fit a sine wave to a set of data points

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C.G.
C.G. on 13 May 2022
Answered: Sam Chak on 13 May 2022
I have the dataset attached and the code below to try and fit a wave to the data. Im getting the following error which I can't get past:
yu = max(Qe_mean);
yl = min(Qe_mean);
yr = (yu-yl); % Range of ‘y’
yz = Qe_mean-yu+(yr/2);
zx = time(yz .* circshift(yz,[0 1]) <= 0); % Find zero-crossings
per = 100; % Estimate period
ym = mean(Qe_mean); % Estimate offset
fit = @(b,x) b(1).*(sin(2*pi*x./per + 2*pi/b(2))) + b(3); % Function to fit
fcn = @(b) sum((fit(b,x) - y).^2); % Least-Squares cost function
s = fminsearch(fcn, [yr; -1; ym]) % Minimise Least-Squares % Minimise Least-Squares
xp = linspace(min(x),max(x),per_in);
plot(x,y,'b', xp,fit(s,xp), 'r')
Unable to perform assignment because the size of the left side is 1-by-1 and the size of the
right side is 1-by-100.
Error in fminsearch (line 201)
fv(:,1) = funfcn(x,varargin{:});

Answers (1)

Sam Chak
Sam Chak on 13 May 2022
I've got this. What do you get?
General model Sin8:
f(x) =
a1*sin(b1*x+c1) + a2*sin(b2*x+c2) + a3*sin(b3*x+c3) +
a4*sin(b4*x+c4) + a5*sin(b5*x+c5) + a6*sin(b6*x+c6) +
a7*sin(b7*x+c7) + a8*sin(b8*x+c8)
Coefficients (with 95% confidence bounds):
a1 = 0.603 (-1.979, 3.185)
b1 = 0.03167 (-0.04371, 0.1071)
c1 = -0.08663 (-13.79, 13.61)
a2 = 0.0364 (-0.02684, 0.09964)
b2 = 0.3738 (0.2646, 0.483)
c2 = -0.5175 (-6.054, 5.019)
a3 = 0.05621 (-0.133, 0.2455)
b3 = 0.1469 (0.02797, 0.2658)
c3 = 4.653 (-1.893, 11.2)
a4 = 0.03751 (-0.0287, 0.1037)
b4 = 0.4343 (0.3727, 0.496)
c4 = 2.639 (-0.5437, 5.822)
a5 = 0.04328 (-0.004699, 0.09126)
b5 = 0.3131 (0.267, 0.3593)
c5 = 2.147 (-0.02915, 4.323)
a6 = 0.2174 (-4.843, 5.277)
b6 = 0.05691 (-0.397, 0.5108)
c6 = 0.4076 (-29.88, 30.69)
a7 = 0.02892 (0.01865, 0.03919)
b7 = 0.5653 (0.5512, 0.5793)
c7 = 0.3736 (-0.4235, 1.171)
a8 = 0.02562 (0.01612, 0.03511)
b8 = 1.103 (1.089, 1.116)
c8 = 1.03 (0.2538, 1.805)
Goodness of fit:
SSE: 0.08528
R-square: 0.9849
Adjusted R-square: 0.9804
RMSE: 0.0335

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