How to perform fft

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Efstathios Kontolatis
Efstathios Kontolatis on 23 Feb 2017
Answered: Rik on 23 Feb 2017
I have 1000 samples from an experiment with frequency Fs=67890 Hz. How can I perform fft on them? I followed the guide here https://uk.mathworks.com/help/matlab/ref/fft.html but it seems that the dominant frequency is zero which has no physical meaning.
These are my data
x =
0.3551
0.2308
0.3209
0.4527
0.4606
0.4511
0.4925
0.4769
0.5424
0.4698
0.4246
0.4502
0.5823
0.5451
0.4235
0.4062
0.3832
0.2749
0.1591
0.1889
0.4155
0.3840
0.3582
0.1852
0.2677
0.2454
0.2458
0.2100
0.1469
0.1186
0
0.4154
0.4807
0.4320
0.4072
0.3352
0.3357
0.2770
0.2801
0.3578
0.2703
0.3626
0.0998
0.3656
0.2590
0.4388
0.4144
0.2631
0
0.1076
0
0.4535
0.4626
0.4159
0.3686
0.4763
0.2582
0.2961
0.3691
0.3860
0.3875
0.4018
0.4292
0.3921
0.3128
0.4884
0.3153
0.2672
0.3448
0.3787
0.4799
0.3870
0.3534
0.3968
0.3006
0.3119
0.3585
0.1352
0.4154
0.3323
0.3733
0.3232
0.4116
0.3276
0.4852
0.3715
0.3991
0.3766
0.4866
0.3483
0.2736
0.3153
0.4049
0.3774
0.3071
0.3831
0.3992
0.3661
0.3337
0.1616
0.3305
0.4556
0.5053
0.4209
0.2868
0.2666
0.3057
0.4016
0.2579
0.4286
0.1672
0.4614
0.3814
0.4272
0.3374
0.4215
0.4788
0.3943
0.4097
0.3937
0.4230
0.4981
0.4821
0.1748
0.4015
0.5066
0.4959
0.4267
0.4692
0.3354
0.2919
0.5676
0.4875
0.4957
0.4122
0.5627
0.4573
0.3724
0.4320
0.4127
0.3655
0.3132
0.1982
0.2905
0.3757
0.5282
0.4584
0.4669
0.4059
0.3229
0.4696
0.3960
0.5024
0.4505
0.4084
0.4720
0.4251
0.3683
0.3791
0.3650
0.2426
0.3169
0.4405
0.4129
0.4839
0.3578
0.3550
0.4090
0.4063
0.4497
0.5195
0.4645
0.4514
0.4375
0.3405
0.5263
0.4195
0.3746
0.2887
0.4121
0.3987
0.4428
0.4065
0.3340
0.3511
0.3328
0.3698
0.4988
0.3478
0.2817
0.2795
0.4926
0.3976
0.3728
0.4816
0.4690
0.4328
0.6150
0.1455
0.3981
0.3184
0.4321
0.3678
0.3407
0.2930
0.3325
0.5747
0.5205
0.4418
0.4604
0.3597
0.3404
0.3153
0.5779
0.3666
0.3215
0.2842
0.2314
0.2940
0.3745
0.3215
0.2711
0.3004
0.3946
0.3942
0.3256
0.2587
0.3177
0.2474
0.2057
0.4025
0.4435
0.4262
0.3123
0.3033
0.3595
0.3224
0.5162
0.5210
0.5185
0.5082
0.5174
0.4634
0.4224
0.5525
0.4637
0.5132
0.5806
0.3519
0.5952
0.5103
0.4021
0.3890
0.3671
0.5863
0.3946
0.3198
0.1014
0.4934
0.4089
0.5890
0.4601
0.5628
0.5392
0.4553
0.4755
0.5468
0.4478
0.4900
0.3323
0.2200
0.4340
0.4119
0.4075
0.3577
0.5101
0.3585
0.3939
0.4366
0.3738
0.3934
0.4416
0.4464
0.3510
0.3791
0.4289
0.3966
0.3113
0.2998
0.4251
0.4033
0.3393
0.3843
0.4246
0.4224
0.4072
0.2900
0.4400
0.5314
0.4580
0.4382
0.4118
0.4298
0.5275
0.4492
0.4100
0.4098
0.4530
0.4531
0.4177
0.5175
0.2001
0.5330
0.4534
0.4613
0.0637
0.4619
0.5318
0.4129
0.3292
0.3293
0.4428
0.3560
0.4558
0.3736
0.2481
0.3881
0.3586
0.3284
0.0465
0.3070
0.4227
0.3891
0.3911
0.5650
0.3529
0.3481
0.3482
0.3682
0.5319
0.5387
0.1824
0.3062
0.4315
0.4625
0.3685
0.5253
0.4801
0.5584
0.4634
0.5326
0.4494
0.4534
0.4064
0.3226
0.1444
0.4603
0.4277
0
0.3656
0.4511
0.5926
0.4544
