How to use harmonic fitting method

Hi,

Please, how can I use Harmonic fiting for the attached data to get a smooth fit.

[Torsten]

Where are the values of the variable you want to plot the data against (time or whatever) ?

[TTA]

x = 10:0.1:60

[Sam Chak]

@TTA, Like this?

y = load('darta1.txt');
x = linspace(10, 60, numel(y));
plot(x, y, 'linewidth', 1.5), grid on
xlabel('x'), ylabel('y')

[TTA]

yes but I want use harmonics to fit it to something like the attached figure

[Torsten]

Tell us precisely what you define as your approximating "harmonic".

Answer 1

[Sam Chak]

Hi @TTA,

I'm interpreting your 'Harmonic' model as the 'Sum of Sine' model. If this is not the case, then you will need to create a custom nonlinear model that suits the name "Harmonic" using the fittype() function.

y = load('darta1.txt');
x = linspace(10, 60, numel(y));
[f, gof] = fit(x', y, 'sin3')

f = 
     General model Sin3:
     f(x) =  
                    a1*sin(b1*x+c1) + a2*sin(b2*x+c2) + a3*sin(b3*x+c3)
     Coefficients (with 95% confidence bounds):
       a1 =        1564  (-8.752e+04, 9.065e+04)
       b1 =     0.04957  (-0.1147, 0.2138)
       c1 =      0.1819  (-4.047, 4.411)
       a2 =        1363  (-8.772e+04, 9.045e+04)
       b2 =     0.05511  (-0.1195, 0.2297)
       c2 =        3.18  (-1.365, 7.725)
       a3 =       2.975  (2.774, 3.176)
       b3 =      0.3159  (0.307, 0.3248)
       c3 =      -4.138  (-4.419, -3.857)

gof = struct with fields:
           sse: 465.0567
       rsquare: 0.9983
           dfe: 492
    adjrsquare: 0.9983
          rmse: 0.9722

plot(f, x, y), grid on, 
legend('data', 'Sum of Sine (type-3)', 'location', 'best')

[TTA]

Thank you @Sam Chak