I was asked to implement a minimum phase DC blocker (offset removal) in real time. As far as I know, a first order IIR DC blocker is not minimum phase. Any idea how to implement a minimum phase one ?
DC blocker
Started by ●February 1, 2006
Reply by ●February 1, 20062006-02-01
in article 43e12005$0$5358$c3e8da3@news.astraweb.com, Tom at Tomdarel@yahoo.com wrote on 02/01/2006 15:56:> I was asked to implement a minimum phase DC blocker (offset removal) in real > time. As far as I know, a first order IIR DC blocker is not minimum phase. > Any idea how to implement a minimum phase one ?y[n] = (1-p)*(x[n] - x[n-1]) + p*y[n-1] (where p = pole, 0 < 1-p << 1) is *virtually* minimum phase, but there is no true DC blocker that has a stable and realizable inverse filter (once the DC is totally destroyed, how can you get it back?) and if having a strictly stable inverse filter is your criterion for calling something "minimum phase", then there is no way to implement a minimum phase DC blocker. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●February 1, 20062006-02-01
in article C0068DAA.EE7B%rbj@audioimagination.com, robert bristow-johnson at rbj@audioimagination.com wrote on 02/01/2006 16:09:> y[n] = (1-p)*(x[n] - x[n-1]) + p*y[n-1] (where p = pole, 0 < 1-p << 1)should be y[n] = x[n] - x[n-1] + p*y[n-1] (where p = pole, 0 < 1-p << 1) i thought i was scaling it so that the gain at Nyquist = 1, but i that was not correct. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●February 1, 20062006-02-01
robert bristow-johnson wrote:> in article 43e12005$0$5358$c3e8da3@news.astraweb.com, Tom at > Tomdarel@yahoo.com wrote on 02/01/2006 15:56: > > >>I was asked to implement a minimum phase DC blocker (offset removal) in real >>time. As far as I know, a first order IIR DC blocker is not minimum phase. >>Any idea how to implement a minimum phase one ? > > > > y[n] = (1-p)*(x[n] - x[n-1]) + p*y[n-1] (where p = pole, 0 < 1-p << 1) > > is *virtually* minimum phase, but there is no true DC blocker that has a > stable and realizable inverse filter (once the DC is totally destroyed, how > can you get it back?) and if having a strictly stable inverse filter is your > criterion for calling something "minimum phase", then there is no way to > implement a minimum phase DC blocker.I never looked at it that way! Does that mean that the RC blocker 0--------||----+--------------------0 C | +--\/\/\/-+ R | ����� ��� � isn't minimum phase either? Its impulse response is 1 - exp(-t/RC). :^) Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 1, 20062006-02-01
Tom wrote:> I was asked to implement a minimum phase DC blocker (offset removal) in real > time. As far as I know, a first order IIR DC blocker is not minimum phase.What?> Any idea how to implement a minimum phase one ? >1 - Z[-1] H(Z) = ------------ 1 + A*Z[-1] A = 0.9999.... Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●February 1, 20062006-02-01
-- -- John E. Hadstate "Jerry Avins" <jya@ieee.org> wrote in message news:n_2dnUEu4tZVsHzenZ2dnUVZ_t2dnZ2d@rcn.net...> robert bristow-johnson wrote: >> in article 43e12005$0$5358$c3e8da3@news.astraweb.com, Tom >> at >> Tomdarel@yahoo.com wrote on 02/01/2006 15:56: >> >> >>>I was asked to implement a minimum phase DC blocker >>>(offset removal) in real >>>time. As far as I know, a first order IIR DC blocker is >>>not minimum phase. >>>Any idea how to implement a minimum phase one ? >> >> >> >> y[n] = (1-p)*(x[n] - x[n-1]) + p*y[n-1] (where p = >> pole, 0 < 1-p << 1) >> >> is *virtually* minimum phase, but there is no true DC >> blocker that has a >> stable and realizable inverse filter (once the DC is >> totally destroyed, how >> can you get it back?) and if having a strictly stable >> inverse filter is your >> criterion for calling something "minimum phase", then >> there is no way to >> implement a minimum phase DC blocker. > > I never looked at it that way! Does that mean that the RC > blocker > > > 0--------||----+--------------------0 > C | > +--\/\/\/-+ > R | > ����� > ��� > � > > isn't minimum phase either? Its impulse response is 1 - > exp(-t/RC). :^) >"Minimum phase" means all the poles and zeros are in the left-half plane (or inside the unit circle). The "DC Blocker" must have a zero at s=0 (or z=1). Consequently, it can't be truly "minimum phase".
Reply by ●February 1, 20062006-02-01
robert bristow-johnson wrote:>....... if having a strictly stable inverse filter is your > criterion for calling something "minimum phase", then........Is the existence of a stable inverse filter a necessary condition for minimum phase? Is the existence of a stable inverse filter a sufficient condition for minimum phase? I never knew this. Thanks Mark
Reply by ●February 1, 20062006-02-01
in article 1138841190.607199.177020@g47g2000cwa.googlegroups.com, Mark at makolber@yahoo.com wrote on 02/01/2006 19:46:> > robert bristow-johnson wrote: >> ....... if having a strictly stable inverse filter is your >> criterion for calling something "minimum phase", then........ > > > Is the existence of a stable inverse filter a necessary condition for > minimum phase?assuming LTI, yes, i think that is the case.> Is the existence of a stable inverse filter a sufficient condition for > minimum phase?i think so. if it isn't, i'll have to think of an exception, but i can't.> I never knew this. Thanksi didn't know it at first either (whatever many decades ago when i first learnt of these), but the concept is simple: the minimum phase filter and its inverse put in series (doesn't matter which one is first) are equivalent to a wire, that means all of the zeros in one are cancelled by the poles in the other. of course poles in the left half s-plane (or inside the unit circle on the z-plane) are the only stable ones, so the zeros that are canceling them have to be in the same region. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●February 2, 20062006-02-02
"Tom" <Tomdarel@yahoo.com> wrote in message news:43e12005$0$5358$c3e8da3@news.astraweb.com...> I was asked to implement a minimum phase DC blocker (offset removal) inreal> time. As far as I know, a first order IIR DC blocker is not minimum phase. > Any idea how to implement a minimum phase one ? > >Far easier to block the DC in the analogue domain before sampling!! Naebad
Reply by ●February 2, 20062006-02-02
robert bristow-johnson wrote:> i didn't know it at first either (whatever many decades ago when i first > learnt of these), but the concept is simple: the minimum phase filter and > its inverse put in series (doesn't matter which one is first) are equivalent > to a wire, that means all of the zeros in one are cancelled by the poles in > the other. of course poles in the left half s-plane (or inside the unit > circle on the z-plane) are the only stable ones, so the zeros that are > canceling them have to be in the same region.What a nice presentation of the situation! Thanks. The one I've used is to appeal to a rational expression of the transfer function. The inverse swaps numerator with denominator so any root in that numerator (the zeros) had better be inside the unit circle when made the denominator (the poles.) Equivalent, of course, but yours is more visualizable. :-) Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein
