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
