I am working on developing a Fourier transform for voltage readings. The goal is to determine voltages at different frequencies (frequency domain). I am taking readings at 100Hz and am measuring both the Average and TRMS voltages over time (time domain). For this question, I am only working with the "avg" data.
I have been utilizing the Fourier Analysis within Excel. I then utilize the =IMABS() function for each of the FFT (avg) values and divide by the amount of sample taken, 512 samples (i.e. =IMABS(FFT Value)/512). I then plot the results against the frequency (Hz).
Below is a table of example data. Apologies for the long list but the Fourier function in Excel only works with certain number of samples (i.e. 2, 4, 8,...256, 512, etc)
Attached is an image of the graph obtained when I graph just the avg values with respect to frequency.
This is a new area for me so I'm hoping to get some insight, guidance, and make sure that I'm not overlooking something. I am also aware of the Nyquist theorem and am therefore not confident with any graphed voltages above 50Hz.
Time (sec.) | Voltage (avg) | Counter | Freq. (Hz) | FFT (avg) | Amplitude (avg) |
---|---|---|---|---|---|
0.0000 | -0.464 | 0 | 0 | -229.039 | 0.447341797 |
0.0100 | -0.521 | 1 | 0.195694716 | 10.1322200016599+1.645257812029i | 0.020048688 |
0.0200 | -0.401 | 2 | 0.391389432 | 9.65075248625337+2.76041332464675i | 0.019605027 |
0.0300 | -0.512 | 3 | 0.587084149 | 9.15268494359245+4.03087189358114i | 0.019533161 |
0.0400 | -0.44 | 4 | 0.782778865 | 8.25681453333612+5.27235979553822i | 0.019133924 |
0.0500 | -0.467 | 5 | 0.978473581 | 7.21324666201885+6.22104757994938i | 0.018604206 |
0.0600 | -0.519 | 6 | 1.174168297 | 6.07955964718428+6.93019294202941i | 0.018005717 |
0.0700 | -0.405 | 7 | 1.369863014 | 4.83143342629608+7.37208937173917i | 0.017215271 |
0.0800 | -0.512 | 8 | 1.56555773 | 3.59291030204946+7.57742009618472i | 0.016379058 |
0.0900 | -0.433 | 9 | 1.761252446 | 2.37433650922022+7.59420275947096i | 0.015540468 |
0.1000 | -0.47 | 10 | 1.956947162 | 1.15340023381173+7.33229089156102i | 0.01449698 |
0.1100 | -0.52 | 11 | 2.152641879 | 0.120712139467973+6.91156950591859i | 0.013501218 |
0.1200 | -0.405 | 12 | 2.348336595 | -0.818067214278053+6.29386664644949i | 0.012396112 |
0.1300 | -0.516 | 13 | 2.544031311 | -1.51563676527916+5.57318532827966i | 0.011280468 |
0.1400 | -0.427 | 14 | 2.739726027 | -2.03711466482809+4.77308097389415i | 0.010135973 |
0.1500 | -0.473 | 15 | 2.935420744 | -2.37469986904867+3.92829794114827i | 0.008965402 |
0.1600 | -0.516 | 16 | 3.13111546 | -2.51483612661896+3.05848270837768i | 0.007733664 |
0.1700 | -0.408 | 17 | 3.326810176 | -2.48721204893401+2.29485333429039i | 0.006609698 |
0.1800 | -0.522 | 18 | 3.522504892 | -2.31824822704003+1.56731883117559i | 0.005465527 |
0.1900 | -0.42 | 19 | 3.718199609 | -1.9729997846832+0.960300569731039i | 0.004285721 |
0.2000 | -0.478 | 20 | 3.913894325 | -1.54872675438711+0.515919754555665i | 0.00318828 |
0.2100 | -0.512 | 21 | 4.109589041 | -1.08489578685385+0.185004760673414i | 0.002149525 |
0.2200 | -0.407 | 22 | 4.305283757 | -0.600187211577808+3.42696351333572E-002i | 0.00117415 |
0.2300 | -0.522 | 23 | 4.500978474 | -0.141753016604165-1.5540399065834E-002i | 0.00027852 |
0.2400 | -0.416 | 24 | 4.69667319 | 0.290088046498194+5.29223345462406E-002i | 0.00057593 |
0.2500 | -0.483 | 25 | 4.892367906 | 0.637581694745883+0.270631882678479i | 0.001352815 |
