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Feb 9, 2016 at 20:46 comment added Matt L. @DilipSarwate: You don't need to see it as a convolution, but just as a decomposition of the signal into shifted and weighted impulses (which is of course essentially the same, but conceptually it's different). Eq. (1) can be understood, even if one doesn't know what convolution is. That was at least the idea here.
Feb 9, 2016 at 20:40 comment added Dilip Sarwate Nice (+1), but it begs the question: why does $(1)$, which is just like a convolution, hold?
Feb 9, 2016 at 9:20 history answered Matt L. CC BY-SA 3.0