Fit a curve, find an equation and then take Fourier Transform of the curve?

Hello everyone, I am working on some data, where I have to fit a curve and find an equation of the curve. This I can do it by simply using "Basic fitting tools" and then I have to take the Fourier Transform of the equation of the curve. Here is my data and equation I found by using basic fitting and then I can find Fourier Transform of the equation by using fft function but it will give in this form "51.5730 + 0.0000i ......".

y=[4 3 3 6 9 10 8 6 4];
x=1:length(y);
plot(x, y, 'rx', 'MarkerSize', 10);

I have two question: 1 - How can I get the equation for the given data without using basic fitting tools? 2 - I have to find the Fourier Transform of the equation and the answer should be in form of "A1*sin(wx)+A2*sin(2wx)+A3*sin(3wx)+....." where w=2*pi()/length(y)

Thanks in advance for helping

Answer 1

[Christiaan]

Dear Khuram,

What I think you need to do is not find the fourier transform of your function, but the fourier series of that function. (since you need to find a function of x) How this can be done is described in the documentation of Mathworks at this website.

Good luck! Christiaan

[Khuram]

thanks alot