Calculate amplitude, phase and energy spectrum using FFT in MATLAB

[whatsoever]

Hello all,

I have a vector, let's say A, which has measured values of the Earth's magnetic field (and if it is relevant, two vectors X and Y with the coordinates of the point each value was measured). I need to calculate the amplitude, phase and energy spectrum using FFT in MATLAB

     X            Y        A
399845.66 399018.66 -3.52
399750.69 399180.44 -3.587
399656 399342.19 -3.653
399561.63 399504.06 -3.721
399467.22 399665.91 -3.788
399372.66 399827.78 -3.849
399277.88 399989.56 -3.906
399183.19 400151.13 -3.955
399088.22 400312.34 -3.997
398992.91 400473.5 -4.031
398897.25 400634.75 -4.058
398801.44 400796.5 -4.079
398705.91 400958.53 -4.095
398610.44 401120.91 -4.104
398515.13 401283.5 -4.107
398420 401446.63 -4.106
398325.16 401610.53 -4.1
398230.88 401774.84 -4.089
398136.81 401938.47 -4.069
398042.25 402101.34 -4.038
397946.97 402263.63 -3.997
397850.97 402425.38 -3.948
397754.88 402587 -3.891
397658.81 402748.88 -3.829
397563.44 402911.34 -3.765
397469.19 403074.34 -3.696
397375.5 403236.94 -3.621
397281.69 403399.25 -3.538
397187.28 403561.13 -3.447
397092.38 403722.84 -3.348
396997 403884.66 -3.243
396901.53 404046.5 -3.132
396806.19 404208.66 -3.016
396711.06 404371.03 -2.895
396616.28 404533.38 -2.768
396521.53 404695.53 -2.633
396426.38 404857.22 -2.49
396330.91 405018.84 -2.34
396235.25 405180.5 -2.183
396139.5 405342.13 -2.018
396043.78 405503.97 -1.847
395948.34 405665.84 -1.668
395853 405827.56 -1.482
395757.66 405989.41 -1.287
395662.63 406151.22 -1.084
395567.94 406312.91 -0.873
395473.59 406474.59 -0.652
395379.41 406635.94 -0.421
395285.59 406797.25 -0.179
395192 406958.78 0.072
395098.44 407120.53 0.332
395004.69 407282.63 0.603
394910.78 407444.94 0.884
394816.66 407607.16 1.178
394722.13 407768.97 1.485
394627.09 407930.34 1.806
394531.66 408091.44 2.142
394436.13 408252.41 2.49
394340.59 408413.5 2.851
394245.38 408574.69 3.226
394150.25 408735.88 3.614
394055.38 408896.91 4.018
393960.75 409057.84 4.438
393865.88 409218.56 4.874
393771.06 409379.41 5.327
393675.91 409540.38 5.798
393580.91 409701.44 6.287
393485.78 409862.41 6.796
393390.88 410023.25 7.323
393296.13 410183.97 7.869
393201.69 410344.88 8.435
393107.66 410506 9.021
393013.94 410667.34 9.626
392920.41 410828.88 10.252
392827 410990.66 10.899
392733.63 411152.63 11.568
392639.75 411314.31 12.261
392545.16 411475.91 12.98
392449.81 411637.25 13.725
392353.66 411798.16 14.497
392257.31 411958.88 15.298
392160.94 412119.38 16.127
392064.88 412279.94 16.984
391969.41 412440.72 17.87
391874.56 412602.03 18.785
391780.41 412763.84 19.73
391686.88 412926.28 20.707
391593.66 413088.81 21.72
391500.13 413250.94 22.773
391405.97 413412.53 23.871
391311.22 413573.5 25.015
391216.03 413733.81 26.207
391120.75 413893.81 27.447
391025.47 414053.91 28.737
390930.59 414214.34 30.077
390836.22 414375.19 31.466
390742.56 414536.31 32.907
390649.22 414697.97 34.4
390556 414859.88 35.946
390462.69 415021.88 37.549
390368.5 415183.91 39.221
390273.53 415345.56 40.96
390177.84 415506.91 42.76
390081.69 415668.09 44.612
389985.53 415829.03 46.509
389889.53 415989.63 48.441
389794.13 416150.22 50.395
389699.38 416310.88 52.362
389605.56 416471.69 54.326
389512.59 416632.66 56.276
389420.13 416793.97 58.197
389327.78 416955.25 60.075
389235.16 417116.56 61.896
389141.81 417277.47 63.644
389047.88 417437.97 65.305
388953.53 417597.81 66.864
388858.88 417757.38 68.315
388764.38 417916.88 69.644
388670.13 418076.41 70.838
388575.88 418236.16 71.883
388481.72 418396.13 72.768
388387.56 418556.06 73.481
388293.34 418716.16 74.012
388198.91 418876.25 74.349
