Suppose we are given the following information about a signal x(t):
1. x(t) is real and even.
2. x(t) is periodic with period T = 4 and Fourier coefficients $ \ a_k $.
3. $ \ a_k = 0 $ for $ \left \vert k \right \vert > 1 $.
4. $ frac{1}{2}\int_{0}^{2} \left \vert x(t) \right \vert ^2 \, dt = 2. $
