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FFT_Example_data_with_window

FFT_Example_data_with_window - Example Problem Generating...

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Example Problem - Generating an FFT from a time signal - including windows J. M. Cimbala Answers: Useful number of data points for FFT: Given: 256 100 Hz Calculations for the frequency spectrum: 3 s 50 Hz The data points are provided below from an experiment. 0.39 Hz 128 Frequency spectrum: See Plot below. Summary about the input signal: 0.46 V 15.6 Hz 1.79 V 46.9 Hz 0.72 V Calculated values: DC = mean value of input signal = 0.4540 volts (average of all the useful input data) 300 256 2.56 s 0.01 Hz 0.39 Hz 50 128 Frequency Spectrum: (also divide first one by 2, and add back the DC value) frequency (Hz) 0 0.000 -1.7527 0 -2.2067 0 0 -0.50315551210155 0.46 1 0.010 -0.5650 0.39 -1.0190 0 0 0.255239484675561-1.44005553334218E-002i 0 2 0.020 0.8801 0.78 0.4261 0 0 -7.76383520072323E-003+1.97186040257435E-002i 0 3 0.030 3.1924 1.17 2.7384 0 0 -4.77206890926481E-003-9.00947987812182E-003i 0 4 0.040 1.2804 1.56 0.8264 0 0 8.94397199299433E-003+4.6398488703775E-003i 0 5 0.050 0.9006 1.95 0.4466 0 0 -7.625940404E-003+3.19708858117488E-003i 0 6 0.060 -2.5214 2.34 -2.9754 0.01 -0.02 3.2332905736084E-002-1.50365761001296E-003i 0 7 0.070 -0.4022 2.73 -0.8562 0.01 -0.01 -3.7466315313763E-002-3.10360773236548E-002i 0 8 0.080 -0.5707 3.13 -1.0247 0.01 -0.01 7.88264087543479E-003+3.46369883642316E-002i 0 9 0.090 3.2201 3.52 2.7661 0.01 0.03 3.35940007579051E-003-1.22673131637587E-002i 0 10 0.100 1.6182 3.91 1.1642 0.01 0.02 7.05476835049565E-003+1.75568281354845E-002i 0 11 0.110 1.6789 4.3 1.2249 0.02 0.02 -2.70535057392308E-002-2.61735615253077E-002i 0 12 0.120 -1.6800 4.69 -2.1340 0.02 -0.05 2.91556747126038E-002+1.28772322275302E-002i 0 13 0.130 -1.2799 5.08 -1.7339 0.03 -0.04 -1.45307213195953E-002-1.66941747572471E-003i 0 14 0.140 -0.6754 5.47 -1.1294 0.03 -0.03 9.85750112550036E-004+1.72181037387782E-002i 0 15 0.150 1.6577 5.86 1.2037 0.03 0.04 1.74654914666632E-002-2.81921894958201E-002i 0 16 0.160 2.8238 6.25 2.3698 0.04 0.09 -3.17427308096476E-002+8.93643772104044E-003i 0 17 0.170 1.3445 6.64 0.8905 0.04 0.04 1.07479807652269E-004+6.6854200995464E-003i 0 18 0.180 0.2188 7.03 -0.2352 0.05 -0.01 2.62823383690665E-002-8.55593579319265E-003i 0 19 0.190 -2.4080 7.42 -2.8620 0.05 -0.15 -3.05550464049493E-002+9.94209197515098E-003i 0 20 0.200 -0.3065 7.81 -0.7605 0.06 -0.04 1.56197832849833E-002+1.94825876097873E-003i 0 21 0.210 -0.1269 8.2 -0.5809 0.06 -0.04 -1.61671990069486E-003-1.70549763019173E-002i 0 22 0.220 3.4371 8.59 2.9831 0.07 0.21 -1.96182706309876E-002+2.54014121468286E-002i 0 23 0.230 1.3243 8.98 0.8703 0.08 0.07 4.24240023381379E-002-1.76080892116027E-002i 0 24 0.240 1.4993 9.38 1.0453 0.08 0.09 -4.66701019348527E-002-1.08292385684645E-002i 0 25 0.250 -2.2204 9.77 -2.6744 0.09 -0.24 