388104.41 419036.34 74.482
388009.53 419196.44 74.401
387914.72 419356.44 74.096
387819.91 419516.44 73.56
387725.22 419676.56 72.784
387630.44 419836.78 71.76
387535.66 419997.22 70.483
387441.31 420157.66 68.948
387347.31 420318.19 67.146
387253.63 420478.56 65.075
387159.75 420638.97 62.738
387065.88 420799.38 60.137
386971.78 420959.66 57.281
386877.53 421120.09 54.178
386783.16 421280.31 50.841
386688.88 421440.41 47.284
386594.78 421600.25 43.526
386500.88 421760.13 39.585
386407.31 421920.28 35.482
386314.06 422080.88 31.241
386220.97 422241.59 26.886
386128.13 422402.38 22.445
386035.16 422563.06 17.944
385941.81 422723.66 13.412
385847.97 422884.19 8.923
385753.38 423044.53 4.505
385658.25 423204.59 0.171
385562.75 423364.53 -4.069
385467.03 423524.28 -8.204
385371.22 423683.91 -12.229
385275.72 423843.88 -16.137
385180.72 424004.03 -19.925
385086.41 424164.38 -23.591
384992.5 424324.91 -27.132
384899.13 424485.84 -30.55
384806.13 424647 -33.845
384713.34 424808.38 -37.019
384620.5 424970.16 -40.076
384527.44 425132 -43.019
384433.91 425293.72 -45.849
384339.63 425455.19 -48.524
384244.63 425616.44 -51.023
384149.13 425777.53 -53.343
384053.41 425938.5 -55.481
383957.84 426099.59 -57.437
383862.34 426260.69 -59.209
383767.25 426421.84 -60.799
383672.28 426583 -62.209
383577.78 426744.38 -63.443
383483.5 426906.06 -64.507
383389.44 427067.72 -65.405
383295.25 427229.41 -66.144
383201.16 427390.84 -66.733
383106.81 427552.31 -67.18
383012.34 427713.91 -67.495
382917.59 427875.38 -67.688
382822.53 428036.91 -67.781
382727.31 428198.31 -67.786
382631.78 428359.53 -67.715
382536.13 428520.63 -67.577
382440.53 428681.94 -67.382
382345.31 428843.47 -67.138
382250.5 429005.19 -66.851
382156.38 429167.09 -66.529
382062.63 429329.22 -66.175
381969.13 429491.31 -65.793
381875.5 429653.41 -65.388
381781.28 429815.22 -64.96
381686.47 429976.63 -64.512
381591.25 430137.81 -64.047
381495.75 430298.81 -63.567
381400.31 430459.69 -63.076
381305.09 430620.56 -62.58
381210.09 430781.53 -62.082
381115.66 430942.69 -61.586
381021.53 431104.03 -61.091
380927.53 431265.72 -60.6
380833.34 431427.44 -60.111
380738.97 431589.25 -59.625
380644.22 431751.22 -59.141
380549.19 431913.09 -58.658
380453.63 432074.66 -58.175
380357.63 432236.34 -57.691
380261.72 432398.06 -57.207
380165.91 432559.84 -56.722
380070.59 432721.84 -56.236
379975.69 432884.16 -55.749
379881.28 433046.88 -55.259
379787.19 433209.69 -54.766
379693.31 433372.72 -54.269
379599.34 433535.75 -53.768
379504.88 433698.59 -53.261
379409.91 433861.38 -52.747
379314.25 434023.72 -52.227
379218.13 434185.78 -51.702
379121.47 434347.75 -51.172
379024.53 434509.5 -50.637
378927.5 434671.28 -50.099
378830.75 434832.94 -49.56
378734.31 434994.66 -49.019
378638.38 435156.72 -48.479
378542.94 435318.97 -47.94
378448 435481.63 -47.403
378353.47 435644.59 -46.869
378259.06 435807.56 -46.336
378164.53 435970.53 -45.803
378070.03 436133.5 -45.274
377975.34 436296.69 -44.748
377880.38 436460.03 -44.227
377785.41 436623.47 -43.712
377690.25 436786.91 -43.204
377595 436950.38 -42.705
377499.69 437114.19 -42.215
377404.28 437278.09 -41.735
377308.88 437442 -41.267
377213.41 437606.06 -40.811
377117.53 437770.13 -40.365
377021.25 437933.97 -39.931
376924.5 438097.75 -39.508
376827.47 438261.53 -39.096
376730.25 438425.22 -38.694
376633 438588.94 -38.303
376535.78 438752.75 -37.921
376438.88 438916.63 -37.547
376342.03 439080.53 -37.181
376245.72 439244.63 -36.822
376149.78 439408.94 -36.469
376054.16 439573.09 -36.12
375958.5 439737.16 -35.773
375862.97 439901.19 -35.429
375767.44 440065.13 -35.086
375671.88 440229.09 -34.743
375576.34 440392.91 -34.401
