How to do 'cos' curve fitting for data obtained.

Hello everyone,

I have been trying to do curve fit for the data given below.

I want to implement 'cosine square' curve fitting for the data obtained and later find the peak. I have already written a program for it and obtained the graph below as attached. But I am unsure if I am correct in implementing it, so that I can find a peak.

Can someone please check my programme if it is correctly implemented and latter how can I find the peak?

The program and also the data is attached.

I request to please help in setting the cosine square curve fitting and also how can I find peak from it please.

Thanking you in advance.

Kind regards

x_axis = [linspace(0, 360, 360)'];
y_axis = 
[3.7560368
    3.8085489
    3.7661638
    3.7799058
    3.8907118
    3.6859937
    3.8746176
    3.8137977
    3.8134153
    4.0203352
    4.1017566
    4.0970173
    3.9302003
    4.1788678
    4.2053556
    4.1945562
    4.2701845
    4.2767544
    4.4449506
    4.2852941
    4.3978033
    4.4853888
    4.6127644
    4.7098279
    4.8618488
    5.1263094
    5.3121061
    5.2374048
    5.4019165
    5.3228474
    5.7068501
    5.8063822
    5.6671882
    6.0611329
    6.3209352
    6.3571095
    6.3894024
    6.3625441
    6.7195029
    6.9633155
    7.1388698
    7.1086278
    7.3036475
    7.7009292
    7.5671926
    7.8018169
    7.8800983
    7.9435253
    8.2067919
    8.0853844
    8.4278364
    8.5053186
    8.7994070
    8.8510847
    8.8690329
    9.1009340
    9.0523500
    9.2792454
    9.1106558
    9.3377943
    9.3589869
    9.5377388
    9.5682468
    9.6855421
    9.9991894
    10.101757
    10.096369
    10.156980
    10.274252
    10.360273
    10.509270
    10.480047
    10.654547
    10.673642
    10.609531
    10.812882
    10.907791
    10.918486
    11.225864
    11.290207
    11.172333
    11.488586
    11.520347
    11.551353
    11.549279
    11.526500
    11.671359
    11.850876
    12.058664
    12.165114
    12.094005
    12.211543
    12.288712
    12.303370
    12.436886
    12.596936
    12.663608
    12.708924
    12.855083
    12.925530
    13.090031
    13.018736
    13.070112
    13.107990
    13.310437
    13.422553
    13.567563
    13.744937
    13.490406
    13.864213
    13.847771
    13.847562
    14.041366
    14.147572
    14.082581
    13.991263
    14.123412
    14.369276
    14.390491
    14.520578
    14.327042
    14.693224
    14.133552
    14.292513
    14.025004
    14.026464
    13.991936
    13.935472
    13.823612
    13.694707
    13.577332
    13.184267
    13.157513
    12.778562
    12.687349
    12.503510
    12.076763
    11.935090
    11.697372
    11.518528
    11.050751
    10.501066
    10.570576
    10.255017
    10.040149
    9.6180134
    9.4150209
    9.1862717
    9.1615105
    8.8085833
    8.4177094
    8.1676283
    7.9493303
    7.8774567
