Now, would you mind doing a little translation (for the laymen), since I didn't understand?

We did Fourier transforms in third--or-fourth semester calculus in college, but then I _was_ an engineer; electrical engineers would go on to do lots more of this stuff, since frequencies and waveforms are their territory. Essentially, you can look at "most" continuous functions in normal time-space, or you can represent them in a frequency space instead, and you can reproduce the original function by transforming from the frequency space back to the time space. The "Lebesgue" bit is a precise definition of "most". (For most of the math I did in college, "Lebesgue" was a phrase meaning "/* you are not expected to understand this */", and it and Measure Theory got trotted out to clarify rigorously when functions are well-behaved enough for the stuff we were learning to apply. Most functions you use are Lebegue integrable, unless you use stuff like "f(x) = 0 if x is rational and 1 if x is irrational".) Discrete Fourier Transforms are a related analysis technique that work on sets of numbers such as equally-spaced samples from a continuous function. The Fast Fourier Transform is a particularly efficient way to do DFTs, which was a breakthrough that made them practical to do on computers, and Jim was reminding the previous poster that for the problem at hand, determining the frequency spectrum of whatever-it-was, that DFTs aren't what you need; you need the regular continuous Fourier transform. At 01:04 PM 7/29/96 +0000, you wrote:

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Jim Choate <ravage@einstein.ssz.com> writes:

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You want a continuous Fourier transform, not a discrete one, to determine the frequency spectrum of the waveform being sampled. The FFT is simply an algorithm for computing the DFT without redundant computation. In general, any Lebesgue integrable complex function will have a Fourier transform, even one with a finite number of discontinuities. The reverse transform will faithfully reproduce the function, modulo the usual caveats about function spaces and sets of measure zero. # Thanks; Bill # Bill Stewart, +1-415-442-2215 stewarts@ix.netcom.com # <A HREF="http://idiom.com/~wcs"> # Dispel Authority!