On 3/27/14 5:27 PM, Ethan Duni wrote:
it is, at least, if you accept the EE notion of the Dirac delta function
and not worry so much about it "not really being a function", which is
literally what the math folks tell us.
I may be misremembering, but can't non-standard analysis be used to make
that whole Dirac delta function approach rigorous?
i dunno what "non-standard analysis" you mean. the only truly rigorous
usage of the Dirac delta is to keep it clothed with a surrounding
integral. so naked Dirac deltas are a no-no. then we can't really have
a notion of a Dirac comb function either.
I know that it works for
the whole "algebraic manipulation of delta-x terms" that we also like to do
in engineering classes, intuitively seems like we could play the same trick
with Dirac delta's and associated stuff. But I don't recall whether it
actually works out entirely... although Wikipedia suggests that maybe it
does (
http://en.wikipedia.org/wiki/Dirac_delta_function#Infinitesimal_delta_functions).
Not that it's worth the trouble to really work out - we already know what
the correct answers are from measure theory/distributions - but it's nice
to keep in mind that these pedantic math complaints are actually kind of
baseless, at least if some care is taken to adhere to the rules of
non-standard analysis and so avoid various pitfalls.
i just treat the Dirac delta in time as if it has a Planck Time
(10^(-43) second) width. then it's a true function and it still has, to
within an immeasureable degree of accuracy, the same properties that i want.
L8r,
--
r b-j r...@audioimagination.com
"Imagination is more important than knowledge."
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