    7.4021716
    7.2626643
    7.0130467
    6.8367281
    6.5165462
    6.2733707
    6.0217953
    5.8303905
    5.7666621
    5.5948973
    5.3705506
    5.0788374
    4.8748956
    4.9039559
    4.7801609
    4.5220037
    4.4644861
    4.3326731
    4.1139574
    4.0280752
    4.0393724
    3.9195518
    3.8203096
    3.9346380
    3.9120667
    3.9352870
    3.7858152
    3.7302327
    3.8530660
    3.8764021
    4.0210533
    3.8053162
    3.7861629
    4.0157118
    3.8974786
    4.0198369
    3.8873518
    4.0392332
    4.1915207
    4.2629776
    4.1356020
    4.2647386
    4.4922714
    4.5622220
    4.4029360
    4.5087366
    4.6259847
    4.6793890
    5.0826612
    4.8744206
    5.1262283
    5.2914929
    5.4136310
    5.5176930
    5.6838617
    5.7043476
    6.1272130
    6.2987809
    6.3886957
    6.7363043
    6.4276047
    6.7431059
    6.8973627
    7.0461044
    7.4170375
    7.5335674
    7.6382785
    7.5001392
    7.8367167
    7.8627295
    8.1570034
    8.2677975
    8.3691025
    8.3157787
    8.6507921
    8.5380859
    8.7457590
    8.8766565
    8.9957819
    9.4086370
    9.2976923
    9.1666203
    9.5562086
    9.4445915
    9.5937271
    9.5391989
    9.7914810
    9.7707987
    10.014866
    9.8694038
    10.086926
    10.070402
    10.140689
    10.358998
    10.547773
    10.397189
    10.616878
    10.850748
    10.820518
    10.890109
    10.967093
    10.936852
    10.996153
    11.312604
    11.382068
    11.275920
    11.237150
    11.464695
    11.733998
    11.555235
    11.594063
    11.750486
    11.719097
    11.809939
    12.001703
    12.123749
    12.068143
    12.305802
    12.398463
    12.620493
    12.616426
    12.758910
    12.791411
    12.814006
    12.958403
    13.033417
    12.982018
    13.097528
    13.326486
    13.099764
    13.440501
    13.762190
    13.757254
    13.685774
    13.790647
    13.996119
    13.993882
    14.195066
    14.017554
    13.993523
    14.137665
    14.068213
    13.908880
    14.126356
    14.090123
    13.816242
    13.845986
    13.771297
    14.081943
    13.869555
    13.688763
    13.756604
    13.374838
    13.495052
    13.327528
    13.196979
    12.910977
    12.892890
    12.608303
    12.453722
    12.261135
    11.895277
    11.831989
    11.474671
    11.331120
    11.078547
    10.780775
    10.553984
    10.312628
    10.234334
    9.8746061
    9.6202841
    9.2517500
    8.9077330
    8.5553513
    8.2447739
    8.2016010
    8.0945034
    7.6051397
    7.3414907
    7.1926098
    6.7445426
    6.6355791
    6.5867977
    6.2250996
    6.1827264
    5.7160850
    5.7975760
    5.6851592
    5.3907700
    5.2925820
    5.1095896
    4.7592812
    4.7868695
    4.6418242
    4.3699365
    4.3055477
    4.3884525
    4.1613369
    4.0429530
    3.8451636
    4.0363250
    4.0363483
    3.7999976
    3.8972006
    3.9059372]

