I am looking for the Fourier Series of this function:
This is a winding function method for calculation of rotor inductances. The distance between each stator slot (each segment) is $10$ degrees or $\dfrac \pi{18}$. Since this function is periodic after each 360 degree I can use Fourier Series. The function is even: $b(n)=0$ and it has only
a(n) = (2/PI)*(int(36*cos(n*w*phi),phi=0..2*PI/18)+int(24*cos(n*w*phi),phi=2*pi/18..3*PI/18)+ int(12*cos(n*w*phi),phi=3*PI/18..4*pi/18)+...)
I wrote this code on MATLAB and got a correct answer(below figure).But I need to calculate the simplified algebraic equation for this figure.
Thanks
If your goal is to have a simple algebraic expression for the original "rugged wave" function, the Fourier series is of no help. It is easier to express the original function itself in a formula. First, calculate $$ n = \left \lfloor \frac{18}{\pi} |\phi| \right\rfloor \bmod 18 $$ so than $n$ is an integer in the range $0,1,\dots,17$, corresponding to the multiples of $\pi/18$ on your sketch. Then let $m=\min(n,17-n,7)$; this reduces the range of $m$ to $0,\dots,7$, which is the first decreasing interval of the function. Finally, the function value is $$ \min(48-m, 36) $$