Comments on The Fourier Transform, explained in one sentenceTypePad2013-11-21T23:08:18ZBlog Administratorhttps://blog.revolutionanalytics.com/tag:typepad.com,2003:https://blog.revolutionanalytics.com/2014/01/the-fourier-transform-explained-in-one-sentence/comments/atom.xml/Carl Witthoft commented on 'The Fourier Transform, explained in one sentence'tag:typepad.com,2003:6a010534b1db25970b019b04516c16970d2014-01-06T16:40:15Z2014-01-06T17:49:47ZCarl WitthoftMay I suggest a minor exception to your claim about FFT: most modern languages, R included, use some variation of...<p>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). <br />
And, of course, the FFT is in fact that equation, just with gobs of like terms grouped together. :-)</p>MasterG commented on 'The Fourier Transform, explained in one sentence'tag:typepad.com,2003:6a010534b1db25970b01a5105bdd1b970c2014-01-05T00:33:13Z2014-01-06T17:49:47ZMasterGhttps://twitter.com/_MasterGpolar form e^iθ is equal to the rectangular form cosθ+isinθ and corresponds to the coordinates (cosθ,sinθ) such that e^i0 =...<p>polar form e^iθ is equal to the rectangular form cosθ+isinθ and corresponds to the coordinates (cosθ,sinθ) such that <br />
e^i0 = 1 = (1,0)<br />
e^iτ/4 = i = (0,1)<br />
e^iτ/2 = -1 = (-1,0)<br />
e^iτ3/4 = -i = (0,-1)<br />
e^iτ = 1 = (1,0)</p>C. Griffith commented on 'The Fourier Transform, explained in one sentence'tag:typepad.com,2003:6a010534b1db25970b01a3fba7df5e970b2014-01-04T18:09:23Z2014-01-06T17:49:47ZC. GriffithVery interesting article, thank you. Please take a moment to rephrase the following key statement, if you would: "...then there...<p>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."</p>