On 2015-06-22, Vadim Zavalishin wrote:
After some googling I rediscovered (I think I already found out it one
year ago and forgot) the Paley-Wiener-Schwartz theorem for tempered
distributions, which is closely related to what I was aiming at.
It'll you land right back at the extended sampling theorem I told about,
above. So why fret about the complex extensions? They won't help you
with bandlimited stuff at all.
Although Hölmander's tightening of the theorem in 1976 might help you
understand those BLEPs of yours. Because it quantifies singular
supports, i.e. every delta train necessary for the analysis of BLITs and
their integrals, starting from continuous time.
It's just that you don't need any of that machinery in order to deal
with that mode of synthesis, and you can easily see from the
distributional theory that you can't do any better. Why make it that
complicated?
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