Amplitude Modulation. Two signals m1(t) and m2(t) are to be transmitted simultaneously over a channel by the scheme shown in the Figure below. mi(t) a(t) b(t) (t) |d(1). AM + m2(t) 2 cos(20000zt) (a) forms of m1(t). Assume m,(t) = 2000 sinc(2000t). Derive and Plot the Fourier trans- (b) Is m1 (t) periodic? if so, what is the period of m¡(t)? (c) What is the energy of m1(t)? Is m¡(t) an energy signal?Why?

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Amplitude Modulation.
Two signals m1(t) and m2(t) are to be transmitted simultaneously over a channel by the
scheme shown in the Figure below.
mi(t)
|a(t)
b(t)
c(t)
d(t)
AM
m2(t)
2 cos(20000zt)
(а)
forms of m1(t).
Assume m, (t) = 2000 sinc(2000t). Derive and Plot the Fourier trans-
(b)
Is m1 (t) periodic? if so, what is the period of m¡(t)?
(c)
What is the energy of m1(t)? Is m¡(t) an energy signal?Why?
(d)
What is the power of m1(t)? Is m1(t) a power signal? Why?
(e)
uses a carrier c(t) = cos(100007 t) and k =0.8.
Derive and Plot the Fourier transforms of a(t). The AM modulation
(f)
of b(t).
Assume m2(t)
cos(2000nt)). Derive and Plot the Fourier transforms
%3D
(g)
What is the bandwidth of b(t)?
(h)
Derive and Plot the Fourier transforms of c(t).
(i)
What is the bandwidth of c(t)?
()
Now assume that
2.
f| < 10000.
H(f)
0,
10000 < |S| < 25000,
A. IS| > 25000.
Derive and Plot the Fourier transform of d(t).
(k)
Show whether or not we can recover m (t). if so how?
Transcribed Image Text:Amplitude Modulation. Two signals m1(t) and m2(t) are to be transmitted simultaneously over a channel by the scheme shown in the Figure below. mi(t) |a(t) b(t) c(t) d(t) AM m2(t) 2 cos(20000zt) (а) forms of m1(t). Assume m, (t) = 2000 sinc(2000t). Derive and Plot the Fourier trans- (b) Is m1 (t) periodic? if so, what is the period of m¡(t)? (c) What is the energy of m1(t)? Is m¡(t) an energy signal?Why? (d) What is the power of m1(t)? Is m1(t) a power signal? Why? (e) uses a carrier c(t) = cos(100007 t) and k =0.8. Derive and Plot the Fourier transforms of a(t). The AM modulation (f) of b(t). Assume m2(t) cos(2000nt)). Derive and Plot the Fourier transforms %3D (g) What is the bandwidth of b(t)? (h) Derive and Plot the Fourier transforms of c(t). (i) What is the bandwidth of c(t)? () Now assume that 2. f| < 10000. H(f) 0, 10000 < |S| < 25000, A. IS| > 25000. Derive and Plot the Fourier transform of d(t). (k) Show whether or not we can recover m (t). if so how?
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