0.2600 | -0.509 | 26 | 5.088062622 | 0.913697152631281+0.525795104052738i | 0.002058952 |
0.2700 | -0.408 | 27 | 5.283757339 | 1.07948700704762+0.877326776329355i | 0.002716877 |
0.2800 | -0.523 | 28 | 5.479452055 | 1.09431775695688+1.18413901721967i | 0.003149148 |
0.2900 | -0.414 | 29 | 5.675146771 | 1.04197490942795+1.49153138884348i | 0.003553602 |
0.3000 | -0.485 | 30 | 5.870841487 | 0.930424506303088+1.75894591194859i | 0.003886464 |
0.3100 | -0.507 | 31 | 6.066536204 | 0.700274984853021+1.98375634269125i | 0.004108845 |
0.3200 | -0.413 | 32 | 6.26223092 | 0.427036374279053+2.18627755520587i | 0.004350767 |
0.3300 | -0.522 | 33 | 6.457925636 | 0.114825551542406+2.30452647107527i | 0.004506612 |
0.3400 | -0.41 | 34 | 6.653620352 | -0.251612518345346+2.25525310623467i | 0.00443212 |
0.3500 | -0.489 | 35 | 6.849315068 | -0.485424402852134+2.06281583436469i | 0.004138988 |
0.3600 | -0.504 | 36 | 7.045009785 | -0.786799114041862+1.99599329978933i | 0.004190371 |
0.3700 | -0.417 | 37 | 7.240704501 | -0.980003621162694+1.72068507267303i | 0.003867564 |
0.3800 | -0.52 | 38 | 7.436399217 | -1.13255633499022+1.50728840390684i | 0.003682354 |
0.3900 | -0.405 | 39 | 7.632093933 | -1.21522126871698+1.18661576554237i | 0.003317335 |
0.4000 | -0.488 | 40 | 7.82778865 | -1.17816222637269+0.911135070016272i | 0.002908933 |
0.4100 | -0.506 | 41 | 8.023483366 | -1.16058223145583+0.593483129168018i | 0.002545944 |
0.4200 | -0.422 | 42 | 8.219178082 | -0.977497440390513+0.338823108580408i | 0.002020614 |
0.4300 | -0.523 | 43 | 8.414872798 | -0.815688606400097+0.173771044887206i | 0.001628893 |
0.4400 | -0.407 | 44 | 8.610567515 | -0.602590140658854+4.03168948966772E-002i | 0.001179565 |
0.4500 | -0.481 | 45 | 8.806262231 | -0.336934811223527-1.93959361379846E-002i | 0.000659165 |
0.4600 | -0.501 | 46 | 9.001956947 | -0.136169857776244-7.50361244454022E-003i | 0.00026636 |
0.4700 | -0.426 | 47 | 9.197651663 | 6.02639217652264E-002+1.85540060806169E-002i | 0.000123155 |
0.4800 | -0.526 | 48 | 9.39334638 | 0.282481666820933+0.121647899267673i | 0.000600706 |
0.4900 | -0.402 | 49 | 9.589041096 | 0.413875144645062+0.323198016919613i | 0.001025622 |
0.5000 | -0.488 | 50 | 9.784735812 | 0.46382645002229+0.468359872354553i | 0.001287428 |
0.5100 | -0.494 | 51 | 9.980430528 | 0.512458090741133+0.692113347663311i | 0.001681996 |
0.5200 | -0.427 | 52 | 10.17612524 | 0.464175821857294+0.885410206930413i | 0.001952549 |
0.5300 | -0.527 | 53 | 10.37181996 | 0.392704495708325+1.00365121409194i | 0.002104969 |
0.5400 | -0.4 | 54 | 10.56751468 | 0.302381753466691+1.19598555887027i | 0.002409412 |
0.5500 | -0.488 | 55 | 10.76320939 | 9.41359784704656E-002+1.28098489205329i | 0.00250867 |
0.5600 | -0.492 | 56 | 10.95890411 | -5.37145520510952E-002+1.33217729659522i | 0.002604023 |
0.5700 | -0.429 | 57 | 11.15459883 | -0.284153335815369+1.33831690461504i | 0.002672169 |
0.5800 | -0.526 | 58 | 11.35029354 | -0.479510056494082+1.23706803934805i | 0.00259131 |
0.5900 | -0.401 | 59 | 11.54598826 | -0.588508197996208+1.14420786763055i | 0.002513053 |
0.6000 | -0.49 | 60 | 11.74168297 | -0.750933338056818+1.02322392513199i | 0.002478921 |
0.6100 | -0.485 | 61 | 11.93737769 | -0.845420982463707+0.850399701728216i | 0.002342054 |
0.6200 | -0.436 | 62 | 12.13307241 | -0.872099113161632+0.688965118144201i | 0.002170721 |