375480.63 440556.88 -34.059
375384.69 440720.84 -33.718
375288.69 440884.91 -33.377
375192.5 441049.13 -33.038
375096.22 441213.44 -32.702
374999.69 441378 -32.368
374903.06 441542.81 -32.037
374806.16 441707.72 -31.709
374709.06 441872.88 -31.385
374611.81 442038.13 -31.066
374514.06 442203.66 -30.751
374416.53 442368.97 -30.439
374318.88 442534.25 -30.132
374221.22 442699.44 -29.828
374123.5 442864.66 -29.528
374025.84 443029.84 -29.232
373928.22 443195.03 -28.939
373830.59 443360.34 -28.649
373733.06 443525.63 -28.361
373635.44 443691.06 -28.076
373537.91 443856.34 -27.792
373440.59 444021.75 -27.51
373343.47 444187.03 -27.229
373246.53 444352.31 -26.949
373150 444517.75 -26.671
373053.78 444683.56 -26.396
372957.88 444849.66 -26.124
372861.97 445015.88 -25.855
372765.91 445182.19 -25.587
372669.13 445348.47 -25.32
372571.59 445514.44 -25.053
372473.38 445680.13 -24.787
372374.63 445845.63 -24.52
372275.5 446010.91 -24.255
372176.5 446176.31 -23.992
372077.97 446341.69 -23.732
371979.72 446507.28 -23.475
371882.13 446673.25 -23.222
371785 446839.44 -22.973
371688.19 447006.06 -22.727
371591.5 447172.78 -22.483
371494.59 447339.38 -22.239
371397.19 447505.59 -21.995
371299.31 447671.5 -21.749
371200.91 447836.97 -21.502
371102.38 448002.13 -21.253
371004.16 448167.16 -21.004
370906.03 448332.19 -20.754
370808.38 448497.22 -20.503
370711.44 448662.28 -20.251
370614.88 448827.56 -19.999
370518.81 448992.91 -19.747
370423.06 449158.47 -19.494
370327.5 449324.25 -19.24
370232.25 449490.13 -18.985
370136.81 449656 -18.728
370041.06 449821.56 -18.468
369944.72 449986.72 -18.204
369847.66 450151.47 -17.936
369749.91 450315.94 -17.665
369652 450480.19 -17.39
369554.03 450644.25 -17.113
369456.38 450808.13 -16.832
369358.91 450971.94 -16.548
369262 451135.69 -16.26
369165.41 451299.66 -15.968
369069.53 451463.78 -15.67
368974.03 451628.03 -15.368
368879.03 451792.44 -15.058
368784.41 451957.06 -14.743
368690.03 452121.91 -14.421
368595.34 452286.75 -14.092
368500.16 452451.31 -13.754
368404.38 452615.44 -13.407
368308.03 452779.41 -13.053
368211.25 452943.16 -12.693
368114.22 453107.16 -12.331
368017.31 453271.38 -11.966
367920.19 453435.47 -11.601
367823.09 453599.81 -11.236
367725.91 453764.38 -10.873
367628.91 453928.84 -10.512
367532.03 454093.5 -10.155
367435.38 454258.38 -9.804
367338.91 454423.34 -9.46
367242.44 454588.41 -9.122
367145.88 454753.5 -8.794
367048.84 454918.38 -8.474
366951.41 455083.09 -8.166
366853.78 455247.59 -7.871
366756.31 455411.94 -7.594
366659.06 455576.31 -7.337
366562.13 455740.75 -7.104
366465.75 455905.5 -6.899
366369.88 456070.47 -6.725
366274.38 456235.84 -6.586
366179.03 456401.53 -6.485
366083.53 456567.34 -6.423
365987.72 456733.06 -6.401
365891.53 456898.38 -6.422
365794.72 457063.25 -6.485
365697.59 457227.72 -6.593
365599.97 457391.91 -6.745
365501.94 457555.75 -6.943
365403.72 457719.41 -7.185
365305.69 457882.94 -7.472
365208.25 458046.56 -7.802
365111.59 458210.34 -8.176
365015.72 458374.53 -8.59
364920.38 458539.13 -9.042
364825.34 458704.13 -9.529
364730.31 458869.16 -10.046
364634.81 459034.22 -10.59
364538.81 459198.75 -11.157
364442.19 459362.88 -11.743
364345.47 459526.66 -12.344
364248.63 459690.25 -12.957
364151.81 459854.06 -13.578
364055.06 460017.75 -14.202
363958.25 460181.31 -14.826
363861.44 460345.03 -15.444
363764.63 460508.94 -16.054
363667.94 460672.84 -16.652
363571.22 460836.75 -17.235
363474.53 461000.56 -17.8
363378.25 461164.69 -18.348
363282.44 461329 -18.877
363187.06 461493.5 -19.388
363091.97 461658.31 -19.881
362996.78 461823.25 -20.359
362901.25 461988.13 -20.822
362804.88 462152.66 -21.269
362707.84 462316.72 -21.703
362610.38 462480.47 -22.125
