Hi All, I have a quick question from newbie to DSP. During my self education of DSP filter design I learnt that digital filter - quite like analog ones- have transient response (sometimes called "warm-up" time). This is easy to understand and calculate/predict for FIR filters of length N the transient last N-1 samples. However I did not find any reference that tell how to calculate length of transient response in samples of IIR filter. I met during my wanderings on web the following statement: "For IIR filters, the length of the transition region is dependent on the filter order and the feedback coefficient values" (link http://www.music.mcgill.ca/~gary/307/week2/filters.html). So my question is how do I know that transients in IIR filters have died out? Thanks for any help in advance Pawel
Length of IIR transients
Started by ●February 21, 2010
Reply by ●February 21, 20102010-02-21
On 21 Feb, 22:49, Pawel <prulikow...@gmail.com> wrote:> Hi All, > > I have a quick question from newbie to DSP. During my self education > of DSP filter design I learnt that digital filter - quite like analog > ones- have transient response (sometimes called "warm-up" time). This > is easy to understand and calculate/predict for FIR filters of length > N the transient last N-1 samples. However I did not find any reference > that tell how to calculate length of transient response in samples of > IIR filter. I met during my wanderings on web the following statement: > "For IIR filters, the length of the transition region is dependent on > the filter order and the feedback coefficient values" (linkhttp://www.music.mcgill.ca/~gary/307/week2/filters.html). > So my question is how do I know that transients in IIR filters have > died out?That's easy: 1) Spell out the expression behind the acronym 'IIR'. 2) Contemplate the word that causes that first 'I'... Rune
Reply by ●February 21, 20102010-02-21
Rune Allnor wrote:> On 21 Feb, 22:49, Pawel <prulikow...@gmail.com> wrote: >> Hi All, >> >> I have a quick question from newbie to DSP. During my self education >> of DSP filter design I learnt that digital filter - quite like analog >> ones- have transient response (sometimes called "warm-up" time). This >> is easy to understand and calculate/predict for FIR filters of length >> N the transient last N-1 samples. However I did not find any reference >> that tell how to calculate length of transient response in samples of >> IIR filter. I met during my wanderings on web the following statement: >> "For IIR filters, the length of the transition region is dependent on >> the filter order and the feedback coefficient values" (linkhttp://www.music.mcgill.ca/~gary/307/week2/filters.html). >> So my question is how do I know that transients in IIR filters have >> died out? > > That's easy: > > 1) Spell out the expression behind the acronym 'IIR'. > 2) Contemplate the word that causes that first 'I'... > > RuneYes. Rune does have a sense of humor. It's educational. As a fellow newbie, I'd raise additional questions: 1. If Schroedinger had a cat, did Heisenberg have a dog? 2. Who can say FIR not IIR used? and why?
Reply by ●February 21, 20102010-02-21
Pawel wrote:> Hi All, > > I have a quick question from newbie to DSP. During my self education > of DSP filter design I learnt that digital filter - quite like analog > ones- have transient response (sometimes called "warm-up" time). This > is easy to understand and calculate/predict for FIR filters of length > N the transient last N-1 samples. However I did not find any reference > that tell how to calculate length of transient response in samples of > IIR filter. I met during my wanderings on web the following statement: > "For IIR filters, the length of the transition region is dependent on > the filter order and the feedback coefficient values" (link > http://www.music.mcgill.ca/~gary/307/week2/filters.html). > So my question is how do I know that transients in IIR filters have > died out? > > Thanks for any help in advance > > PawelHi Pawel, By "transient", it sounds like you mean something that is related to the "impulse reponse" and/or "step response" of an IIR filter. As the name "IIR" implies, the impulse response is theoretically infinite. However, in practice, in a stable filter, it will die out to some value that can be considered zero. So, mathematically, you'll need to determine what that "die out" threshold is for your application. For example, it could be an average output level that is -80 dB below the impulse input value for the last N samples. Impuse and step responses can be directly computed from the IIR filter that has been designed. If you're ready to actually implement the filter, computing these responses is easy. The way to see the impulse response of the filter is to input a single 1.0 sample followed by a series of 0.0 samples. If you graph the filter output, you will see one or more transients in the output waveform and it will head towards zero. In most practical cases using finite-precision arithmetic (as computed by a computer rather than a mathemetician), it will get to _exactly zero_, unless it finally converges on some small cyclic set of values that it continues to put out, which is called a "limit cycle". Similarly, you can see the step response of the filter by putting in a series of 1.0 values. In the case of a lowpass filter, you can expect the output to have a transient