QUOTE (Woodinville @ Jun 16 2013, 08:34) <{POST_SNAPBACK}>
I have no idea whatsoever you're talking about here.
You seem to have the idea that I actually did write choice of 'transform' ...
A 19 kHz symmetric triangular and a 19 kHz sine are different. What does that difference mean in practice? Likely you would get one of two answers: (i) nothing, or (ii) if anything, the triangular is worse, as its useless higher order components are good for nothing and potentially bad for something.
Without choice of basis, it is absolutely no reason to claim that the latter has higher order components at all. It would not be so if we used triangular functions ( http://dx.doi.org/10.1016/S0898-1221(99)00075-9 - I am somewhat surprised that this had publishable news value as a research article as late as 1999 ...). We could do that, but there is a good reason why we don't. (Here's a lecturer who has or at last has a fond hope to have, students bright enough to spot that it isn't obvious: http://www.cv.nrao.edu/course/astr534/FourierTransforms.html .)