# Sinusoidal curve from discrete dataset

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Ashfaq Ahmed on 6 Mar 2023
Commented: William Rose on 17 May 2023 at 4:12
Hi!
I have a few discrete data-set and when I plot them it looks like this -
Can anyone please tell me how can I fit these discrete points into a sinusoidal curve like this?
The data is a small 23x4000 matrix and I added the .mat file to the question. Any feedback will be really helpful. Thank you!

William Rose on 6 Mar 2023
Edited: William Rose on 7 Mar 2023
[edit: I changed the comments in the code for t1 and t. I added a line to display the fitted values.]
[rows,cols]=size(Sinusoidal); % read data form file
t1=(1:rows)'; % t1=vector
t=repmat(t1,1,cols); % t=array
Sinusoidal=reshape(Sinusoidal,rows*cols,1); % convert array to vector
T=Sinusoidal(~isnan(Sinusoidal)); % remove NaNs
t=t(~isnan(Sinusoidal)); % remove corresponding times
% next: define the model equation
myfittype=fittype('a*sin(w*t+p)','dependent',{'T'},'independent',{'t'},'coefficients',{'a','w','p'});
x0=[30,.1,0]; % initial guess for [a,b,c]
myfit=fit(t,T,myfittype,'StartPoint',x0); % fit the data
plot(myfit,'-b',t,T,'r.'); % plot results
xlabel('Time'); ylabel('Temperature')
% Display best-fit parameters on console.
fprintf('y=a*sin(wt+p): a=%.4f, w=%.4f, p=%.4f\n',myfit.a,myfit.w,myfit.p)
y=a*sin(wt+p): a=22.4003, w=0.1006, p=-0.1809
Try it.
William Rose on 17 May 2023 at 4:12
@Ashfaq Ahmed, This is rather complicated to do properly, because the data in T.mat has values in datetime format, for the sample times. It also has the numeric values for time. Matlab is telling users to stop using numeric times, and start using datetime values. Therefore I am trying to adapt. The data in T.mat spans approximately 10 years, with uneven time intervals between samples (long data gaps every winter). Please contact me through Matab Central by clicking on my name above, then click on the envelope icon in the pop-up box. Please provide your email in the message, so we can discuss offline.

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