The signal x(n) = 1 + sinn 3 cos n + cos n + cos is periodic with period N, and we can expand x[n] directly in terms of complex exponentials to obtain Collecting terms, we find that Thus for Fourier series coefficients for this example are a₀ = 1, a₁ = + = -j, a_-1 = - = +j, a₂ = j, a_-2 = -j.