1. what application area's are min phase IIR's used? 2. what is the design procedure for the same. Recenltly I was going thru the book of proakis and stumbled upon topic on min phase IIR's. so this got me curious to know more. I know min phase FIR's and how to design them but want to know more about min phase IIR's. Regards Bharat
minimum phase IIR : application and design technique?
Started by ●January 4, 2011
Reply by ●January 4, 20112011-01-04
On 01/04/2011 09:46 AM, bharat pathak wrote:> 1. what application area's are min phase IIR's used? > > 2. what is the design procedure for the same. > > Recenltly I was going thru the book of proakis and stumbled > upon topic on min phase IIR's. so this got me curious to know > more. I know min phase FIR's and how to design them but want > to know more about min phase IIR's.Certainly when one is designing control systems there is very little use for non-minimum phase filters*. Design is easy -- just write sensible control rules, and with the exception of integrators** the resulting filter will pretty much automatically be minimum phase. * There is some limited use -- but only in bizarre cases. ** Which are honorary minimum phase filters, as far as I'm concerned. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by ●January 4, 20112011-01-04
On Jan 4, 12:46=A0pm, "bharat pathak" <bharat@n_o_s_p_a_m.arithos.com> wrote:> 1. what application area's are min phase IIR's used? > > 2. what is the design procedure for the same. > > Recenltly I was going thru the book of proakis and stumbled > upon topic on min phase IIR's. so this got me curious to know > more. I know min phase FIR's and how to design them but want > to know more about min phase IIR's. > > Regards > BharatIIRC, you can transform any non-minimum-phase filter to its minimum- phase equivalent easily. Find the zeros of the filter, remove any zeros that are outside the unit circle, then replace them with zeros at the inverse locations (e.g. if you have a zero at z =3D 1 + j, then replace it with one at z =3D 1 / (1 + j)). The resulting transfer function will have all of its zeros inside the unit circle, and will have the same magnitude response. This process is equivalent to cascading the non-MP filter with an allpass filter that cancels the zero you want to remove and adds the zero inside the circle. Jason
Reply by ●January 4, 20112011-01-04
On Jan 4, 1:01=A0pm, Jason <cincy...@gmail.com> wrote:> On Jan 4, 12:46=A0pm, "bharat pathak" <bharat@n_o_s_p_a_m.arithos.com> > wrote: > > > 1. what application area's are min phase IIR's used? > > > 2. what is the design procedure for the same. > > > Recenltly I was going thru the book of proakis and stumbled > > upon topic on min phase IIR's. so this got me curious to know > > more. I know min phase FIR's and how to design them but want > > to know more about min phase IIR's. > > > Regards > > Bharat > > IIRC, you can transform any non-minimum-phase filter to its minimum- > phase equivalent easily. Find the zeros of the filter, remove any > zeros that are outside the unit circle, then replace them with zeros > at the inverse locations (e.g. if you have a zero at z =3D 1 + j, then > replace it with one at z =3D 1 / (1 + j)). The resulting transfer > function will have all of its zeros inside the unit circle, and will > have the same magnitude response. This process is equivalent to > cascading the non-MP filter with an allpass filter that cancels the > zero you want to remove and adds the zero inside the circle. > > JasonThat would be an unstable allpass filter (poles outside the unit circle). Dirk
Reply by ●January 4, 20112011-01-04
On Jan 4, 3:34=A0pm, Dirk Bell <bellda2...@cox.net> wrote:> On Jan 4, 1:01=A0pm, Jason <cincy...@gmail.com> wrote: > > > > > On Jan 4, 12:46=A0pm, "bharat pathak" <bharat@n_o_s_p_a_m.arithos.com> > > wrote: > > > > 1. what application area's are min phase IIR's used? > > > > 2. what is the design procedure for the same. > > > > Recenltly I was going thru the book of proakis and stumbled > > > upon topic on min phase IIR's. so this got me curious to know > > > more. I know min phase FIR's and how to design them but want > > > to know more about min phase IIR's. > > > IIRC, you can transform any non-minimum-phase filter to its minimum- > > phase equivalent easily. Find the zeros of the filter, remove any > > zeros that are outside the unit circle, then replace them with zeros > > at the inverse locations (e.g. if you have a zero at z =3D 1 + j, then > > replace it with one at z =3D 1 / (1 + j)). The resulting transfer > > function will have all of its zeros inside the unit circle, and will > > have the same magnitude response. This process is equivalent to > > cascading the non-MP filter with an allpass filter that cancels the > > zero you want to remove and adds the zero inside the circle. > > That would be an unstable allpass filter (poles outside the unit > circle).pole/zero cancellation, Dirk. i know in practice it's dangerous, but this is a conceptual thing regarding design. a better way to put it is that a stable non-minimum phase IIR can be thought of as the cascade of the minimum phase counterpart (have the same magnitude response) and a stable APF that cancels some of the zeroes inside the unit circle with its poles and plops in the corresponding zeros outside. it hasn't needed to come up yet, but there is a relationship between phase (measured in radians) and magnitude (measured in nepers which is dB/8.685889638) involving the Hilbert transform applied to these functions of frequency. you can spell out a magnitude response and then, if you also specify it as minimum-phase, there is no choice to what the phase response is. r b-j