[Csaba]

I would say that your data can be described with two sinus function with different phase parameter.

[Alex Sha]

@Paramjit Yadav The original fitting function is not good for your data, try the function below:

Fitting result:

Sum Squared Error (SSE): 6.91129594176633
Root of Mean Square Error (RMSE): 0.1385570073388
Correlation Coef. (R): 0.999222888083962
R-Square: 0.998446380070854

Parameter	Best Estimate    
---------	-------------    
a1       	0.238948803230066
b1       	9.42672548601341 
c1       	0.795056999679539
a2       	1.20658677913231 
b2       	-14.2617939394349
c2       	-1.95421762967456
a3       	-4.79700609782976
b3       	-28.3377665740981
c3       	140.304593586862 
d        	9.03378373900727 

[Paramjit Yadav]

@Alex Sha

Dear Alex

Thank you so much for repyling and help. I would like to know how did you implement the code to get all the values. Sum, root......

Can you please give me the code which you implemented.

Thanking you,

Kind regards

Paramjit

Answer 1

[Mathieu NOE]

hello

you can do a cos/sin series approximation , using this simple code :

here I opted for 6 terms :

x_axis = [linspace(0, 360, 360)'];
y_axis = [3.7560368
3.8085489
3.7661638
3.7799058
3.8907118
3.6859937
3.8746176
3.8137977
3.8134153
4.0203352
4.1017566
4.0970173
3.9302003
4.1788678
4.2053556
4.1945562
4.2701845
4.2767544
4.4449506
4.2852941
4.3978033
4.4853888
4.6127644
4.7098279
4.8618488
5.1263094
5.3121061
5.2374048
5.4019165
5.3228474
5.7068501
5.8063822
5.6671882
6.0611329
6.3209352
6.3571095
6.3894024
6.3625441
6.7195029
6.9633155
7.1388698
7.1086278
7.3036475
7.7009292
7.5671926
7.8018169
7.8800983
7.9435253
8.2067919
8.0853844
8.4278364
8.5053186
8.7994070
8.8510847
8.8690329
9.1009340
9.0523500
9.2792454
9.1106558
9.3377943
9.3589869
9.5377388
9.5682468
9.6855421
9.9991894
10.101757
10.096369
10.156980
10.274252
10.360273
10.509270
10.480047
10.654547
10.673642
10.609531
10.812882
10.907791
10.918486
11.225864
11.290207
11.172333
11.488586
11.520347
11.551353
11.549279
11.526500
11.671359
11.850876
12.058664
12.165114
12.094005
12.211543
12.288712
12.303370
12.436886
12.596936
12.663608
12.708924
12.855083
12.925530
13.090031
13.018736
13.070112
13.107990
13.310437
13.422553
13.567563
13.744937
13.490406
13.864213
13.847771
13.847562
14.041366
14.147572
14.082581
13.991263
14.123412
14.369276
14.390491
14.520578
14.327042
14.693224
14.133552
14.292513
14.025004
14.026464
13.991936
13.935472
13.823612
13.694707
13.577332
13.184267
13.157513
12.778562
12.687349
12.503510
12.076763
11.935090
11.697372
11.518528
11.050751
10.501066
10.570576
10.255017
10.040149
9.6180134
9.4150209
9.1862717
9.1615105
8.8085833
8.4177094
8.1676283
7.9493303
7.8774567
7.4021716
7.2626643
7.0130467
6.8367281
6.5165462
6.2733707
6.0217953
5.8303905
5.7666621
5.5948973
5.3705506
5.0788374
4.8748956
4.9039559
4.7801609
4.5220037
4.4644861
4.3326731
4.1139574
4.0280752
4.0393724
3.9195518
3.8203096
3.9346380
3.9120667
3.9352870
3.7858152
3.7302327
3.8530660
3.8764021
4.0210533
3.8053162
3.7861629
4.0157118
3.8974786
4.0198369
3.8873518
4.0392332
4.1915207
4.2629776
4.1356020
4.2647386
4.4922714
4.5622220
4.4029360
4.5087366
4.6259847
4.6793890
5.0826612
4.8744206
5.1262283
5.2914929
5.4136310
5.5176930
5.6838617
5.7043476
6.1272130
6.2987809
6.3886957
6.7363043
6.4276047
6.7431059
6.8973627
7.0461044
7.4170375
7.5335674
7.6382785
7.5001392
7.8367167
7.8627295
8.1570034
8.2677975
8.3691025
8.3157787
8.6507921
8.5380859
8.7457590
8.8766565
8.9957819
9.4086370
9.2976923
9.1666203
9.5562086
9.4445915
9.5937271
9.5391989
9.7914810
9.7707987
10.014866
9.8694038
10.086926
10.070402
10.140689
10.358998
10.547773
10.397189
10.616878
10.850748
10.820518
10.890109
10.967093
10.936852
10.996153
11.312604
11.382068
11.275920
11.237150
11.464695
11.733998
11.555235
11.594063
11.750486
11.719097
11.809939
12.001703
12.123749
12.068143
12.305802
12.398463
12.620493
12.616426
12.758910
12.791411
12.814006
12.958403
13.033417
12.982018
13.097528
13.326486
13.099764
13.440501
13.762190
13.757254
13.685774
13.790647
13.996119
13.993882
14.195066
14.017554
13.993523
14.137665
14.068213
13.908880
14.126356
14.090123
13.816242
13.845986
13.771297
14.081943
13.869555
13.688763
13.756604
13.374838
13.495052
13.327528
13.196979
12.910977
12.892890
12.608303
12.453722
12.261135
11.895277
11.831989
11.474671
11.331120
11.078547
10.780775
10.553984
10.312628
10.234334
9.8746061
9.6202841
9.2517500
8.9077330
8.5553513
8.2447739
8.2016010
8.0945034
7.6051397
7.3414907
7.1926098
6.7445426
6.6355791
6.5867977
6.2250996
6.1827264
5.7160850
5.7975760
5.6851592
5.3907700
5.2925820
5.1095896
4.7592812
4.7868695
4.6418242
4.3699365
4.3055477
4.3884525
4.1613369
4.0429530
3.8451636
4.0363250
4.0363483
3.7999976
3.8972006
3.9059372];