362512.84 462644 -22.539
362415.28 462807.66 -22.945
362317.84 462971.41 -23.346
362220.81 463135.47 -23.742
362124.31 463299.94 -24.132
362028.13 463465.06 -24.518
361932.44 463630.91 -24.897
361837.03 463797.22 -25.266
361741.78 463963.5 -25.621
361646.53 464129.59 -25.96
361550.75 464295.13 -26.276
361454.38 464460.16 -26.567
361357.59 464624.41 -26.832
361260.41 464788.38 -27.069
361163 464952.38 -27.28
361065.72 465116.34 -27.464
360968.56 465280.66 -27.621
360871.59 465445.06 -27.75
360774.63 465609.69 -27.852
360677.72 465774.63 -27.926
360580.88 465939.69 -27.974
360483.88 466105 -27.996
360386.78 466270.09 -27.991
360289.88 466435.16 -27.962
360192.94 466599.88 -27.91
360096.13 466764.75 -27.837
359999.41 466929.59 -27.743
359903 467094.63 -27.632
359806.5 467259.91 -27.506
359710.13 467425.38 -27.367
359613.47 467590.88 -27.217
359516.78 467756.28 -27.058
359420.13 467921.47 -26.894
359323.41 468086.22 -26.726
359226.88 468250.94 -26.558
359130.41 468415.78 -26.393
359034 468580.72 -26.234
358937.53 468745.66 -26.081
358840.84 468910.63 -25.937
358744.19 469075.81 -25.802
358647.44 469240.88 -25.677
358550.78 469406.19 -25.562
358453.84 469571.38 -25.458
358356.81 469736.38 -25.363
358259.56 469901.28 -25.276
358162.13 470065.72 -25.196
358064.66 470230.09 -25.123
357967.19 470394.31 -25.057
357869.84 470558.78 -24.997
357772.5 470723.47 -24.943
357675.22 470888.69 -24.894
357577.56 471054.28 -24.848
357479.91 471220.09 -24.803
357382.19 471386.03 -24.758
357284.75 471551.94 -24.712
357187.91 471717.81 -24.664
357091.44 471883.78 -24.613
356995.47 472049.81 -24.558
356899.53 472216.22 -24.499
356803.31 472382.94 -24.435
356706.56 472549.94 -24.364
356609.09 472716.84 -24.287
356510.94 472883.38 -24.2
356412.41 473049.47 -24.105
356313.53 473215.25 -24.003
356214.88 473380.69 -23.895
356116.56 473546.13 -23.783
356018.94 473711.63 -23.668
355921.84 473877.41 -23.554
355825.06 474043.5 -23.44
355728.66 474210.03 -23.327
355632.19 474376.59 -23.216
355535.53 474543.03 -23.104
355438.47 474709.25 -22.99
355340.88 474875.09 -22.876
355246.59 475034.41 -22.768
355189.84 475129.84 -22.704
355091.66 475295.16 -22.598
354993.63 475460.69 -22.5
354896.06 475626.41 -22.414
354799.19 475792.41 -22.342
354702.75 475958.88 -22.287
354606.41 476125.5 -22.253
354509.88 476292.41 -22.24
354413 476459.31 -22.252
354315.59 476625.91 -22.29
354217.53 476792.34 -22.358
354119.13 476958.22 -22.458
354020.34 477123.94 -22.588
353921.66 477289.41 -22.75
353823.03 477454.88 -22.944
353725.03 477620.53 -23.175
353627.53 477786.47 -23.443
353530.66 477953.06 -23.751
353434.19 478120.16 -24.097
353337.84 478287.72 -24.481
353241.31 478455.41 -24.897
353144.41 478622.78 -25.344
353046.78 478789.84 -25.817
352948.59 478956.63 -26.314
352849.97 479123 -26.83
352751.44 479289.03 -27.364
352653.28 479454.91 -27.912
352555.72 479620.56 -28.47
352458.72 479786.28 -29.031
352362.22 479952.5 -29.59
352265.88 480119.19 -30.14
352169.44 480286.09 -30.676
352072.63 480453.25 -31.193
351975.25 480620.22 -31.683
351877.25 480786.78 -32.143
351778.84 480952.69 -32.567
351680.31 481118.16 -32.953
351581.88 481283.22 -33.299
351483.5 481448.13 -33.604
351385.34 481613.25 -33.866
351287.38 481778.63 -34.084
351189.44 481943.94 -34.258
351091.53 482109.5 -34.387
350993.69 482275.06 -34.474
350896.16 482440.72 -34.521
350798.81 482606.16 -34.532
350701.56 482771.56 -34.51
350604.53 482937.09 -34.46
350507.5 483102.72 -34.388
350410.56 483268.34 -34.297
350313.63 483434.06 -34.195
350216.91 483599.91 -34.087
350120.09 483765.84 -33.978
350023.19 483931.81 -33.873
349911.16 484123.34 -33.764
349814.19 484289.41 -33.683

