Problem Sheet Seven
1. Over an interval 0 t 1, an angle modulated signal is given by
(t) = 10 cos 13000t
The carrier frequency is c = 10000.
(a) If this were a PM signal with kp = 1000, determine m(t)
Communications I
Problem Sheet One
1. Find the mean value (time average) and the power for the following signals
(a) v(t) = 3 cos(2103 t),
[0, 9/2]
(b) v(t) = 3,
[3, 9]
(c) v(t) = 3 sin(40t) + 4 cos(1
(a) If g(t) = g(t) (even symmetry), then all the sine terms in the trigonometric Fourier series vanish (bn = 0).
(b) If g(t) = g(t) (odd symmetry), then the dc and all the cosine terms
in the Fourier
Problem Sheet Five
1. Consider the two baseband signals x1 (t) = cos 2000t and x2 (t) = cos 1900t.
Plot the magnitude spectrum of the signal s(t) = x1 (t) cos 10000t+x2 (t) cos 20000t.
(a) The signal
Problem Sheet Two
1. Find the energy Ex and Ey of the signals x(t) and y(t) shown in Figure 1.
Find the correlation coecient between x(t) and y(t). Sketch the signal
x(t) + y(t) and show that the ener
Problem Sheet Four
1. Find the Power Spectral Density Sg () of the power signal g(t) = cos 0 t.
(Hint: Compute the autocorrelation function rst, and then use the property Rg ( ) Sg ().
[ [( 0 ) + ( +
Problem Sheet Six
1. Consider the amplitude modulated signal s(t) = (A + m(t) cos c t, where
A = 2, c = 10000rad/s and m(t) = cos 100t + sin 100t. Compute:
(a) the peak amplitude mp of m(t).
(Hint: us
Communications I
Problem Sheet One
1. Find the mean value (time average) and the power for the following signals
(a) v(t) = 3 cos(2103 t),
[0, 9/2]
(b) v(t) = 3,
[3, 9]
(c) v(t) = 3 sin(40t) + 4 cos(1
Problem Sheet Nine
1. A 50 line is connected to a 75 line with a matched termination, and a
sine wave of 1.0V amplitude propagating in the former is incident on the
junction. Find the voltage and the
Problem Sheet Eight
1. Consider the FM signal
(t) = 10 cos[2f0 t + kf
t
x()d]
where kf = 10. The message x(t) is given by
2
mn (t)
x(t) =
n=0
with
mn (t) =
2n
sinc(t) cos(2nt).
(a) Sketch and dimensio
Problem Sheet Three
1. Show that the Fourier transform of g(t) may be expressed as
G() =
g(t) cos tdt j
g(t) sin tdt
Hence, show that
if g(t) is a real and even function of t, then G() is real and ev