I want to fit a sine curce to my data for a given period value. How should I do it?
MATLAB: Sine curve for a given period value.
fitperiodsine curve
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This works:
data = [1 4.2101; 2 -33.0595; 3 -5.6488; 4 76.2462];x = data(:,1);y = data(:,2);yu = max(y);yl = min(y);yr = (yu-yl); % Range of ‘y’
yz = y-yu+(yr/2);zx = x(yz(:) .* circshift(yz(:),[1 0]) <= 0); % Find zero-crossings
per = 2*mean(diff(zx)); % Estimate period
ym = mean(y); % Estimate offset
fit = @(b,x) b(1).*(sin(2*pi*x./b(2) + 2*pi/b(3))) + b(4); % Function to fit
fcn = @(b) sum((fit(b,x) - y).^2); % Least-Squares cost function
s = fminsearch(fcn, [yr; per; -1; ym]) % Minimise Least-Squares
xp = linspace(min(x),max(x));figure(1)plot(x,y,'b', xp,fit(s,xp), 'r')grid
This produces a reasonable approximation, however the signal appears to be changing its frequency toward the end:
D = load('Ampf.mat');t = D.Ampf(:,1);s = D.Ampf(:,2);s = detrend(s,7);yu = max(s);yl = min(s);yr = (yu-yl); % Range of ‘y’
yz = s-yu+(yr/2);zt = t(yz(:) .* circshift(yz(:),[1 0]) <= 0); % Find zero-crossings
per = 2*mean(diff(zt)); % Estimate period
ym = mean(s); % Estimate offset
fit = @(b,x) b(1) .* exp(b(2).*x) .* (sin(2*pi*x./b(3) + 2*pi/b(4))) + b(5); % Objective Function to fit
fcn = @(b) norm(fit(b,t) - s); % Least-Squares cost function
B = fminsearch(fcn, [yr; -1; per; -1; ym]) % Minimise Least-Squares
xp = linspace(min(t),max(t));yp = fit(B,xp);figureplot(t, s, '-p')hold onplot(xp, yp, '-r')hold offgridIt may be necessary to change ‘fit’ to something more closely approximating the process that produced your data. Retain the detrending step in the code.
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