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January 03, 2014

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Very interesting article, thank you. Please take a moment to rephrase the following key statement, if you would: "...then there is frequency corresponding the pole's rotational frequency is represented in the sound."

polar form e^iθ is equal to the rectangular form cosθ+isinθ and corresponds to the coordinates (cosθ,sinθ) such that
e^i0 = 1 = (1,0)
e^iτ/4 = i = (0,1)
e^iτ/2 = -1 = (-1,0)
e^iτ3/4 = -i = (0,-1)
e^iτ = 1 = (1,0)

May I suggest a minor exception to your claim about FFT: most modern languages, R included, use some variation of the "pure" 2^N Cooley-Tukey FFT algorithm as appropriate to support factors of 3, 5, etc. in the length of the dataset, and even default to the "raw" DFT for other data lengths (unless specifically suppressed by the user).
And, of course, the FFT is in fact that equation, just with gobs of like terms grouped together. :-)

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