3.
we showed how the AM signal is easily demodulated using a simple envelope detector. This problem
shows that the AM signal can be easily generated using a simple square-law device.
Consider a general message signal $m(t)$ with bandwidth W. We create the signal
$v_1(t) = c(t) + m(t) = A_c \cos(2\pi f_c t) + m(t)$
and $v_2(t) = a_1 v_1(t) + a_2 v_1^2(t)$. Here, $a_1$ and $a_2$ are known constants.
(a) First, if a signal $m(t)$ has bandwidth W, what would be the bandwidth of $m^2(t)$? There's a
mathematical proof of this, but try to figure it out without the math.
(b) Again using the \"triangle\" message signal, sketch $V_2(f)$, the Fourier transform of $v_2(t)$.
(c) We wish to extract an AM modulated signal from $v_2(t)$ using an ideal BPF. Determine the
center frequency and cutoff frequencies of the required BPF. Basically, look at $V_2(f)$ and convince
yourself that one of the terms is the AM signal.