and eventually converge on 1.0. The transient time is the time implied by the number of samples it takes to converge on 1.0. You will need to define "converge on 1.0" for your application. In the case of finite-precision arithmetic, you may find that it eventually hits exactly 1.0 and stays there. So, you could just consider the transient time to be the time it takes to reach and perpetually stay at 1.0, as seen in your (finite precision) implementation. The transient time can be thought of as some combination of the impulse response and step response transient times. For example, one application may need an impulse or step response value to settle to 1% of its final value whereas another may need it to settle to 0.001%. So, the transient time is a function of both the filter characteristics and the needs of your application: an application that requires a greater degree of settling, that is, a smaller convergence threshold, will have a longer "transient time" for a given filter. Grant -- _____________________________________________________________________ Grant R. Griffin Publisher of dspGuru http://www.dspguru.com Iowegian International Corporation http://www.iowegian.com See http://www.iowegian.com/img/contact.gif for e-mail address
Reply by ●February 21, 20102010-02-21
Rune Allnor wrote:> On 21 Feb, 22:49, Pawel <prulikow...@gmail.com> wrote: >> Hi All, >> >> I have a quick question from newbie to DSP. During my self education >> of DSP filter design I learnt that digital filter - quite like analog >> ones- have transient response (sometimes called "warm-up" time). This >> is easy to understand and calculate/predict for FIR filters of length >> N the transient last N-1 samples. However I did not find any reference >> that tell how to calculate length of transient response in samples of >> IIR filter. I met during my wanderings on web the following statement: >> "For IIR filters, the length of the transition region is dependent on >> the filter order and the feedback coefficient values" (linkhttp://www.music.mcgill.ca/~gary/307/week2/filters.html). >> So my question is how do I know that transients in IIR filters have >> died out? > > That's easy: > > 1) Spell out the expression behind the acronym 'IIR'. > 2) Contemplate the word that causes that first 'I'... > > Rune"Yeah, well, sometimes nothin' can be a real Cool Hand." ;-) Grant -- _____________________________________________________________________ Grant R. Griffin Publisher of dspGuru http://www.dspguru.com Iowegian International Corporation http://www.iowegian.com See http://www.iowegian.com/img/contact.gif for e-mail address
Reply by ●February 21, 20102010-02-21
Rune Allnor wrote:> On 21 Feb, 22:49, Pawel <prulikow...@gmail.com> wrote: > >>Hi All, >> >>I have a quick question from newbie to DSP. During my self education >>of DSP filter design I learnt that digital filter - quite like analog >>ones- have transient response (sometimes called "warm-up" time). This >>is easy to understand and calculate/predict for FIR filters of length >>N the transient last N-1 samples. However I did not find any reference >>that tell how to calculate length of transient response in samples of >>IIR filter. I met during my wanderings on web the following statement: >>"For IIR filters, the length of the transition region is dependent on >>the filter order and the feedback coefficient values" (linkhttp://www.music.mcgill.ca/~gary/307/week2/filters.html). >>So my question is how do I know that transients in IIR filters have >>died out? > > > That's easy: > > 1) Spell out the expression behind the acronym 'IIR'. > 2) Contemplate the word that causes that first 'I'...For engineering and technical purposes, the eternity equals to the filter order divided by bandwidth. VLV
Reply by ●February 21, 20102010-02-21
Richard Owlett wrote:> Rune Allnor wrote: >> On 21 Feb, 22:49, Pawel <prulikow...@gmail.com> wrote: >>> Hi All, >>> >>> I have a quick question from newbie to DSP. During my self education >>> of DSP filter design I learnt that digital filter - quite like analog >>> ones- have transient response (sometimes called "warm-up" time). This >>> is easy to understand and calculate/predict for FIR filters of length >>> N the transient last N-1 samples. However I did not find any reference >>> that tell how to calculate length of transient response in samples of >>> IIR filter. I met during my wanderings on web the following statement: >>> "For IIR filters, the length of the transition region is dependent on >>> the filter order and the feedback coefficient values" >>> (linkhttp://www.music.mcgill.ca/~gary/307/week2/filters.html). >>> So my question is how do I know that transients in IIR filters have >>> died out? >> >> That's easy: >> >> 1) Spell out the expression behind the acronym 'IIR'. >> 2) Contemplate the word that causes that first 'I'... >> >> Rune > > Yes. Rune does have a sense of humor. It's educational. > As a fellow newbie, I'd raise additional questions: > 1. If Schroedinger had a cat, did Heisenberg have a dog? > 2. Who can say FIR not IIR used? and why?What!? You mean fir filters aren't made of wood? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 22, 20102010-02-22