Reply by ●January 4, 20112011-01-04
On Jan 4, 4:02�pm, robert bristow-johnson <r...@audioimagination.com> wrote:> On Jan 4, 3:34�pm, Dirk Bell <bellda2...@cox.net> wrote: > > > > > > > On Jan 4, 1:01�pm, Jason <cincy...@gmail.com> wrote: > > > > On Jan 4, 12:46�pm, "bharat pathak" <bharat@n_o_s_p_a_m.arithos.com> > > > wrote: > > > > > 1. what application area's are min phase IIR's used? > > > > > 2. what is the design procedure for the same. > > > > > Recenltly I was going thru the book of proakis and stumbled > > > > upon topic on min phase IIR's. so this got me curious to know > > > > more. I know min phase FIR's and how to design them but want > > > > to know more about min phase IIR's. > > > > IIRC, you can transform any non-minimum-phase filter to its minimum- > > > phase equivalent easily. Find the zeros of the filter, remove any > > > zeros that are outside the unit circle, then replace them with zeros > > > at the inverse locations (e.g. if you have a zero at z = 1 + j, then > > > replace it with one at z = 1 / (1 + j)). The resulting transfer > > > function will have all of its zeros inside the unit circle, and will > > > have the same magnitude response. This process is equivalent to > > > cascading the non-MP filter with an allpass filter that cancels the > > > zero you want to remove and adds the zero inside the circle. > > > That would be an unstable allpass filter (poles outside the unit > > circle). > > pole/zero cancellation, Dirk. �i know in practice it's dangerous, but > this is a conceptual thing regarding design. > > a better way to put it is that a stable non-minimum phase IIR can be > thought of as the cascade of the minimum phase counterpart (have the > same magnitude response) and a stable APF that cancels some of the > zeroes inside the unit circle with its poles and plops in the > corresponding zeros outside. > > it hasn't needed to come up yet, but there is a relationship between > phase (measured in radians) and magnitude (measured in nepers which is > dB/8.685889638) involving the Hilbert transform applied to these > functions of frequency. �you can spell out a magnitude response and > then, if you also specify it as minimum-phase, there is no choice to > what the phase response is. > > r b-j- Hide quoted text - > > - Show quoted text -Hi r b-j, I know about pole-zero cancellation. Inside the unit circle, it is not such a big deal. Outside the unit circle I would have said it is "mathematically equivalent with infinite precision" rather than "equivalent to". If for some reason I tried to implement the unstable compensating filter separately I would be very careful to look for possible problems, like runaway internal values (as in a CIC filter which prohibits a floating-point implementation, because of a pole on the unit circle), or a lack of perfect cancellation which leaves you with an unstable result. I don't know that there would be always be a problem, but implementing an unstable filter raises a red flag for me (that's why you factor out before implementation). Dirk
Reply by ●January 5, 20112011-01-05
On Jan 5, 1:54�am, Dirk Bell <bellda2...@cox.net> wrote:> I know about pole-zero cancellation. Inside the unit circle, it is not > such a big deal. Outside the unit circle I would have said it is > "mathematically equivalent with infinite precision" rather than > "equivalent to".I agree with you, but it's confusing to separate the inside and outside of the unit circle separately, and bringing in all sorts of numerical considerations. Why not just say 'formally equivalent' and leave it at that? Rune
Reply by ●January 5, 20112011-01-05
On 01/04/2011 12:46 PM, bharat pathak wrote:> 1. what application area's are min phase IIR's used? > > 2. what is the design procedure for the same. > > Recenltly I was going thru the book of proakis and stumbled > upon topic on min phase IIR's. so this got me curious to know > more. I know min phase FIR's and how to design them but want > to know more about min phase IIR's.Hi Bharat, A minimum-phase filter is one that is causal and stable, and whose inverse is also causal and stable. This implies that all poles and zeros are inside the unit circle. This should explain better Jason's technique for creating a minimum-phase filter from a non-minimum-phase filter. They are used anywhere the inverse needs to be utilized, See, for example, spectral factorization and the whitening problem. -- Randy Yates % "My Shangri-la has gone away, fading like Digital Signal Labs % the Beatles on 'Hey Jude'" yates@digitalsignallabs.com % http://www.digitalsignallabs.com % 'Shangri-La', *A New World Record*, ELO
