Suppose you have the Fourier series of two periodic signals x(t)and y(t)of fundamental periods T₁ and T₂, respectively. Let X_k and Y_k be the Fourier series coefficients corresponding to x(t) and y(t).

(a) If T₁ =T₂ what would be the Fourier series coefficients of z(t) = x(t) + y(t) in terms of X_k and Y_k?

(b) If T₁=2T₂ determine the Fourier series coefficients of w(t) = x(t) + y(t) in terms of X_k and Y_k?