On 21 Feb, 23:22, Richard Owlett <rowl...@pcnetinc.com> wrote:> Rune Allnor wrote: > > On 21 Feb, 22:49, Pawel <prulikow...@gmail.com> wrote: > >> Hi All, > > >> I have a quick question from newbie to DSP. During my self education > >> of DSP filter design I learnt that digital filter - quite like analog > >> ones- have transient response (sometimes called "warm-up" time). This > >> is easy to understand and calculate/predict for FIR filters of length > >> N the transient last N-1 samples. However I did not find any reference > >> that tell how to calculate length of transient response in samples of > >> IIR filter. I met during my wanderings on web the following statement: > >> "For IIR filters, the length of the transition region is dependent on > >> the filter order and the feedback coefficient values" (linkhttp://www.music.mcgill.ca/~gary/307/week2/filters.html). > >> So my question is how do I know that transients in IIR filters have > >> died out? > > > That's easy: > > > 1) Spell out the expression behind the acronym 'IIR'. > > 2) Contemplate the word that causes that first 'I'... > > > Rune > > Yes. Rune does have a sense of humor. It's educational.What is? My sense of humor? Or the fact that I *have* a sense of humor...? Rune
Reply by ●February 22, 20102010-02-22
On Feb 21, 10:30�pm, Grant Griffin <nob...@example.com> wrote:> Pawel wrote: > > Hi All, > > > I have a quick question from newbie to DSP. During my self education > > of DSP filter design I learnt that digital filter - quite like analog > > ones- have transient response (sometimes called "warm-up" time). This > > is easy to understand and calculate/predict for FIR filters of length > > N the transient last N-1 samples. However I did not find any reference > > that tell how to calculate length of transient response in samples of > > IIR filter. I met during my wanderings on web the following statement: > > "For IIR filters, the length of the transition region is dependent on > > the filter order and the feedback coefficient values" (link > >http://www.music.mcgill.ca/~gary/307/week2/filters.html). > > So my question is how do I know that transients in IIR filters have > > died out? > > > Thanks for any help in advance > > > Pawel > > Hi Pawel, > > By "transient", it sounds like you mean something that is related to the > "impulse reponse" and/or "step response" of an IIR filter. > > As the name "IIR" implies, the impulse response is theoretically > infinite. �However, in practice, in a stable filter, it will die out to > some value that can be considered zero. �So, mathematically, you'll need > to determine what that "die out" threshold is for your application. �For > example, it could be an average output level that is -80 dB below the > impulse input value for the last N samples. > > Impuse and step responses can be directly computed from the IIR filter > that has been designed. �If you're ready to actually implement the > filter, computing these responses is easy. �The way to see the impulse > response of the filter is to input a single 1.0 sample followed by a > series of 0.0 samples. �If you graph the filter output, you will see one > or more transients in the output waveform and it will head towards zero. > � In most practical cases using finite-precision arithmetic (as computed > by a computer rather than a mathemetician), it will get to _exactly > zero_, unless it finally converges on some small cyclic set of values > that it continues to put out, which is called a "limit cycle". > > Similarly, you can see the step response of the filter by putting in a > series of 1.0 values. �In the case of a lowpass filter, you can expect > the output to have a transient and eventually converge on 1.0. �The > transient time is the time implied by the number of samples it takes to > converge on 1.0. �You will need to define "converge on 1.0" for your > application. �In the case of finite-precision arithmetic, you may find > that it eventually hits exactly 1.0 and stays there. �So, you could just > � consider the transient time to be the time it takes to reach and > perpetually stay at 1.0, as seen in your (finite precision) implementation. > > The transient time can be thought of as some combination of the impulse > response and step response transient times. �For example, one > application may need an impulse or step response value to settle to 1% > of its final value whereas another may need it to settle to 0.001%. �So, > the transient time is a function of both the filter characteristics and > the needs of your application: an application that requires a greater > degree of settling, that is, a smaller convergence threshold, will have > a longer "transient time" for a given filter. > > Grant > -- > _____________________________________________________________________ > > Grant R. Griffin > Publisher of dspGuru � � � � � � � � � � � � �http://www.dspguru.com > Iowegian International Corporation � � � � � �http://www.iowegian.com > Seehttp://www.iowegian.com/img/contact.giffor e-mail addressThanks all for the replies, (yes, indeed Rune is a funny guy), I think there ius misunderstanding of my question - I guess as not much advanced in filter design I did not make it very clear. I understand that IIR has infinite impulse response. By transients I meant the time before steady state response is achieved - in FIR filter it is before the whole filter is "immersed" in signal - graphical explanation of the phenomenon can be found here https://ccrma.stanford.edu/~jos/fp/IIR_Example.html . Would criterion devised by Vladimir still be applicable here?
