On Jul 26, 6:15�am, Rune Allnor <all...@tele.ntnu.no> wrote:> On 26 Jul, 04:42, HardySpicer <gyansor...@gmail.com> wrote: > > > > > > > On Jul 26, 11:22�am, Tim Wescott <t...@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! > > Would be surprised if our friends at the wrong side of the > pond would be familiar with The Doctor... > > Dr Rune- Hide quoted text - > > - Show quoted text -I have a copy of everthing from Hartnell on (at least those that were not lost). My USB expander is a miniature Tardis. Jelly baby, anyone? Maurice
paley-Weiner criterion (causality)
Started by ●July 25, 2010
Reply by ●July 26, 20102010-07-26
Reply by ●July 26, 20102010-07-26
On 7/26/2010 7:16 AM, Rune Allnor wrote:> On 25 Jul, 22:08, "fisico32"<marcoscipioni1@n_o_s_p_a_m.gmail.com> > 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? > > No.I can offer a non-rigorous explanation that is at the root of the rigorous one. Every exact zero in the transfer function is the result of a point zero of that function. A zero continuum requires an infinity of point zeros. That is difficult to achieve with limited resources. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 26, 20102010-07-26
On 26 Jul, 20:14, Jerry Avins <j...@ieee.org> wrote:> On 7/26/2010 7:16 AM, Rune Allnor wrote: > > > On 25 Jul, 22:08, "fisico32"<marcoscipioni1@n_o_s_p_a_m.gmail.com> > > 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? > > > No. > > I can offer a non-rigorous explanation that is at the root of the > rigorous one.Not at the zero...?> Every exact zero in the transfer function is the result of a point zero > of that function. A zero continuum requires an infinity of point zeros. > That is difficult to achieve with limited resources.To me, this is the same as saying that the integrand is not analytic. Which is merely a repharsing of the starting position, where one investigates the integral. Rune
Reply by ●July 26, 20102010-07-26
On 7/26/2010 3:30 PM, Rune Allnor wrote:> On 26 Jul, 20:14, Jerry Avins<j...@ieee.org> wrote: >> On 7/26/2010 7:16 AM, Rune Allnor wrote: >> >>> On 25 Jul, 22:08, "fisico32"<marcoscipioni1@n_o_s_p_a_m.gmail.com> >>> 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? >> >>> No. >> >> I can offer a non-rigorous explanation that is at the root of the >> rigorous one. > > Not at the zero...? > >> Every exact zero in the transfer function is the result of a point zero >> of that function. A zero continuum requires an infinity of point zeros. >> That is difficult to achieve with limited resources. > > To me, this is the same as saying that the integrand > is not analytic. Which is merely a repharsing of the > starting position, where one investigates the integral.Ii is certainly a different way to look at the same information. I had hoped that fisico might find it more intuitive. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
