f(t) =
{+2, for -2 <= t < -1
-4, for -1 <= t < +1
+2, for +1 <= t < +2}
where f(t) = f(t+4)
The question wants me to find the fourier coefficients, a0, an and bn of f(t). I have already determined that the function is even so bn = 0.
I tried using the half range formulas for a0 and an and substituted in the values but it ended up different from the answer given by the teacher. I am not sure if I substituted in the wrong values or I used the wrong formulas but the supposed answer is a0 = -2 but he didn't give the answer for an. Could I have some help to get to the correct answer and also to the answer for an.
By definition, $a_0$ is supposed to be the mean value of the function if you write $$f(t) = a_0 + ...$$ Clearly, $$a_0 = \frac{1}{4} \left(2\cdot 1 -4\cdot 2 + 2\cdot 1\right) = - 1$$ Probably, your teacher defined $f(t)$ as: $$f(t) = \frac{a_0}{2} + ...$$