Reply by ●February 22, 20102010-02-22
On 22 Feb, 11:04, Pawel <prulikow...@gmail.com> wrote:> On Feb 21, 10:30�pm, Grant Griffin <nob...@example.com> wrote: > > > > > > > Pawel wrote: > > > Hi All, > > > > I have a quick question from newbie to DSP. During my self education > > > of DSP filter design I learnt that digital filter - quite like analog > > > ones- have transient response (sometimes called "warm-up" time). This > > > is easy to understand and calculate/predict for FIR filters of length > > > N the transient last N-1 samples. However I did not find any reference > > > that tell how to calculate length of transient response in samples of > > > IIR filter. I met during my wanderings on web the following statement: > > > "For IIR filters, the length of the transition region is dependent on > > > the filter order and the feedback coefficient values" (link > > >http://www.music.mcgill.ca/~gary/307/week2/filters.html). > > > So my question is how do I know that transients in IIR filters have > > > died out? > > > > Thanks for any help in advance > > > > Pawel > > > Hi Pawel, > > > By "transient", it sounds like you mean something that is related to the > > "impulse reponse" and/or "step response" of an IIR filter. > > > As the name "IIR" implies, the impulse response is theoretically > > infinite. �However, in practice, in a stable filter, it will die out to > > some value that can be considered zero. �So, mathematically, you'll need > > to determine what that "die out" threshold is for your application. �For > > example, it could be an average output level that is -80 dB below the > > impulse input value for the last N samples. > > > Impuse and step responses can be directly computed from the IIR filter > > that has been designed. �If you're ready to actually implement the > > filter, computing these responses is easy. �The way to see the impulse > > response of the filter is to input a single 1.0 sample followed by a > > series of 0.0 samples. �If you graph the filter output, you will see one > > or more transients in the output waveform and it will head towards zero. > > � In most practical cases using finite-precision arithmetic (as computed > > by a computer rather than a mathemetician), it will get to _exactly > > zero_, unless it finally converges on some small cyclic set of values > > that it continues to put out, which is called a "limit cycle". > > > Similarly, you can see the step response of the filter by putting in a > > series of 1.0 values. �In the case of a lowpass filter, you can expect > > the output to have a transient and eventually converge on 1.0. �The > > transient time is the time implied by the number of samples it takes to > > converge on 1.0. �You will need to define "converge on 1.0" for your > > application. �In the case of finite-precision arithmetic, you may find > > that it eventually hits exactly 1.0 and stays there. �So, you could just > > � consider the transient time to be the time it takes to reach and > > perpetually stay at 1.0, as seen in your (finite precision) implementation. > > > The transient time can be thought of as some combination of the impulse > > response and step response transient times. �For example, one > > application may need an impulse or step response value to settle to 1% > > of its final value whereas another may need it to settle to 0.001%. �So, > > the transient time is a function of both the filter characteristics and > > the needs of your application: an application that requires a greater > > degree of settling, that is, a smaller convergence threshold, will have > > a longer "transient time" for a given filter. > > > Grant > > -- > > _____________________________________________________________________ > > > Grant R. Griffin > > Publisher of dspGuru � � � � � � � � � � � � �http://www.dspguru.com > > Iowegian International Corporation � � � � � �http://www.iowegian.com > > Seehttp://www.iowegian.com/img/contact.giffore-mail address > > Thanks all for the replies, (yes, indeed Rune is a funny guy), > > I think there ius misunderstanding of my question - I guess as not > much advanced in filter design I did not make it very clear. > I understand that IIR has infinite impulse response. By transients I > meant the time before steady state response is achievedFrom a purely mathemathical point of view, that never happens. That's what the 'Infinite' in 'IIR' means. From a practical point of view, one might define some empirically specified limit from a number of possible criteria: 1) When the coefficients of the impulse response has decreased below some limit 2) When the coefficients of the impulse response are dominated by system noise 3) When the coefficients of the impulse response are dominated by numerical quantization effects Rune