0.4301
0.3542
0.3607
0.3684
0.4694
0.5180
0.3940
0.4657
0.3901
0.4060
0.3740
0.3351
0.3571
0.3845
0.3225
0.4296
0.3675
0.4469
0.3926
0.3571
0.3877
0.2835
0.4564
0.4695
0.3038
0.4322
0.3454
0.4157
0.4131
0.3656
0.3244
0.3835
0.3835
0.3669
0.3769
0.3392
0.4072
0.4156
0.4026
0.4092
0.3624
0.4615
0.3921
0.4848
0.4077
0.2904
0.3404
0.3485
0.4472
0.4097
0.3488
0.3555
0.2958
0.1905
0.2594
0.5082
0.3526
0.5096
0.2486
0.3777
0.3662
0.4036
0.4170
0.4132
0.4760
0.4813
0.2767
0.4714
0.3762
0.3883
0.2067
0.1974
0.3166
0.3852
0.2576
0.3949
0.2443
0.3779
0.4300
0.3881
0.3786
0.3516
0.4147
0.3850
0.4277
0.4620
0.4737
0.4113
0.3448
0.3532
0.3431
0.2336
0.4660
0.4304
0.4478
0.2664
0.3472
0.3404
0.3530
0.5004
0.4685
0.4902
0.5056
0.4876
0.3388
0.3673
0.4873
0.3627
0.3553
0.3385
0.3725
0.5111
0.4345
0.3356
0.3316
0.3864
0.3736
0.3033
0.4409
0.4224
0.3873
0.3507
0.3317
0.3222
0.2853
0.3617
0.4143
0.4293
0.3870
0.3259
0.4120
0.3762
0.3981
0.4022
0.3711
0.3616
0.4801
0.3860
0.2593
0.5820
0.4110
0.4032
0.4109
0.3933
0.4776
0.2430
0.4151
0.4863
0.3633
0.1881
0.1723
0.4596
0.3971
0.3804
0.4301
0.2390
0.4319
0.3753
0.4073
0.4224
0.4255
0.4830
0.3504
0.3461
0.1993
0.4117
0.4678
0.4710
0.3577
0.3979
0.3993
0.3446
0.3214
0.3113
0.3695
0.3847
0.4664
0.4420
0.3579
0.5084
0.4741
0.4416
0.4036
0.3741
0.4747
0.5657
0.4787
0.4972
0.3841
0.2781
0.4447
0.5256
0.4557
0.4701
0.4399
0.3622
0.3493
0.3782
0.3784
0.6737
0.5224
0.4507
0.2935
0.4661
0.3368
0.3713
0.4094
0.3704
0.4510
0.3874
0.4808
0.3836
0.4163
0.2954
0.4038
0.3723
0.3454
0.3572
0.2956
0.3123
0.3045
0.3775
0.3586
0.3899
0.3283
0.2579
0.3975
0.3386
0.3333
0.3667
0.2439
0.3291
0.4948
0.4187
0.4469
0.3125
0.2881
0.1765
0.3667
0.4266
0.4227
0.4985
0.3694
0.3063
0.3647
0.3031
0.4227
0.4508
0.3426
0.2608
0.3380
0.4410
0.2822
0.3007
0.2079
0.3175
0.2548
0.2257
0.2664
0.2629
0.3153
0.2829
0.1878
0.2932
0.4240
0.3506
0.3450
0.3436
0.3147
0.4307
0.3297
0.3263
0.2626
0.3670
0.3903
0.3504
0.3635
0.3506
0.3645
0.3349
0.3742
0.4376
0.3087
0.1669
0.5031
0.4398
0.3169
0.1251
0.3737
0.4122
0.3529
0.3419
0.3728
0.3230
0.3516
0.3272
0.4056
0.4307
0.4187
0.3042
0.3735
0.3499
0.4240
0.1846
0.2853
0.2608
0.3536
0.3915
0.4461
0.4830
0.4267
0.2480
0.4508
0.1829
0.2214
0.3592
0.4563
0.2695
0.3125
0.2981
0.4959
0.3519
0.1361
0.3236
0.3682
0.3274
0.4352
0.3589
0.3794
0.3441
0.4345
0.3739
0.3811
0.3532
0.3125
0.4182
0.2854
0.3541
0.3988
0.4035
0.3540
0.3104
0.4531
0.5163
0.5809
0.3362
0.4588
0.4724
0.4871
0.4134
0.4033
0.3325
0.4309
0.3734
0.3137
0.3562
0.4370
0.2704
0.3935
0.3315
0.3020
0.3531
0.2427
0.3931
0.3654
0.3365
0.5205
0.3245
0.6086
0.4521
0.3837
0.4901
0.3527
0.4278
0.2909
0.3649
0.3479
0.2947
0.5558
0.4566
0.5902
0.4304
0.5311
0.5395
0.3745
0.5311
0.3001
0.4030
0.4117
0.3925
0.4652
0.3820
0.2739
0.4634
0.3541
0.3096
0.3282
0.3180
0.2612
0.2147
0.4373
0.4462
0.4324
0.4857
0.2976
0.3247
0.3276
0.3106
0.5885
0.5510
0.3492
0.3284
0.4325
0.4530
0.5664
0.5522
0.4787
0.4568
0.4210
0.5093
0.4775
0.4069
