minimum phase signal recovery....
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From: fisico32 on 25 Jul 2010 17:01 Hello Forum, I have read that in some applications a signal is distorted by an LTI system... To recover the original signal we could filter with inverse filter. But this procedure would only work with minimum-phase systems... Is that true? Why? thanks fisico32
From: Tim Wescott on 25 Jul 2010 19:15 On 07/25/2010 02:01 PM, fisico32 wrote: > Hello Forum, > > I have read that in some applications a signal is distorted by an LTI > system... > To recover the original signal we could filter with inverse filter. But > this procedure would only work with minimum-phase systems... > > Is that true? Why? As yourself: what filter would you need to restore a signal back to its original form if it had been run through an LTI filter (system)? Then ask yourself: would this filter be stable if the LTI system that I'm correcting for isn't minimum phase? Check back here if you can't figure out the answers. -- 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
From: HardySpicer on 27 Jul 2010 15:19 On Jul 26, 9:01 am, "fisico32" <marcoscipioni1(a)n_o_s_p_a_m.gmail.com> wrote: > Hello Forum, > > I have read that in some applications a signal is distorted by an LTI > system... > To recover the original signal we could filter with inverse filter. But > this procedure would only work with minimum-phase systems... > > Is that true? Why? > > thanks > fisico32 There are solutions to this problem but they involve either delays of some sort or running the data backwards in time! Hardy
From: fisico32 on 27 Jul 2010 22:09 >On 07/25/2010 02:01 PM, fisico32 wrote: >> Hello Forum, >> >> I have read that in some applications a signal is distorted by an LTI >> system... >> To recover the original signal we could filter with inverse filter. But >> this procedure would only work with minimum-phase systems... >> >> Is that true? Why? > >As yourself: what filter would you need to restore a signal back to its >original form if it had been run through an LTI filter (system)? > >Then ask yourself: would this filter be stable if the LTI system that >I'm correcting for isn't minimum phase? > >Check back here if you can't figure out the answers. > >-- > >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 > Ok, so I guess that for a stable and causal filter to have a stable and causal inverse filter, the filter can only be minimum phase. So, in real life all filters must be minimum phase? Surely we could have a causal and stable filter whose inverse is not stable and causal, correct?
From: Tim Wescott on 28 Jul 2010 00:42 On 07/27/2010 07:09 PM, fisico32 wrote: >> On 07/25/2010 02:01 PM, fisico32 wrote: >>> Hello Forum, >>> >>> I have read that in some applications a signal is distorted by an LTI >>> system... >>> To recover the original signal we could filter with inverse filter. But >>> this procedure would only work with minimum-phase systems... >>> >>> Is that true? Why? >> >> As yourself: what filter would you need to restore a signal back to its >> original form if it had been run through an LTI filter (system)? >> >> Then ask yourself: would this filter be stable if the LTI system that >> I'm correcting for isn't minimum phase? >> >> Check back here if you can't figure out the answers. >> >> -- >> >> 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 >> > > Ok, so I guess that for a stable and causal filter to have a stable and > causal inverse filter, the filter can only be minimum phase. > So, in real life all filters must be minimum phase? > > Surely we could have a causal and stable filter whose inverse is not stable > and causal, correct? > Google "all pass filter". -- 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
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