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Asked by S on 24 Mar 2013

How can I write code for smooth cosine fit for given data and find residual ?

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Answer by Image Analyst on 25 Mar 2013

Any signal is composed of lots of cosines - that's basically what the Fourier transform (spectrum) is. It's the strength (weight) of all the cosines that can go into building up your signal. Maybe just take the Fourier Transform and look for the highest frequency to determine the frequency of cosine that is contributing most to your signal. Once you know the frequency, just construct a signal and subtract it from your original signal, etc.

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Image Analyst on 26 Mar 2013

I guess I'd start by making X and Y have the same number of elements. Why don't they?

S on 29 Mar 2013

I have X and Y data and want to smooth, cosine fit and then find the residual, in Y there is some zero values also?

I have this data as X data column

[624.0397 743.4188 641.3096 764.2928 698.1912 832.8933 799.6397 767.3729 735.1792 703.093 671.0012 638.9143 605.9839 668.0182 0 0 0 0 0 0] Y column

[8.071650105 8.144216751 8.177926597 8.171846343 8.073710465 7.999249364 8.00676841 8.064808175 8.061246346 8.064100517 8.041524691 8.045426565 8.068412239 8.225694432 0 0 0 0 0 0] and want to smooth, cosine fit and want to compute residual for this I have tried

x=[]; y=[]; for j=1:519 x=AC(:,j+1); y=AC(:,j); xx=find(y); xxx=max(xx); y1=smooth(x,y(1:xxx),'moving',5); fitted_curve=cos(x); end errors are ??? Error using ==> smooth at 131 X and Y must be the same length.

So how can I fit in cosine and compute residual of fit.

## 2 Comments

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/68441#comment_138775

Please post, what you have done so far and ask a specific question.

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/68441#comment_140635

I have this data as X data column

Y column

As the same way I am having data set for third column having x data set and again fourth column I am having y data set as so on upto 520, and also all having same number of element mean column having same number of element and some zero values also.

and want to smooth, cosine fit and want to compute residual for this I have tried

errors are ??? Error using ==> smooth at 131 X and Y must be the same length.

So how can I fit in cosine and compute residual of fit.