Let x(t) be a real-valued signal with fundamental period T and Fourier series coefficien...

Let x(t) be a real-valued signal with fundamental period T and Fourier series coefficients .

(a) Show that must be real.

(b) Show that if x(t) is even, then its Fourier series coefficients must be real and even.

(c) Show that if x(t) is odd, then its Fourier series coefficients are imaginary and odd and

(d) Show that the Fourier coefficients of the even part of x(t) are equal to

(e) Show that the Fourier coefficients of the odd part of x(t) are equal to