%% harmonic series decomposition 
orders = 1:6; % define up to wich order you want to proceed

% model fit : X = sum(A*cos(orders(k)*theta) + B*sin(orders(k)*theta)) + C
C = mean(y_axis);

% loop over the A,B cos and sin components
theta = x_axis*pi/180;
yfit = 0;
n = numel(theta);

for k = 1:numel(orders)
    A = 2/n*trapz(y_axis.*cos(orders(k)*theta));
    B = 2/n*trapz(y_axis.*sin(orders(k)*theta));
    yfit = yfit + A*cos(orders(k)*theta) + B*sin(orders(k)*theta);
end
yfit = yfit + C; % add the constant term

% plot
figure(1),
plot(x_axis, y_axis, 'b',x_axis, yfit, 'r')
legend('data','series fit');

[Mathieu NOE]

hello again

problem solved ?

[Paramjit Yadav]

@Mathieu NOE

Dear Mathieu,

Thank you so much for repyling and help. The code is useful. But I want to implement something with cosine and phase in it and also get the different values of root and sum. The value of phase will be helpful for me to find the amount of shift or the peak shift from the real curve.

Can you please help me to impelement that.

Thanking you,

Kind regards

Paramjit

[Mathieu NOE]

hello again

this is the new code with cos and angle implementation (simple trogonometric conversion)

