predictive filter (phase response)
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From: Markus on 10 Sep 2005 12:35 Hi everyone, Its a very a common question, so if a phase reponse of an digital filter has an positiv phase shift could I say it works as an predictor? Thanksal
From: Fred Marshall on 10 Sep 2005 14:04 "Markus" <Markus.Schweikhardt(a)web.de> wrote in message news:1126370154.161155.177510(a)o13g2000cwo.googlegroups.com... > Hi everyone, > > Its a very a common question, so if a phase reponse of an digital > filter has an positiv phase shift could I say it works as an predictor? > That seems a much too simple way of putting it. A positive phase shift as in cos(wt + phi) where phi is a positive number could also be written: cos(w*(t +phi/w)) so, a positive phase shift relates to a positive shift in time which puts the function into negative time as in cos(0) = cos(w*(0)) when t=-phi/w In that sense it could be viewed as a predictor. However, it's ambiguous whether the phase is really leading or lagging because phase is a measure at a single frequency and, in some sense, a long-time measure. If phi is greater than pi radians then is the phase shift a lead or a lag? It's hard to tell. An adaptive filter can be constructed and might be viewed as a predictor as follows: +--------------------+ | | | | | | input---+------------------------|------------>(+)----+----> e[n] | | ^ | | | | +-----------+ v | +--| Delay |------>[LMS]------------+----------> o[n] | +-----------+ | | | | | | v +--------------------->[LMS]-----------------------> p[n] Adaptive predictor LMS adaptive filter adjusts to minimize e[n] which uses a delayed version of the input as a reference signal. So, the filter adapts to "predict" the input to the delay. Then, input the real time signal into the same filter to view a prediction of the input. I have no idea how well or poorly this would work..... Fred
From: robert bristow-johnson on 10 Sep 2005 17:44 in article 2L2dnZ2dnZ1qw6u4nZ2dnbO9vt6dnZ2dRVn-z52dnZ0(a)centurytel.net, Fred Marshall at fmarshallx(a)remove_the_x.acm.org wrote on 09/10/2005 14:04: > An adaptive filter can be constructed and might be viewed as a predictor as > follows: > +--------------------+ | | | | | | input---+------------------------|------------>(+)----+----> e[n] | | ^ | | | | +-----------+ v | +--| Delay |------>[LMS]------------+----------> o[n] | +-----------+ | | | | | | v +--------------------->[LMS]-----------------------> p[n] > > > Adaptive predictor > > LMS adaptive filter adjusts to minimize e[n] which uses > a delayed version of the input as a reference signal. > So, the filter adapts to "predict" the input to the delay. > Then, input the real time signal into the same filter to > view a prediction of the input. > > I have no idea how well or poorly this would work..... but it's a well-defined realizable algorithm that has some promise of working, at least for short negative delay. (press file save) i still think the OP's question is about negative phase delay (or negative group delay, perhaps) in some filter. a negative phase delay could accurately predict the phase of a single constant amplitude sinusoid. no promises for the more general case. -- r b-j rbj(a)audioimagination.com "Imagination is more important than knowledge."
From: Markus on 11 Sep 2005 04:48 Thanks for your reply. OK I will try to tryspecify my problem. I work with an adaptive FxLMS-Filter (its quite similar to an LMS-Filter). I developed an ANC-Headset (active noise control). It`s a bit complicated to explain. But when I put the coefficients of the adaptive filter after it is converged I could see a positive phase shift (lead) and a negative group delay in the frequency range of the input signal.
From: Fred Marshall on 11 Sep 2005 20:32
"Markus" <Markus.Schweikhardt(a)web.de> wrote in message news:1126428523.597552.269070(a)g49g2000cwa.googlegroups.com... > Thanks for your reply. OK I will try to tryspecify my problem. I work > with an adaptive FxLMS-Filter (its quite similar to an LMS-Filter). I > developed an ANC-Headset (active noise control). It`s a bit complicated > to explain. But when I put the coefficients of the adaptive filter > after it is converged I could see a positive phase shift (lead) and a > negative group delay in the frequency range of the input signal. > OK - that makes sense. Even though the delay is positive the phase can appear to be leading. That is, 290 degrees phase lag will appear to be 70 degrees phase lead. If the ambiguity of phase isn't resolved otherwise and the preference is to define phase from -pi to +pi then that's what you'll get. I think that Robert and I have answered your original question but I get the impression that you have more in mind. Fred |