[TROLLING] From: FFT Analysis for Dummies 2012-01-15 10:25:42 Quote from: Woodinville on 2012-01-15 00:26:42Quote from: Gumboot on 2012-01-14 23:25:42Quote from: Woodinville on 2010-03-28 00:00:35Some points, an FFT is not an approximation, nor is it a model. It is a precise transform with a precise inverse, one that obeys power and amplitude conservation both in the time and short-term frequency domain.I take exception to this. An FFT, like anything else, is a model and/or an approximation if it is used as such. Sometimes 3 is an approximation of pi. There's no fantastic mathematical property that can stop something from being used as a very blunt instrument.No, an FFT is an orthonormal projection, no matter how it's used. It's not the FFT's fault (it has no violition, so how can it be) if somebody uses it in a particular way.I don't disagree with that in any way, but the point still stands that the statement is somewhere between vacuous and disingenuous.Similarly, I could calculate the area of a circle by multiplying the square of the radius by three. I could then assert that three is not an approximation because it is the precise midpoint between 2 and 4, and that it is also the sum of 1 and 2, and that it's even itself to the first power. It is precisely what it is.