way to +/- inf > � � � can this system be classified as IIR?If you read the definition of an IIR filter by the letter, "An IIR filter is a filter which has an impulse response of infinite duration," then yes, the ideal brick-wall filter is an IIR filter. On the other hand, the presently accepted definition of the terms FIR and IIR include filter structure, i.e. that FIRs are on the form K y[n] = sum x[n-k]b[k] k=0 (no feedback terms) whereas the IIRs are on the form M K y[n] = sum y[n-m]a[m] + sum x[n-k] b[k]. m=1 k=0 So by the present use of the term IIR, which defines a filter structure that includes feedback terms, the ideal brick-wall filter is *not* an IIR filter since it lacks feedback terms.> � � � Though i understand that it might be physically possible to > � � � implement it.Finite-length *approximations* to the ideal filter can only be implemented in off-line applications, meaning that one processes finite amounts of data already in storage.> � � � So my question is can an ideal LPF be called as Linear Phase > � � � IIR?Yes. Or a zero-phase IIR, again, with the usual definitions. A standard way to implement a zero-phase IIR filter is to run a standard IIR first forward and then backwards on a finite amount of data already stored. Again, the filter can only be used in off-line applications. Rune
Reply by ●August 2, 20082008-08-02
Rune Allnor wrote: ...> If you read the definition of an IIR filter by the letter, > "An IIR filter is a filter which has an impulse response of > infinite duration," then yes, the ideal brick-wall filter > is an IIR filter. > > On the other hand, the presently accepted definition of the > terms FIR and IIR include filter structure, i.e. that FIRs are > on the form > > K > y[n] = sum x[n-k]b[k] > k=0 > > (no feedback terms) whereas the IIRs are on the form > > M K > y[n] = sum y[n-m]a[m] + sum x[n-k] b[k]. > m=1 k=0 > > So by the present use of the term IIR, which defines a filter > structure that includes feedback terms, the ideal brick-wall > filter is *not* an IIR filter since it lacks feedback terms. > >> Though i understand that it might be physically possible to >> implement it. > > Finite-length *approximations* to the ideal filter can only > be implemented in off-line applications, meaning that one > processes finite amounts of data already in storage.I think you confound the definitions with their common implementations. An IIR filter's impulse response stretches out to (positive) infinity, while an FIR's does not. Your math is about implementation with a particular technology. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●August 2, 20082008-08-02
On 2008-08-02, Jerry Avins <jya@ieee.org> wrote:> Rune Allnor wrote: >> FIRs are on the form >> >> K >> y[n] = sum x[n-k]b[k] >> k=0 >> >> (no feedback terms) > > I think you confound the definitions with their common implementations. > An IIR filter's impulse response stretches out to (positive) infinity, > while an FIR's does not.To slightly restate Jerry's point: IIR and FIR are terms used to categorize realizable, discrete-time filters. A system such as the OP described has infinite impulse response but it's not an "IIR filter". To pick a nit with Rune's definitions: Although FIR filters *can* always be evaluated non-recursively, there are also recursive implementations of FIR filters, and the recursive implementation does not make them IIR. The most common example would be a moving average filter along the lines of: y[n] = y[n-1] - x[n-m] + x[n] which could also be written: y[n] = x[n-(m-1)] + x[n-(m-2)] ... + x[n] -- Ben Jackson AD7GD <ben@ben.com> http://www.ben.com/
Reply by ●August 3, 20082008-08-03
Rune Allnor wrote:> On 2 Aug, 16:35, "bharat pathak" <bha...@arithos.com> wrote: > >>As we all know that the brickwall filters h(n) response >>extends from -inf to inf.> I would agree with the proviso that we talk about the impulse > response and not the frequency response...The impulse responce of a brickwall LPF doesn't have to be infinite in time. It can be casual and semi infinite. While ago Andor had a topic about the brickwall IIR; there are infinitely many solutions. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●August 3, 20082008-08-03
Vladimir Vassilevsky wrote:> > > Rune Allnor wrote: > >> On 2 Aug, 16:35, "bharat pathak" <bha...@arithos.com> wrote: >> >>> As we all know that the brickwall filters h(n) response >>> extends from -inf to inf. > >> I would agree with the proviso that we talk about the impulse >> response and not the frequency response... > > The impulse responce of a brickwall LPF doesn't have to be infinite in > time. It can be casual and semi infinite. > > While ago Andor had a topic about the brickwall IIR; there are > infinitely many solutions.The response of any filter with a finite number of elements can be zero only at isolated frequencies*. There can be no analog brick-wall filter. Since the spectra of all sampled systems are necessarily discrete, a digital filter's transition band can me no narrower than a bin of the corresponding DFT. There can be no digital brick-wall filter. There can be pretty good approximations. Jerry _____________________________ * I.e. it cannot be identically zero over any non-zero interval. -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●August 3, 20082008-08-03
Jerry Avins wrote:> Vladimir Vassilevsky wrote: >> Rune Allnor wrote: >> >>> On 2 Aug, 16:35, "bharat pathak" <bha...@arithos.com> wrote: >>> >>>> As we all know that the brickwall filters h(n) response >>>> extends from -inf to inf. >> >> >>> I would agree with the proviso that we talk about the impulse >>> response and not the frequency response... >> >> >> The impulse responce of a brickwall LPF doesn't have to be infinite in >> time. It can be casual and semi infinite. >> >> While ago Andor had a topic about the brickwall IIR; there are >> infinitely many solutions. > > > The response of any filter with a finite number of elements can be zero > only at isolated frequencies*. There can be no analog brick-wall filter.I am not arguing that. What I said is despite of the popular belief, there are infinitely many solutions for the brick wall filters other then the textbook sin(x)/x, and those solutions can be causal as well. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●August 3, 20082008-08-03
Jerry Avins <jya@ieee.org> writes:> Since the spectra of all sampled systems are necessarily > discrete,Huh? The spectrum of all sampled (discrete) systems is periodic. The spectrum of all periodic systems is discrete. -- % Randy Yates % "She has an IQ of 1001, she has a jumpsuit %% Fuquay-Varina, NC % on, and she's also a telephone." %%% 919-577-9882 % %%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO http://www.digitalsignallabs.com
