fft example

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FFT Number of data points: Total time analysed: Folding frequency: Time FFT input Range FFT freq. 0.0E+00 23.4835335467358 0 3.0E-05 22.7488466959291 16.28 6.0E-05 21.914972676784 32.55 9.0E-05 21.0113577307105 48.83 1.2E-04 20.0698559412243 65.10 1.5E-04 19.1236008010963 81.38 1.8E-04 18.205831461366 97.66 2.1E-04 17.3487152429299 113.93 2.4E-04 16.5822081238169 130.21 2.7E-04 15.9329935699552 146.48 3.0E-04 15.4235373018749 162.76 3.3E-04 15.0712914827051 179.04 3.6E-04 14.8880765194966 195.31 3.9E-04 14.8796623778643 211.59 4.2E-04 15.0455642420782 227.86 4.5E-04 15.3790597594436 244.14 4.8E-04 15.8674272580721 260.42 5.1E-04 16.492396499053 276.69 5.4E-04 17.2307959948991 292.97 5.7E-04 18.0553739626788 309.24 6.0E-04 18.9357638291538 325.52 6.3E-04 19.8395600844124 341.80 6.6E-04 20.7334663713373 358.07 6.9E-04 21.5844751392577 374.35 7.2E-04 22.3610370719566 390.63 7.5E-04 23.0341788624511 406.90 7.8E-04 23.5785297368088 423.18 8.1E-04 23.973220361867 439.45 8.4E-04 24.2026222925919 455.73 8.7E-04 24.2569017637723 472.01 9.0E-04 24.132368207688 488.28 9.3E-04 23.8316051513274 504.56 9.6E-04 23.363378856042 520.83 9.9E-04 22.7423279361079 537.11 1.0E-03 21.9884449515972 553.39 1.1E-03 21.1263683403751 569.66 1.1E-03 20.1845097728683 585.94 www.kpap.net/notes

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fast fourier transform example

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Sheet1

FFTFFT settingsTime-series settingswww.kpap.net/notesNumber of data points:2048.0Sampling frequency:33333.3333333333Amplitude 1:20phase angle 1:0radFrequency 1:50HzTotal time analysed:0.0614 secSampling interval:3.00E-05Amplitude 2:5Phase angle 2:0.8radFrequency 2:1000HzFolding frequency:16.3 Hzfrequency ratio sampling/signal: 33.3

TimeFFT input RangeFFT freq.FFT Output RangeAmplitudePhase0.0E+0023.48353354670902.7801229997890.881621213903.0E-0522.748846695916.281012.71272380204+78.4217203009367i0.99193805460.0772830516.0E-0521.914972676832.551585.15197484602+242.614482349346i1.5660264680.15187578789.0E-0521.011357730748.8319998.320988447+4502.09477924858i20.01838077290.22143211991.2E-0420.069855941265.10-1358.78735157791-396.891701287561i1.3823883231-2.85740606891.5E-0419.123600801181.38-587.491030083866-207.178350342295i0.6083510804-2.8025595331.8E-0418.205831461497.66-354.648174346066-143.904006986721i0.3737616001-2.75612588842.1E-0417.3487152429113.93-246.465696038683-111.085642437112i0.264006875-2.71814477682.4E-0416.5822081238130.21-185.760005749662-90.4776397791239i0.2017800818-2.68834456282.7E-0415.93299357146.48-147.788000866411-76.0622552289544i0.1623173784-2.66627694343.0E-0415.4235373019162.76-122.282682693686-65.2516887961i0.1353546534-2.65141723953.3E-0415.0712914827179.04-104.264490131304-56.7384318364431i0.115920616-2.64323036733.6E-0414.8880765195195.31-91.0486646675745-49.78546900459i0.1013390169-2.64120907553.9E-0414.8796623779211.59-81.0718049674918-43.9430056033973i0.090053812-2.64489231784.2E-0415.0455642421227.86-73.368375918901-38.9194132799213i0.0811054959-2.65387050374.5E-0415.3790597594244.14-67.313731168334-34.5163527853204i0.0738743359-2.66778259664.8E-0415.8674272581260.42-62.4882651316224-30.5935717072606i0.0679448222-2.68630842141. note that when plotting I use the first 1024 points (half of the points). The rest of the points are effectively a "mirror" of the these first points5.1E-0416.4923964991276.69-58.6012154811025-27.0486005340163i0.0630297469-2.70915835075.4E-0417.2307959949292.97-55.4457973779461-23.8044400536726i0.0589255564-2.73606176715.7E-0418.0553739627309.24-52.8716925656736-20.8017747699319i0.0554849925-2.7667552576.0E-0418.9357638292325.52-50.7675898430309-17.9938688343011i0.0525997222-2.80097129136.3E-0419.8395600844341.80-49.0497727937626-15.3431141187969i0.0501889603-2.83842808876.6E-0420.7334663713358.07-47.6544675978321-12.8186296333174i0.0481918064-2.87882136766.9E-0421.5844751393374.35-46.532597332886-10.3945488358387i0.0465619558-2.9218186942 the folding frequency is in fact the frequency step for which the FFT components are calculated. The calculation of this is directly related to Nyquists theoreum of sampling; the maximum frequency component that can be determined using a give dataset of points equally spaced 1.5E-5 seconds apart is equal to 1/(2*1.5e-5) = 33,333Hz in our example. 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