How do I get an expression for the sinusodial function in the graph?

158 Views Asked by At

Note on Guitar

This is essentially a note I played on my guitar. I really need an equation for it though and am wondering if I should make it like a piecewise function and do the fourier transform thrice. I don't know if this is right.

My goal is to can apply Fourier transforms on it (the function) to get the coefficients/frequencies.

When I say piecewise function I mean separating the function into three groups. A negative parabola (the one at the top) and then two positive ones below.

I'd appreciate any amount of help and please try and keep it relatively simple for me. I do already have a decent amount of background in fourier transforms and inverse fourier transform and series but lack the conceptual understanding and linear algebra. I'm only in highschool! Thanks!