# Sinusoidal fit with fixed points

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curoi on 19 Jan 2015
Edited: Matt J on 22 Jan 2015
Is there a way to fit a sine curve to some data points but hold some of the fitted points at known locations? I'm trying to hold the extrema constant because they are known points but the rest of the fit can be anything.
Matt J on 19 Jan 2015
The location of the extrema determine everything about a sine curve: frequency, amplitude, and phase. There's nothing left to fit.
curoi on 22 Jan 2015
Edited: curoi on 22 Jan 2015
You're absolutely right. I didn't explain that I didn't mean a single sine term but multiple sine terms. Is there a way to hold the summation of the terms fixed at certain points?

Matt J on 22 Jan 2015
Edited: Matt J on 22 Jan 2015
If the unknown curve is given by y=F(x,p) where p is the vector of unknown parameters, and x and y are vectors of curve samples, then fmincon could be used to estimate p, with a sufficiently good initial guess p0,
p_fit = fmincon(@(p) norm(F(xdata,p) - ydata)^2, p0, [],[],[],[],[],[],...
@(p) F(xfixed,p)-yfixed, options)
where xfixed and yfixed are the x,y pairs that you want constrained. Then, of course, you get the curve with
y_fit=F(xdata,p_fit);