paley-Weiner criterion (causality)
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From: fisico32 on 25 Jul 2010 16:08 Hello Forum, the Paley-Wiener criterion is the frequency equivalent of the causality condition in the time domain. It states that the magnitude of the transfer function can be exactly zero only a discrete frequencies but not over a finite band of frequencies... Why not? Is there a more conceptual explanation for that beside looking at the integral and its derivation? Realizable physical system must be causal....Is that always true? Do systems with memory not obey causality and therefore the PAley-Wiener criterion? Or are ALL time-domain system that exist in real life "causal"? What if there is an output before the input is applied due to the fact that the system was already in action before the input was fed? Causality does not need to be satisfied in the spatial domain. Are there some criteria like the Paley-Wiener in the spatial frequency domain? thanks fisico32
From: Tim Wescott on 25 Jul 2010 19:22 On 07/25/2010 01:08 PM, fisico32 wrote: > Hello Forum, > > the Paley-Wiener criterion is the frequency equivalent of the causality > condition in the time domain. > It states that the magnitude of the transfer function can be exactly zero > only a discrete frequencies but not over a finite band of frequencies... > Why not? Is there a more conceptual explanation for that beside looking at > the integral and its derivation? > > > Realizable physical system must be causal....Is that always true? Name a non-causal system, then. > Do systems with memory not obey causality and therefore the PAley-Wiener > criterion? Can you describe a non-causal system mathematically? Can you realize a non-causal system? > Or are ALL time-domain system that exist in real life "causal"? What if > there is an output before the input is applied due to the fact that the > system was already in action before the input was fed? I think you're confused about the definition of "causality". Causality doesn't mean "it moves before it gets an input". Causality means "effects always follow causes". A system that spontaneously moves, then gets an input telling it to move, is only violating causality if it moves _as a response to_ an input that hasn't happened yet. Causality is a property of the physical world that physicists can't explain. The math allows for effects to precede causes -- yet they have never been observed to do so, ever. Physicists who turn their minds to figuring out the "why" to go with this unassailable "what" tend to twist their brains into pretzels, without ever coughing up any testable theorems other than "causality is". > Causality does not need to be satisfied in the spatial domain. Are there > some criteria like the Paley-Wiener in the spatial frequency domain? "Causality" specifically relates to temporal phenomenon, and doesn't _mean_ anything in a purely spatial domain. So attempting to "satisfy" it in the spatial domain is meaningless. If causality doesn't mean anything in the spatial domain then it doesn't matter. If it doesn't matter -- do you _need_ any criteria to satisfy? -- 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 25 Jul 2010 22:42 On Jul 26, 11:22 am, Tim Wescott <t...(a)seemywebsite.com> wrote: > On 07/25/2010 01:08 PM, fisico32 wrote: > > > Hello Forum, > > > the Paley-Wiener criterion is the frequency equivalent of the causality > > condition in the time domain. > > It states that the magnitude of the transfer function can be exactly zero > > only a discrete frequencies but not over a finite band of frequencies.... > > Why not? Is there a more conceptual explanation for that beside looking at > > the integral and its derivation? > > > Realizable physical system must be causal....Is that always true? > > Name a non-causal system, then. > Duhh - The Tardis of course! Hardy
From: Jerry Avins on 25 Jul 2010 23:20 On 7/25/2010 7:22 PM, Tim Wescott wrote: ... > Name a non-causal system .... How about getting blamed for something you didn't do? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
From: glen herrmannsfeldt on 25 Jul 2010 23:48
Jerry Avins <jya(a)ieee.org> wrote: > On 7/25/2010 7:22 PM, Tim Wescott wrote: > ... >> Name a non-causal system .... > How about getting blamed for something you didn't do? Before or after you didn't do it? -- glen |