Q) If $m(t) = 6\cos(2\pi500t) + 4\cos(2\pi1000t)$ is passed through the following system:
m(t)
Hilbert
Transform
b(t)
+
d(t)
$10\cos(2\pi10^4t)$
$-\pi/2$
a(t)
c(t)
a) Sketch the frequency spectra (Magnitude and Phase) of m(t), a(t), b(t), c(t), and d(t).
b) Write a time-domain expression for d(t), and determine the type of modulation.
$\sin(a)\sin(b) = 0.5[\cos(a-b)-\cos(a+b)]$,
Hint:
$\cos(a)\cos(b) = 0.5[\cos(a-b)+\cos(a+b)]$,
$\sin(a)\cos(b) = 0.5[\sin(a-b)+\sin(a+b)]$.