0.6300 | -0.526 | 63 | 12.32876712 | -0.867696056991852+0.510911890146492i | 0.001966679 |
0.6400 | -0.394 | 64 | 12.52446184 | -0.846118361750733+0.312787409309037i | 0.001761879 |
0.6500 | -0.494 | 65 | 12.72015656 | -0.700763258734886+0.223785630558508i | 0.001436774 |
0.6600 | -0.482 | 66 | 12.91585127 | -0.594363584722293+4.34415449685877E-002i | 0.001163963 |
0.6700 | -0.441 | 67 | 13.11154599 | -0.443418702758577-2.81778533350083E-002i | 0.000867799 |
0.6800 | -0.526 | 68 | 13.3072407 | -0.274173268602233-7.75294764816895E-002i | 0.000556493 |
0.6900 | -0.393 | 69 | 13.50293542 | -9.19087189277066E-002-3.67290016722993E-002i | 0.000193312 |
0.7000 | -0.494 | 70 | 13.69863014 | 8.35034877995999E-002-2.88689128021349E-002i | 0.000172564 |
0.7100 | -0.478 | 71 | 13.89432485 | 0.14501529433385+0.119597410589135i | 0.00036713 |
0.7200 | -0.445 | 72 | 14.09001957 | 0.228733084556724+0.235312617319269i | 0.000640943 |
0.7300 | -0.525 | 73 | 14.28571429 | 0.240052412637727+0.373773413956849i | 0.000867618 |
0.7400 | -0.398 | 74 | 14.481409 | 0.255815600480613+0.462556756670193i | 0.001032389 |
0.7500 | -0.49 | 75 | 14.67710372 | 0.251409383369858+0.627395398931579i | 0.001320104 |
0.7600 | -0.47 | 76 | 14.87279843 | 0.162566798954433+0.725722332958638i | 0.001452554 |
0.7700 | -0.45 | 77 | 15.06849315 | 0.104515512093105+0.834013887905941i | 0.001641674 |
0.7800 | -0.528 | 78 | 15.26418787 | -2.0872726813188E-002+0.934920308584918i | 0.001826471 |
0.7900 | -0.399 | 79 | 15.45988258 | -0.228172660942765+0.927106694266334i | 0.001864789 |
0.8000 | -0.495 | 80 | 15.6555773 | -0.297715370895055+0.882984934377287i | 0.00181997 |
0.8100 | -0.464 | 81 | 15.85127202 | -0.459154214398574+0.858790262541157i | 0.00190201 |
0.8200 | -0.454 | 82 | 16.04696673 | -0.531759684345087+0.71193743420169i | 0.001735562 |
0.8300 | -0.528 | 83 | 16.24266145 | -0.582897694831826+0.648138862991088i | 0.001702531 |
0.8400 | -0.401 | 84 | 16.43835616 | -0.691101659464284+0.514854162590408i | 0.0016832 |
0.8500 | -0.503 | 85 | 16.63405088 | -0.781199731191186+9.11054335093847E-002i | 0.001536122 |
0.8600 | -0.454 | 86 | 16.8297456 | -0.65640093657412+0.436884039324661i | 0.001540036 |
0.8700 | -0.456 | 87 | 17.02544031 | -0.711289955077337+0.215317467471172i | 0.001451495 |
0.8800 | -0.522 | 88 | 17.22113503 | -0.523077156180344+6.50100020610644E-002i | 0.001029495 |
0.8900 | -0.404 | 89 | 17.41682975 | -0.457063477012903+9.40734203869213E-002i | 0.000911414 |
0.9000 | -0.504 | 90 | 17.61252446 | -0.401939026899766-3.82318024054948E-002i | 0.00078858 |
0.9100 | -0.45 | 91 | 17.80821918 | -0.25558274486654-6.18114199989203E-002i | 0.000513576 |
0.9200 | -0.458 | 92 | 18.00391389 | -0.198769059902799-5.67941326050739E-002i | 0.000403757 |
0.9300 | -0.523 | 93 | 18.19960861 | -9.53852009466001E-003-9.94636251704868E-002i | 0.000195156 |
0.9400 | -0.402 | 94 | 18.39530333 | 0.118108733560192+0.174798543633572i | 0.000412032 |
0.9500 | -0.509 | 95 | 18.59099804 | 0.160432037943916+0.453369992858463i | 0.000939294 |
0.9600 | -0.447 | 96 | 18.78669276 | 4.47208878848853E-002+0.125845924705548i | 0.000260851 |
0.9700 | -0.462 | 97 | 18.98238748 | -0.17915405379133+0.384195382993815i | 0.000827955 |
0.9800 | -0.522 | 98 | 19.17808219 | -0.372308771368194-2.34528788216604E-002i | 0.000728607 |
0.9900 | -0.401 | 99 | 19.37377691 | 7.52035605307099E-002-1.36890952288607E-002i | 0.000149296 |
