Consider the signals of Figure P4.11(a) and (d). (a) Change the period of x0(t) to T0=4...

Consider the signals of Figure P4.11(a) and (d).

(a) Change the period of x0(t) to T0=4. Use Table 4.3 to find the Fourier coefficients of the exponential form for this signal.

(b) Use Table 4.3 to find the Fourier coefficients of the exponential form for x_d(t).

(c) Consider the signal

where X_a(t) is defined in part (a). By inspection of Figure P4.11(a) and (d), find a₁, b₁ and _T such that x(t) is constant for all time; that is, x(t) = A, where A is a constant. In addition, evaluate A.

(d) Use the results of parts (a) and (b) to show that all the Fourier coefficients of x(t) in part (c) are zero except for C₀=A.