2.64370828428918E-002+2.77830114842836E-002i 0 26 0.260 -0.8385 10.16 -1.2925 0.1 -0.13 -9.36904478246288E-003-8.61130181348074E-003i 0 27 0.270 -0.7018 10.55 -1.1558 0.11 -0.12 -2.40795877594664E-002-3.28476977244172E-003i 0 28 0.280 2.3923 10.94 1.9383 0.11 0.22 2.1994674106765E-002+6.76995487475133E-003i 0 29 0.290 2.3541 11.33 1.9001 0.12 0.23 -2.91958319467153E-002-7.85366356044334E-003i 0 30 0.300 1.4472 11.72 0.9932 0.13 0.13 4.75207550090926E-003+2.40311075128391E-002i 0 31 0.310 -0.5389 12.11 -0.9929 0.14 -0.14 -5.77783706203459E-003-4.60248210139838E-002i 0 32 0.320 -2.0954 12.5 -2.5494 0.15 -0.37 -4.47573549954556E-002+4.17468631709641E-002i 0 33 0.330 -0.3373 12.89 -0.7913 0.16 -0.12 -1.39307293698942E-003+8.58091923857509E-003i 0 34 0.340 0.4861 13.28 0.0321 0.16 0.01 -5.0392501623855E-002-1.73806778365439E-003i 0 35 0.350 3.4043 13.67 2.9503 0.17 0.51 -0.101443826725748+2.50027830840298E-002i 0 36 0.360 1.1702 14.06 0.7162 0.18 0.13 -0.125883666283133-7.31658041148201E-004i 0 37 0.370 1.1327 14.45 0.6787 0.19 0.13 -0.390479569335504+0.107902459812318i 0.01 38 0.380 -2.5331 14.84 -2.9871 0.2 -0.6 -1.65065469431809+0.342761744049556i 0.02 39 0.390 -0.4727 15.23 -0.9267 0.21 -0.2 75.6051933798702-15.4303498448109i 0.98 40 0.400 -0.5956 15.63 -1.0496 0.22 -0.23 -137.586329124979+28.0505311730327i 1.79 41 0.410 2.9921 16.02 2.5381 0.23 0.59 62.4003014115217-12.7116692087143i 0.81 42 0.420 1.8784 16.41 1.4244 0.24 0.35 1.31012306259834-0.257677610212755i 0.02 43 0.430 1.5123 16.8 1.0583 0.25 0.27 0.334847157319583-0.109794128323887i 0 44 0.440 -1.2921 17.19 -1.7461 0.26 -0.46 0.146710439083681+2.58884464787161E-002i 0 45 0.450 -1.6372 17.58 -2.0912 0.28 -0.58 4.20036247964484E-002-4.31943254263914E-002i 0 46 0.460 -0.4200 17.97 -0.8740 0.29 -0.25 4.34565333097129E-002-2.05611331106323E-002i 0 47 0.470 1.2142 18.36 0.7602 0.3 0.23 4.9722720391448E-002-2.69713781920067E-003i 0 48 0.480 3.1516 18.75 2.6976 0.31 0.83 1.74156934229801E-002+7.5164364510498E-003i 0 49 0.490 1.1361 19.14 0.6821 0.32 0.22 1.68019784911801E-003+1.06023933800854E-003i 0 50 0.500 0.5830 19.53 0.1290 0.33 0.04 6.66606239392722E-004-1.31552748754942E-002i 0 51 0.510 -2.5788 19.92 -3.0328 0.34 -1.04 3.77448558621438E-002+3.04620964957392E-002i 0 52 0.520 -0.2479 20.31 -0.7019 0.35 -0.25 -3.06718829715886E-002-3.52268901436459E-002i 0 53 0.530 -0.2993 20.7 -0.7533 0.37 -0.28 2.0305511689949E-002+5.46790033305413E-003i 0 54 0.540 3.3843 21.09 2.9303 0.38 1.11 -1.60054637318944E-002+4.5941399698822E-003i 0 55 0.550 1.4647 21.48 1.0107 0.39 0.39 2.55908346197432E-002-1.08995322472634E-002i 0 56 0.560 1.4632 21.88 1.0092 0.4 0.41 -1.51975673985388E-003+1.49311619460452E-002i 0 57 0.570 -1.9404 22.27 -2.3944 0.41 -0.99 5.55619066419713E-003-1.86451785159896E-002i 0 58 0.580 -1.1379 22.66 -1.5919 0.43 -0.68 -2.12103919476283E-002+1.81471943293718E-002i 0 59 0.590 -0.5031
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