I am not sure what you mean with root and sum

x_axis = [linspace(0, 360, 360)'];
y_axis = [3.7560368
3.8085489
3.7661638
3.7799058
3.8907118
3.6859937
3.8746176
3.8137977
3.8134153
4.0203352
4.1017566
4.0970173
3.9302003
4.1788678
4.2053556
4.1945562
4.2701845
4.2767544
4.4449506
4.2852941
4.3978033
4.4853888
4.6127644
4.7098279
4.8618488
5.1263094
5.3121061
5.2374048
5.4019165
5.3228474
5.7068501
5.8063822
5.6671882
6.0611329
6.3209352
6.3571095
6.3894024
6.3625441
6.7195029
6.9633155
7.1388698
7.1086278
7.3036475
7.7009292
7.5671926
7.8018169
7.8800983
7.9435253
8.2067919
8.0853844
8.4278364
8.5053186
8.7994070
8.8510847
8.8690329
9.1009340
9.0523500
9.2792454
9.1106558
9.3377943
9.3589869
9.5377388
9.5682468
9.6855421
9.9991894
10.101757
10.096369
10.156980
10.274252
10.360273
10.509270
10.480047
10.654547
10.673642
10.609531
10.812882
10.907791
10.918486
11.225864
11.290207
11.172333
11.488586
11.520347
11.551353
11.549279
11.526500
11.671359
11.850876
12.058664
12.165114
12.094005
12.211543
12.288712
12.303370
12.436886
12.596936
12.663608
12.708924
12.855083
12.925530
13.090031
13.018736
13.070112
13.107990
13.310437
13.422553
13.567563
13.744937
13.490406
13.864213
13.847771
13.847562
14.041366
14.147572
14.082581
13.991263
14.123412
14.369276
14.390491
14.520578
14.327042
14.693224
14.133552
14.292513
14.025004
14.026464
13.991936
13.935472
13.823612
13.694707
13.577332
13.184267
13.157513
12.778562
12.687349
12.503510
12.076763
11.935090
11.697372
11.518528
11.050751
10.501066
10.570576
10.255017
10.040149
9.6180134
9.4150209
9.1862717
9.1615105
8.8085833
8.4177094
8.1676283
7.9493303
7.8774567
7.4021716
7.2626643
7.0130467
6.8367281
6.5165462
6.2733707
6.0217953
5.8303905
5.7666621
5.5948973
5.3705506
5.0788374
4.8748956
4.9039559
4.7801609
4.5220037
4.4644861
4.3326731
4.1139574
4.0280752
4.0393724
3.9195518
3.8203096
3.9346380
3.9120667
3.9352870
3.7858152
3.7302327
3.8530660
3.8764021
4.0210533
3.8053162
3.7861629
4.0157118
3.8974786
4.0198369
3.8873518
4.0392332
4.1915207
4.2629776
4.1356020
4.2647386
4.4922714
4.5622220
4.4029360
4.5087366
4.6259847
4.6793890
5.0826612
4.8744206
5.1262283
5.2914929
5.4136310
5.5176930
5.6838617
5.7043476
6.1272130
6.2987809
6.3886957
6.7363043
6.4276047
6.7431059
6.8973627
7.0461044
7.4170375
7.5335674
7.6382785
7.5001392
7.8367167
7.8627295
8.1570034
8.2677975
8.3691025
8.3157787
8.6507921
8.5380859
8.7457590
8.8766565
8.9957819
9.4086370
9.2976923
9.1666203
9.5562086
9.4445915
9.5937271
9.5391989
9.7914810
9.7707987
10.014866
9.8694038
10.086926
10.070402
10.140689
10.358998
10.547773
10.397189
10.616878
10.850748
10.820518
10.890109
10.967093
10.936852
10.996153
11.312604
11.382068
11.275920
11.237150
11.464695
11.733998
11.555235
11.594063
11.750486
11.719097
11.809939
12.001703
12.123749
12.068143
12.305802
12.398463
12.620493
12.616426
12.758910
12.791411
12.814006
12.958403
13.033417
12.982018
13.097528
13.326486
13.099764
13.440501
13.762190
13.757254
13.685774
13.790647
13.996119
13.993882
14.195066
14.017554
13.993523
14.137665
14.068213
13.908880
14.126356
14.090123
13.816242
13.845986
13.771297
14.081943
13.869555
13.688763
13.756604
13.374838
13.495052
13.327528
13.196979
12.910977
12.892890
12.608303
12.453722
12.261135
11.895277
11.831989
11.474671
11.331120
11.078547
10.780775
10.553984
10.312628
10.234334
9.8746061
9.6202841
9.2517500
8.9077330
8.5553513
8.2447739
8.2016010
8.0945034
7.6051397
7.3414907
7.1926098
6.7445426
6.6355791
6.5867977
6.2250996
6.1827264
5.7160850
5.7975760
5.6851592
5.3907700
5.2925820
5.1095896
4.7592812
4.7868695
4.6418242
4.3699365
4.3055477
4.3884525
4.1613369
4.0429530
3.8451636
4.0363250
4.0363483
3.7999976
3.8972006
3.9059372];
%% harmonic series decomposition 
orders = 1:6; % define up to wich order you want to proceed
% model fit : X = sum(A*cos(orders(k)*theta) + B*sin(orders(k)*theta)) + C
C = mean(y_axis);
% loop over the A,B cos and sin components
theta = x_axis*pi/180;
yfit = 0;
n = numel(theta);
for k = 1:numel(orders)
    A = 2/n*trapz(y_axis.*cos(orders(k)*theta));
    B = 2/n*trapz(y_axis.*sin(orders(k)*theta));
    % new version 
    amplitude(k) = sqrt(A^2+B^2);
    phase(k) = atan2(A,B)  - pi/2 ; % in radian
    yfit = yfit + amplitude(k)*cos(orders(k)*theta + phase(k));

end
yfit = yfit + C; % add the constant term
% plot
figure(1),
plot(x_axis, y_axis, 'b',x_axis, yfit, 'r')
legend('data','series fit');

[Paramjit Yadav]

Dear @Mathieu NOE

Thank you so much for prompt reply.

