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See my earlier comment about the definition of the Fourier transform and the impulse response. On Saturday, July 6, 2024 at 12:28:57 PM CDT, Chuck Harris <cfharris@...> wrote: Is it really a breach of causality if the output that displays the breach doesn't actually occur until some processing delay after the input that caused the output? I remember discussing this stuff at length some 50 years ago in a class on linear systems.... all I remember is discussing it, not what we decided, nor how we got there. I do recall that simplicity in the math required that certain apparently non-causal things would appear in the results. There is a whole lot of blue ink underlining way too much, in the section on convolution of the impulse function, and causality, in my copy of Linear Systems Analysis by Liu & Liu... which, for me, usually meant I was hopelessly confused... -Chuck Harris On Sat, 6 Jul 2024 16:37:12 +0000 (UTC) "Reginald Beardsley via
groups.io" <pulaskite@...> wrote: > ?This?is?a?general?reply?to?Jeff,?Mike?and?Dave.?I?initially?looked > at: > > Digital?Design?Handbook > Fred?J.?Taylor > Marcel?Dekker?1983 > > Digital?Signal?Processing > Oppenheim?and?Shafer > Prentice-Hall?1975 > > Theory?and?Application?of?Digital?Signal?Processing > Rabiner?and?Gold > Prentice-Hall?1975 > > Digital?Signal?Processing?with?Kernel?Method > Rojo-Alvarez?et?al > Wiley/IEEE?2018 > > Advanced?Digital?Signal?Processing > and?Noise?Reduction > Vaseghi > Wiley?4th?ed?2008 > > ?Subsequent?to?the?responses?I?checked: > > Spectral?Analysis?and?Time?Series > Priestly > Academic?Press?1981 > > Continuous?a?Signals?and?System?Analysis?and?Discrete > McGillem?and?Cooper > Holt,?Reinhart?and?Winston?1974 > > None?of?them?properly?discuss?the?issue?of?causality. > > I?did?NOT?look?at?any?of?the?many?monographs?by?Enders?Robinson, > Robinson?&?Treitel?or?John?H.?Karl?as?I?know?they?have?the?matter > stated?very?clearly.?Robinson?and?Treitel?were?members?of?Norbert > Weiner's?Geophysical?Analysis?Group?at?MIT?and?founded?the?entire > basis?of?DSP.?I?spent?4?years?at?UT?Austin?under?another?member?of > the?GAG,?Milo?Backus.?Robinson?performed?the?first?digital > deconvolution?problem?in?1952?using?pencil,?paper?and?a?desk > calculator.??Robinson?has?pride?of?place?as?the?first?person?to?apply > DSP?to?data. > > Causality?requires?that?the?real?and?imaginary?parts?be?a?Hilbert > transform?pair.?This?is?well?stated?in: > > The?Fourier?Integral?and?Some?of?Its?Applications > Ronald?Bracewell > McGraw-Hill?2nd?ed?1978 > > Causality?simply?states?that?there?is?no?output?prior?to?the?input. > If?a?filter?is?not?causal?it?produces?output?before?the?event.?The?EE > community?appears?to?consistently?label?a?zero?phase?signal?as?linear > phase?with?a?phase?delay.?As?Bracewell?provides?a?proof?and?I?spent?2 > semesters?studying?Churchill's?"Operational?Mathematics"?under?Bill > Guy?in?"Integral?Transforms"?at?Austin?in?addition?to?the?semester?I > spent?with?Bracewell?in?"Linear?Systems",?if?the?EE?community?wants > to?redefine?the?math?they?may.?I?shall?stick?to?what?the > mathematicians?wrote. > > Have?Fun! > Reg > > > > > |