1.0000 | -0.512 | 100 | 19.56947162 | -1.62976042411506-0.174785300615682i | 0.003201379 |
. . . Table Cont'd
Time (sec.) | Voltage (avg) | Counter | Freq. (Hz) | FFT (avg) | Amplitude (avg) |
---|---|---|---|---|---|
4.7500 | -0.439 | 475 | 92.95499022 | -0.980003621162715-1.72068507267302i | 0.003867564 |
4.7600 | -0.526 | 476 | 93.15068493 | -0.786799114041881-1.99599329978933i | 0.004190371 |
4.7700 | -0.394 | 477 | 93.34637965 | -0.485424402852159-2.06281583436469i | 0.004138988 |
4.7800 | -0.494 | 478 | 93.54207436 | -0.25161251834537-2.25525310623467i | 0.00443212 |
4.7900 | -0.479 | 479 | 93.73776908 | 0.114825551542379-2.30452647107527i | 0.004506612 |
4.8000 | -0.446 | 480 | 93.9334638 | 0.427036374279046-2.18627755520587i | 0.004350767 |
4.8100 | -0.525 | 481 | 94.12915851 | 0.700274984852997-1.98375634269126i | 0.004108845 |
4.8200 | -0.398 | 482 | 94.32485323 | 0.93042450630307-1.7589459119486i | 0.003886464 |
4.8300 | -0.492 | 483 | 94.52054795 | 1.04197490942793-1.49153138884349i | 0.003553602 |
4.8400 | -0.47 | 484 | 94.71624266 | 1.09431775695686-1.18413901721968i | 0.003149148 |
4.8500 | -0.45 | 485 | 94.91193738 | 1.07948700704761-0.877326776329368i | 0.002716877 |
4.8600 | -0.528 | 486 | 95.10763209 | 0.913697152631271-0.525795104052749i | 0.002058952 |
4.8700 | -0.4 | 487 | 95.30332681 | 0.637581694745876-0.27063188267849i | 0.001352815 |
4.8800 | -0.495 | 488 | 95.49902153 | 0.290088046498189-5.29223345462469E-002i | 0.00057593 |
4.8900 | -0.465 | 489 | 95.69471624 | -0.141753016604169+1.554039906583E-002i | 0.00027852 |
4.9000 | 0 | 490 | 95.89041096 | -0.600187211577812-3.42696351333574E-002i | 0.00117415 |
4.9100 | 0 | 491 | 96.08610568 | -1.08489578685386-0.185004760673409i | 0.002149525 |
4.9200 | 0 | 492 | 96.28180039 | -1.54872675438712-0.515919754555661i | 0.00318828 |
4.9300 | 0 | 493 | 96.47749511 | -1.97299978468321-0.960300569731027i | 0.004285721 |
4.9400 | 0 | 494 | 96.67318982 | -2.31824822704005-1.56731883117558i | 0.005465527 |
4.9500 | 0 | 495 | 96.86888454 | -2.48721204893404-2.29485333429037i | 0.006609698 |
4.9600 | 0 | 496 | 97.06457926 | -2.51483612661897-3.05848270837768i | 0.007733664 |
4.9700 | 0 | 497 | 97.26027397 | -2.37469986904871-3.92829794114825i | 0.008965402 |
4.9800 | 0 | 498 | 97.45596869 | -2.03711466482813-4.77308097389414i | 0.010135973 |
4.9900 | 0 | 499 | 97.65166341 | -1.51563676527921-5.57318532827965i | 0.011280468 |
5.0000 | 0 | 500 | 97.84735812 | -0.818067214278094-6.29386664644949i | 0.012396112 |
5.0100 | 0 | 501 | 98.04305284 | 0.12071213946791-6.9115695059186i | 0.013501218 |
5.0200 | 0 | 502 | 98.23874755 | 1.15340023381167-7.33229089156104i | 0.01449698 |
5.0300 | 0 | 503 | 98.43444227 | 2.37433650922015-7.59420275947099i | 0.015540468 |
5.0400 | 0 | 504 | 98.63013699 | 3.59291030204943-7.57742009618474i | 0.016379058 |
5.0500 | 0 | 505 | 98.8258317 | 4.83143342629601-7.37208937173923i | 0.017215271 |
5.0600 | 0 | 506 | 99.02152642 | 6.07955964718423-6.93019294202947i | 0.018005717 |
5.0700 | 0 | 507 | 99.21722114 | 7.2132466620188-6.22104757994946i | 0.018604206 |
5.0800 | 0 | 508 | 99.41291585 | 8.25681453333609-5.27235979553828i | 0.019133924 |
5.0900 | 0 | 509 | 99.60861057 | 9.15268494359242-4.03087189358123i | 0.019533161 |
5.1000 | 0 | 510 | 99.80430528 | 9.65075248625335-2.76041332464683i | 0.019605027 |
5.1100 | 0 | 511 | 100 | 10.1322200016599-1.6452578120291i | 0.020048688 |