By root and sum i mean something like this.

Sum Squared Error (SSE): 6.91129594176633

Root of Mean Square Error (RMSE): 0.1385570073388

Correlation Coef. (R): 0.999222888083962

R-Square: 0.998446380070854

Parameter Best Estimate

--------- -------------

a1 0.238948803230066

b1 9.42672548601341

c1 0.795056999679539

a2 1.20658677913231

b2 -14.2617939394349

c2 -1.95421762967456

a3 -4.79700609782976

b3 -28.3377665740981

c3 140.304593586862

d 9.03378373900727

[Mathieu NOE]

ok, so this is the code with R-Square metric added

if my answer has helped you, do you mind accepting it ? tx

x_axis = [linspace(0, 360, 360)'];
y_axis = [3.7560368
3.8085489
3.7661638
3.7799058
3.8907118
3.6859937
3.8746176
3.8137977
3.8134153
4.0203352
4.1017566
4.0970173
3.9302003
4.1788678
4.2053556
4.1945562
4.2701845
4.2767544
4.4449506
4.2852941
4.3978033
4.4853888
4.6127644
4.7098279
4.8618488
5.1263094
5.3121061
5.2374048
5.4019165
5.3228474
5.7068501
5.8063822
5.6671882
6.0611329
6.3209352
6.3571095
6.3894024
6.3625441
6.7195029
6.9633155
7.1388698
7.1086278
7.3036475
7.7009292
7.5671926
7.8018169
7.8800983
7.9435253
8.2067919
8.0853844
8.4278364
8.5053186
8.7994070
8.8510847
8.8690329
9.1009340
9.0523500
9.2792454
9.1106558
9.3377943
9.3589869
9.5377388
9.5682468
9.6855421
9.9991894
10.101757
10.096369
10.156980
10.274252
10.360273
10.509270
10.480047
10.654547
10.673642
10.609531
10.812882
10.907791
10.918486
11.225864
11.290207
11.172333
11.488586
11.520347
11.551353
11.549279
11.526500
11.671359
11.850876
12.058664
12.165114
12.094005
12.211543
12.288712
12.303370
12.436886
12.596936
12.663608
12.708924
12.855083
12.925530
13.090031
13.018736
13.070112
13.107990
13.310437
13.422553
13.567563
13.744937
13.490406
13.864213
13.847771
13.847562
14.041366
14.147572
14.082581
13.991263
14.123412
14.369276
14.390491
14.520578
14.327042
14.693224
14.133552
14.292513
14.025004
14.026464
13.991936
13.935472
13.823612
13.694707
13.577332
13.184267
13.157513
12.778562
12.687349
12.503510
12.076763
11.935090
11.697372
11.518528
11.050751
10.501066
10.570576
10.255017
10.040149
9.6180134
9.4150209
9.1862717
9.1615105
8.8085833
8.4177094
8.1676283
7.9493303
7.8774567
7.4021716
7.2626643
7.0130467
6.8367281
6.5165462
6.2733707
6.0217953
5.8303905
5.7666621
5.5948973
5.3705506
5.0788374
4.8748956
4.9039559
4.7801609
4.5220037
4.4644861
4.3326731
4.1139574
4.0280752
4.0393724
3.9195518
3.8203096
3.9346380
3.9120667
3.9352870
3.7858152
3.7302327
3.8530660
3.8764021
4.0210533
3.8053162
3.7861629
4.0157118
3.8974786
4.0198369
3.8873518
4.0392332
4.1915207
4.2629776
4.1356020
4.2647386
4.4922714
4.5622220
4.4029360
4.5087366
4.6259847
4.6793890
5.0826612
4.8744206
5.1262283
5.2914929
5.4136310
5.5176930
5.6838617
5.7043476
6.1272130
6.2987809
6.3886957
6.7363043
6.4276047
6.7431059
6.8973627
7.0461044
7.4170375
7.5335674
7.6382785
7.5001392
7.8367167
7.8627295
8.1570034
8.2677975
8.3691025
8.3157787
8.6507921
8.5380859
8.7457590
8.8766565
8.9957819
9.4086370
9.2976923
9.1666203
9.5562086
9.4445915
