Fourier series expansion from data points

Hi all,

I was trying to find Fourer approximation for any function data set. I managed to write algorythm that gives me exact shape that i wanted, but for some reason when i exceed ~320 itarations graph starts to scale up. I spent too much time looking through code and maybe anyone else had simmilar problem.

Here are functions I used to find Foureir coefficients and final function:

Thank you for any help!

My code:

%Cleaning comand window
close all
clear 
clc 

%Number of iterations
it = 500;

%Data points input
%loop just to create dropdown
for data_input = 1:1
t = [0 
0.017952
0.035904
0.053856
0.071808
0.08976
0.107712
0.125664
0.143616
0.161568
0.17952
0.197472
0.215423
0.233375
0.251327
0.269279
0.287231
0.305183
0.323135
0.341087
0.359039
0.376991
0.394943
0.412895
0.430847
0.448799
0.466751
0.484703
0.502655
0.520607
0.538559
0.556511
0.574463
0.592415
0.610367
0.628319
0.64627
0.664222
0.682174
0.700126
0.718078
0.73603
0.753982
0.771934
0.789886
0.807838
0.82579
0.843742
0.861694
0.879646
0.897598
0.91555
0.933502
0.951454
0.969406
0.987358
1.00531
1.023262
1.041214
1.059166
1.077117
1.095069
1.113021
1.130973
1.148925
1.166877
1.184829
1.202781
1.220733
1.238685
1.256637
1.274589
1.292541
1.310493
1.328445
1.346397
1.364349
1.382301
1.400253
1.418205
1.436157
1.454109
1.472061
1.490013
1.507964
1.525916
1.543868
1.56182
1.579772
1.597724
1.615676
1.633628
1.65158
1.669532
1.687484
1.705436
1.723388
1.74134
1.759292
1.777244
1.795196
1.813148
1.8311
1.849052
1.867004
1.884956
1.902908
1.92086
1.938811
1.956763
1.974715
1.992667
2.010619
2.028571
2.046523
2.064475
2.082427
2.100379
2.118331
2.136283
2.154235
2.172187
2.190139
2.208091
2.226043
2.243995
2.261947
2.279899
2.297851
2.315803
2.333755
2.351706
2.369658
2.38761
2.405562
2.423514
2.441466
2.459418
2.47737
2.495322
2.513274
2.531226
2.549178
2.56713
2.585082
2.603034
2.620986
2.638938
2.65689
2.674842
2.692794
2.710746
2.728698
2.74665
2.764602
2.782553
2.800505
2.818457
2.836409
2.854361
2.872313
2.890265
2.908217
2.926169
2.944121
2.962073
2.980025
2.997977
3.015929
3.033881
3.051833
3.069785
3.087737
3.105689
3.123641
3.141593
3.159545
3.177497
3.195449
3.2134
3.231352
3.249304
3.267256
3.285208
3.30316
3.321112
3.339064
3.357016
3.374968
3.39292
3.410872
3.428824
3.446776
3.464728
3.48268
3.500632
3.518584
3.536536
3.554488
3.57244
3.590392
3.608344
3.626296
3.644247
3.662199
3.680151
3.698103
3.716055
3.734007
3.751959
3.769911
3.787863
3.805815
3.823767
3.841719
3.859671
3.877623
3.895575
3.913527
3.931479
3.949431
3.967383
3.985335
4.003287
4.021239
4.039191
4.057143
4.075094
4.093046
4.110998
4.12895
4.146902
4.164854
4.182806
4.200758
4.21871
4.236662
4.254614
4.272566
4.290518
4.30847
4.326422
4.344374
4.362326
4.380278
4.39823
4.416182
4.434134
4.452086
4.470038
4.48799
4.505941
4.523893
4.541845
4.559797
4.577749
4.595701
4.613653
4.631605
4.649557
4.667509
4.685461
4.703413
4.721365
4.739317
4.757269
4.775221
4.793173
4.811125
4.829077
4.847029
4.864981
4.882933
4.900885
4.918836
4.936788
4.95474
4.972692
4.990644
5.008596
5.026548
5.0445
5.062452
5.080404
5.098356
5.116308
5.13426
5.152212
5.170164
5.188116
5.206068
5.22402
5.241972
5.259924
5.277876
5.295828
5.31378
5.331732
5.349683
5.367635
5.385587
5.403539
5.421491
5.439443
5.457395
5.475347
5.493299
5.511251
5.529203
5.547155
5.565107
5.583059
5.601011
5.618963
5.636915
5.654867
5.672819
5.690771
5.708723
5.726675
5.744627
5.762579
5.78053
5.798482
5.816434
5.834386
5.852338
5.87029
5.888242
5.906194
5.924146
5.942098
5.96005
5.978002
5.995954
6.013906
6.031858
6.04981
6.067762
6.085714
6.103666
6.121618
6.13957
6.157522
6.175474
6.193426
6.211377
6.229329
6.247281
6.265233
6.283185];

