2.17 Consider a baseband signal:

X(t) = x₁(1) + jxq(t),

where x/(t) and xo(t) are baseband signals with frequency content limited to [-W, +W]. Let X₁(f) and Xo(f) be the frequency

content of the signals. So

X₁(f) = XQ(f) = 0 for f * [-W, W].

The energy of the lowpass complex signal is

The passband signal is

= f ₁8010³d₁.

E₁ =

x(t) = x1(1) √2 cos(2n fet) - xo(t) √2 sin(2n fet),

where fe < W. The energy of the passband signal is

138

Ep = fix(0)³dt.

Show that E = Ep.

Hint: Derive expressions for the energy in the frequency domain for x(f). Use Parseval's theorem:

fut² (1dt = fuvas,