I need to deal with fourier transforms for a high school research paper, and my school really isn't helping me out. Basically I had a function of this form after regression, on which I applied the fourier transform and got an equation of this form
a friend of a friend helped me out with the graphing bit which I couldn't figure out, and got this graph and this graph.
Unfortunately, I have no idea how to interpret this. I need to find the constituent frequency of the original signal but I legitimately don't know how to interpret the graphs. Is it just the peak of the graph? The frequency I'm supposed to get is approximately 349.228 Hz, and I can have a range of error of say 50 Hz, but it really doesn't look like that.
Could someone outline how exactly to interpret the fourier transform graph? I need to repeat this process a couple times so I need to figure out whether the function I got was wrong or I'm just interpreting the graph wrong.
Your original signal is: $$ f(t) = A\sin(\omega(t+\phi)) + B $$ What the Fourier transform does is bringing a signal from the time domain ($t$) to the frequency domain ($\omega$). The frequency-domain contains all the frequencies of the original signal. Since you have a sine wave (a single frequency function of frequency $\omega$) and a constant (a single frequency function of frequency $0$) you should expect a graph in the frequency domain with three spikes. The first spike for the $B$ term at $\omega = 0$, the second spike at $+\omega$ and the third spike at $-\omega$. This is a consequence of the transform but you should not bother yourself with that.
So reading the $x$-axis value of the frequency content for these spikes should give you your desired frequency. The one problem that you have in your plots is that you probably don't know the units of it so the graph might not be scaled properly (you should label the graphs or tell us the unit of the $x$-axis). The second thing is that in order to graph the function and find the desired frequency you need to give us the values of the constants ($\omega, \phi, B, A$).