Let x(t) be a real periodic signal with Fourier series representation given in the sine-...

Let x(t) be a real periodic signal with Fourier series representation given in the sine-cosine form of eq. (3.32); i.e.,

(a) Find the exponential Fourier series representation of the even and odd parts of x(t); that is, find the coefficients in terms of the coefficients in eq. (P3.45-1) so that

(b) What is the relationship between

(c) Suppose that the signals x(t) and z(t) shown in Figure P3.45 have the sine-cosine series representations

Sketch the signal