I try to do it like this.
First I load the data into a vector A, then:

L=numel(A);
Nfft=2^nextpow2(L);
amp=abs(fft(A,Nfft))/Nfft;
pha=angle(fft(A,Nfft));
ene=amp.^2;
enl=2.*log(amp);

But it doesn't seem to work properly, because i have the 513th values of each spectrum
for the amplitude it's 0.001935, for phase 0, for power 0.000004 and for log(energy) -12.495

 

[chiro]

I've noticed that you use ^ and / instead of .^ and ./ but you use the dot operator for the other commands. Is there a reason for this?

 

[whatsoever]

Yes there is a reason, ./ and .* are used when handling vectors and matrices and * and / are used when handling scalars

 

[chiro]

What about the vector A? How did you load it in the MATLAB environment? Did you use a routine to load it from a file or is completely generated within the MATLAB environment itself?

This might seem pedantic, but if its loaded externally maybe you should print off the vector just to make sure it has the right values.

 

[whatsoever]

The data is loaded from an external file, but I've already checked if it is correct.
Thanks anyway :)

 

[chiro]

Maybe you could just print out the values of L and Nfft in MATLAB just to verify you get the right values for your FFT.

 

[whatsoever]

I've checked the values L=523 and Nfft=1024

 

[chiro]

One final question: Do you have to normalize your amplitude (divide by Nfft) or does fft do it for you?

 

[whatsoever]

Yes i have normalized the results

 

[chiro]

Yes i have normalized the results

No, I meant by asking the question is "Do you have to normalize them yourself, or does the fft do this for you?"

The reason I ask is because in MATLAB it does do a 1/N calculation:

http://www.mathworks.com.au/help/techdoc/ref/fft.html

 

[whatsoever]

I have normalized them by myself, if I don't I get very large values.

 

[chiro]

Well the only I got left to ask is if you have another data set to be used as a reference set to check the answers?

At least if you have another reference set, you can check if the values calculated match was is output. At least if you get an error here, then you can use a different routine.

One other suggestion is to re-construct the signal to see what the output gives.

Finally if it's only a narrow range of components in your output vector, check for precision errors and make sure MATLAB is set to a high precision.

Other than that, you've got me!

Good luck!

 

[whatsoever]

Thanks for the help, I'll keep working on it