0.4151
0.4295
0.4312
0.3926
0.3863
0.3583
0.4121
0.3848
0.3773
0.3826
0.3374
0.3023
0.3368
0.4261
0.2167
0.4879
0.3032
0.2540
0.5302
0.4484
0.4872
0.3173
0.3800
0.4337
0.3698
0.3272
0.2498
0.3854
0.4042
0.4299
0.4018
0.3248
0.3756
0.3824
0.4029
0.4295
0.3573
0.3036
0.0557
0.4097
0.5186
0.4060
0.3733
0.2700
0.4013
0.2437
0.4369
0.3374
0.3853
0.4096
0.3145
0.3664
0.4738
0.2346
0.3548
0.2804
0.4698
0.4039
0.4628
0.4387
0.3089
0.3981
0.4727
0.4335
0.3591
0.4623
0.3922
0.4100
0.3585
0.4101
0.3834
0.2742
0.2886
0.4118
0.4812
0.4434
0.4607
0.3134
0.0859
0.1066
0.3441
0.2788
0.3310
0.4330
0.3551
0.4324
0.4427
0.3585
0.4497
0.1920
0.3622
0.4184
0.4762
0.4427
0.4545
0.4054
0.4440
0.3977
0.5034
0.5101
0.3951
0.5061
0.4242
0.4591
0.5080
0.4194
0.6229
0.3667
0.4874
0.4718
0.4996
0.2885
0.4989
0.5071
0.4529
0.5001
0.4165
0.4620
0.4430
0.3566
0.3709
0.4315
0.4694
0.3501
0.3343
0.4227
0.3484
0.3737
0.1854
0.4691
0.4328
0.4059
0.4462
0.4397
0.3578
0.3274
0.4586
0.4864
0.5225
0.3509
0.4212
0.4003
0.4854
0.1942
0.4785
0.4362
0.4213
0.4979
0.4989
0.3758
0.4904
0.6655
0.4860
0.4498
0.4712
0.3502
0.3666
0.3871
0.5061
0.3993
0.2872
0.3147
0.3531
0.4126
0.4546
0.4136
0.4674
0.4634
0.4877
0.4136
0.3401
0.4442
0.3997
0.3753
0.4675
0.3769
0.3556
0.3799
0.5048
0.3805
0.4656
0.4621
0.3986
0.2977
0.3280
0.4630
0.4375
0.3109
0.3265
0.4582
0.4432
0.3801
0.4558
0.4408
0.4279
0.3974
0.3856
0.4107
0.4463
0.4646
0.3674
0.4938
0.3389
0.4625
0.3187
0.3233
0.4389
0.3224
0.3140
0.4371
0.3664
0.4664
0.4350
0.4211
0.3415
and here is the code I have used for the fft
fs=67890;
T = 1/fs; % Sampling period
L = 1000; % Length of signal
t = (0:L-1)*T; % Time vector
y = fft(x);
P2 = abs(y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);
f = fs*(0:(L/2))/L;
subplot(2,1,1), plot(t,x),title('original data'),ylabel('x'),xlabel('t')
subplot(2,1,2), plot(f,P1),title('fft'),ylabel('magnitude'),xlabel('frequency')
This gives me this image
Hope it's clear
  5 Comments
Show 3 older comments
Adam
Adam on 23 Feb 2017
So just do what Rik Wisselink suggests to zero-centre your data or simply remove the 0-frequency component from the final result and plot it without if you just want to look at the frequency spectrum.
Efstathios Kontolatis
Efstathios Kontolatis on 23 Feb 2017
Yes indeed that worked. Thank you very much. I would have accepted the answer if I knew how to do it.

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Accepted Answer

Rik
Rik on 23 Feb 2017
[moved from comments]
To remove the 0Hz-component from the analysis, use y=fft(x-mean(x));

More Answers (1)

Pooja Patel
Pooja Patel on 23 Feb 2017
  • amp1 = abs(fft(x1)); %Retain Magnitude
  • % amp11 = amp1(1:Nsamps1/2); %Discard Half of Points
  • % f11 = Fs*(0:Nsamps1/2-1)/Nsamps1; %Prepare freq data for plot
  • f11 = 0:(fs1/Nsamps1):1000; %Prepare freq data for plot
  • amp11 = amp1(1:length(f11)); % keep data till 1kHz
  • plot(f11,amp11);

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