9.5937271
9.5391989
9.7914810
9.7707987
10.014866
9.8694038
10.086926
10.070402
10.140689
10.358998
10.547773
10.397189
10.616878
10.850748
10.820518
10.890109
10.967093
10.936852
10.996153
11.312604
11.382068
11.275920
11.237150
11.464695
11.733998
11.555235
11.594063
11.750486
11.719097
11.809939
12.001703
12.123749
12.068143
12.305802
12.398463
12.620493
12.616426
12.758910
12.791411
12.814006
12.958403
13.033417
12.982018
13.097528
13.326486
13.099764
13.440501
13.762190
13.757254
13.685774
13.790647
13.996119
13.993882
14.195066
14.017554
13.993523
14.137665
14.068213
13.908880
14.126356
14.090123
13.816242
13.845986
13.771297
14.081943
13.869555
13.688763
13.756604
13.374838
13.495052
13.327528
13.196979
12.910977
12.892890
12.608303
12.453722
12.261135
11.895277
11.831989
11.474671
11.331120
11.078547
10.780775
10.553984
10.312628
10.234334
9.8746061
9.6202841
9.2517500
8.9077330
8.5553513
8.2447739
8.2016010
8.0945034
7.6051397
7.3414907
7.1926098
6.7445426
6.6355791
6.5867977
6.2250996
6.1827264
5.7160850
5.7975760
5.6851592
5.3907700
5.2925820
5.1095896
4.7592812
4.7868695
4.6418242
4.3699365
4.3055477
4.3884525
4.1613369
4.0429530
3.8451636
4.0363250
4.0363483
3.7999976
3.8972006
3.9059372];
%% harmonic series decomposition 
orders = 1:6; % define up to wich order you want to proceed
% model fit : X = sum(A*cos(orders(k)*theta) + B*sin(orders(k)*theta)) + C
C = mean(y_axis);
% loop over the A,B cos and sin components
theta = x_axis*pi/180;
yfit = 0;
n = numel(theta);
for k = 1:numel(orders)
    A = 2/n*trapz(y_axis.*cos(orders(k)*theta));
    B = 2/n*trapz(y_axis.*sin(orders(k)*theta));
    % new version 
    amplitude(k) = sqrt(A^2+B^2);
    phase(k) = atan2(A,B)  - pi/2 ; % in radian
    yfit = yfit + amplitude(k)*cos(orders(k)*theta + phase(k));

end
yfit = yfit + C; % add the constant term

R2 = my_R2_coeff(y_axis,yfit); % correlation coefficient


% plot
figure(1),
plot(x_axis, y_axis, 'b',x_axis, yfit, 'r')
title(['Cos Fit / R² = ' num2str(R2) ], 'FontSize', 15)

legend('data','series fit');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function R2 = my_R2_coeff(data,data_fit)
    % R2 correlation coefficient computation
    
    % The total sum of squares
    sum_of_squares = sum((data-mean(data)).^2);
    
    % The sum of squares of residuals, also called the residual sum of squares:
    sum_of_squares_of_residuals = sum((data-data_fit).^2);
    
    % definition of the coefficient of correlation (R squared) is
    R2 = 1 - sum_of_squares_of_residuals/sum_of_squares;
    
    
end

[Paramjit Yadav]

@Mathieu NOE

Thank you so much for help. This is helpful.

But I wanted something where I can use "fitoptions and fittype"and then gain coefficients and error bars. I have attached two programs for example.

I kindly request if you can help me something with something like this. I will be very very thankful to you.

Thanking you,

Kind regards

Paramjit

[Mathieu NOE]

hello again

unfortunately I don't have the Curve Fitting Tbx so I cannot do this