Take the piecewise function:
F(x) = 1, x < L/2 and 2, x > L/2
Now a fourier series is defined over a full period of -L < x < L
Just using the fourier sine coefficiencts as an example, they are usually calculated as: (1/L) Int(-L,L) f(x) sin[(n pi x)/L]
But over th full period i have my function f(x) equaling two values, do i use the sum of the values?
I.e: (1/L) Int(-L,L/2) (1)sin[(n pi x)/L] +(1/L) Int(L/2, L) (2)sin[(n pi x)/L]