On 3/27/14 10:58 PM, Theo Verelst wrote:
I'm glad to see some influence of my repeated mention of some of my
theoretical concerns leads to thoughts getting formulated, and more,
up to quite some, precision being present.
well, Theo, i've been thinking (and writing about
http://www.aes.org/e-lib/browse.cfm?elib=5122 ) the sampling theorem and
reconstruction issues for longer ago than this mailing list existed.
robert bristow-johnson wrote:> 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. ...
That, like what some others have phrased/quoted, sound good.
but it's *convenient* to be able to express and make use of naked delta
functions. i *want* to be able to say:
+inf +inf
T SUM{ delta(t-nT) } = SUM{ e^(i 2 pi k/T t) }
n=-inf k=-inf
and the summation on the left is a bunch of naked delta functions. no
integral surrounding them (at least not until later).
I had the good fortune when I graduated to have had a nice subject
with influence from university and some commercial lab (HP) influence,
and can't help to think when some people feel properly in place and
motivated to influence the world of science and connected interested
people, that there would be very, very many interesting subjects
possible to think about and work on, without having to go rough on the
lower regions of theory.
prognosticating about whether the Dirac delta is a function or not is
less useful to me than just moving past that and treating it as if it
were a function defined by the limit of some nascent delta function
(which is not the way the math guys do it). it still has all the
properties i need from it.
--
r b-j [email protected]
"Imagination is more important than knowledge."
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