f = [0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.345656
1.345656
1.46359
1.46359
1.46359
1.46359
1.46359
1.46359
1.46359
1.46359
1.46359
1.46359
1.46359
1.853533
1.853533
1.853533
1.908695
1.908695
1.908695
1.908695
1.908695
1.859239
1.859239
1.731795
1.731795
1.731795
1.731795
1.611959
1.611959
1.611959
1.611959
1.611959
0.938595
0.938595
0.234796
0.234796
0.234796
0.234796
0.234796
0.234796
0.234796
0.234796
0.234796
0.234796
0.234796
0.234796
0.234796
0.234796
0.234796
0.234796
0.234796
0.234796
0.234796
1.739403
1.739403
1.739403
1.739403
1.739403
1.739403
1.904891
1.904891
1.904891
1.904891
1.904891
1.904891
1.904891
1.904891
1.904891
1.904891
1.904891
1.904891
1.904891
1.904891
1.904891
1.904891
1.904891
1.581524
1.581524
1.581524
1.581524
1.581524
1.581524
1.581524
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.969029
0.390773
0.390773
0.390773
0.858758
1.022642
1.117587
1.19447
1.259128
1.315828
1.36746
1.414924
1.45791
1.496073
1.530751
1.565343
1.594598
1.608704
1.614128
1.613152
1.606161
1.585375
1.55787
1.52766
1.493909
1.452975
1.401511
1.344671
1.285349
1.220261
1.146139
1.059762
1.059762
1.059762
1.059762
1.059762
1.970569
1.970569
1.970569
1.970569
1.970569
1.970569
1.970569
2.228344
2.228344
2.228344
2.228344
2.228344
2.195105
2.098704
2.002302
1.905901
1.809499
1.713098
1.616696
1.520295
1.423893
1.327491
1.23109
1.134688
1.038287
0.941885
0.845484
0.749082
0.652681
0.556279
0.459878
0.363476
0.267075
0.203542
0.203542
0.203542
0.203542
0.203542
0.203542
0.203542
0.203542
0.203542
0.203542
0.203542
0.203542
0.203542
0.737289
0.737289
0.737289
0.737289
0.737289
0.737289
0.737289
0.737289
0.737289
0.737289
0.737289
0.737289
0.737289
0.737289
0.737289
0.737289
0.737289
0.737289
0.737289
0.648332
0.648332
0.648332
0.860617
0.860617
0.860617
0.860617
0.860617
1.126093
1.126093
1.126093
1.126093
1.126093
1.126093
1.126093
1.126093
1.126093
1.126093
1.126093
1.126093
1.126093
1.126093
1.126093
1.126093
1.126093
1.126093
1.126093
1.126093
1.126093
1.126093
1.126093
1.126093
0.604427
0.604427
0.604427
0.604427
0.604427
0.604427
0.604427
0.604427
0.604427
0.10148
0.10148
0.10148
0.10148
0.10148
0.10148
0.116437
0.138592
0.154547
0.167611
0.174579
0.178716
0.18133
0.182603
0.183212
0.183552
0.183756
0.183878
0.183948
0.183981
0.263889
0.327583
0.354472
0.625727
0.674006
0.700521
0.719297
0.731877
0.740955
0.748438
0.760127
0.782385
0.799697
0.780789
0.76188
0.750682
0.745784
0.739718
0.730804
0.715644
0.689119
0.639306
0.237436
0.132665
0.132665
0.132665
0
0
0
0
0
0
0
0
0
0
0
0
0
0];
end

%Ploting graphs 
f1 = figure;
title('Skyline graph from datapoints')
hold on 
plot(t,f,"Color",[0,0,0])
scatter(t,f,'red')
hold off

%Period and array size
T = 2*pi;
m = size(t);
m = m(1);
m1 = m;

%Fourier 0 coefficient 

a0 = (2/m)*sum(f,"all");

%Finding array for sin and cosine Fourier coefficiants for all iterations

    for i = 1:it
    
        san = 0;
        sbn = 0;
        j=0;
        
        for j = 1:m
            
                san = san + (f(j)*cos((2*pi/T)*i*t(j)));
                sbn = sbn + (f(j)*sin((2*pi/T)*i*t(j)));
                
                an(i) = (2/m)*san;
                bn(i) = (2/m)*sbn; 
                
        end
    end
    
%Final an and bn arrays 
    fan = an;
    fbn = bn;

%Finding function array values
    for ifn = 1:m
    sfn = 0; 
        for jfn = 1:it
           
            sfn = sfn + (fan(jfn)*cos(jfn*t(ifn))+fbn(jfn)*sin(jfn*t(ifn)));
            fn(ifn) = (a0/2) + sfn;
            
        end
        
    end
   
fnn = fn;

%Data for plotting graphs
t = t(1:m1);
f = f(1:m1);
fnn = fnn(1:m1);
fn = (1:m1);

f2 = figure;
title('Best fourier approximation over graph from data points')
hold on 
plot(t,fnn)
plot(t,f)
hold off

%Finidning quality of function
vi = fnn - f;
vi2 = vi.^2;
vi = sum(vi2,'all');

RMS = sqrt((vi)/m1)

RMS = 51.0386