I have some data (18 points) which are plotted on the attached image, f(x), the red line.

I donotknow if this line can be described by a combination of known functions, but I am trying to find out.

It looks somewhat similar to sin(x), the blue line, and tan(x), the green line.

At this point I am trying random combinations of functions to see if I can find a function that accurately describes f(x):

1) f(x) = M*x + B + C*sin(x) + D*cos(x)

2) f(x) = M*x + B + sin(C*x) +cos(D*x)

3) f(x) = M*x + B + C*sin(x)*cos(x)

4) f(x) = M*x + B + C*sin^{2}(x)*cos(x)

5) f(x) = M*x + B + C*sin(x)*cos^{2}(x)

etc., etc.

where M, B, C, and D are real constants.

I am pretty much just making random guesses hoping to get lucky.

However, since the function looks so close to a portion of a sine curve, I am wondering if a Fourier Transform might reveal something. Assuming f(x) is composed of a mix of sine and cosine terms, isn't the whole point of a Fourier Transform to reveal these separate components?

This is new territory for me; I was briefly exposed to Fourier Transforms during my undergraduate engineering studies but, since then, haven't touched them.

So . . . I have lots of questions.

If I perform a Fourier Transform on the data, even if it does not reveal the complete function, will it at least reveal if f(x) includes a linear term (i.e. - M*x + B)?

Does a Fourier Transform reveal onlylinearterms of cosine and sine? In other words, if the actual function were to take a form such as equations 4 and 5 above (which includes a power of 2), would a Fourier Transform reveal it?

Do I need more than 18 data points to make this work? If so, I will have to go back and get some more data points.

Any suggestions or advice is appreciated.