University of Management and Technology

School of Science and Technology

Homework No. 2 EE-410 Communication Systems

Question 1

A test pulse g(t) bandlimited to B Hz is transmitted over a channel ( mismatched transmission

line) whose transfer function is shown in figure. Draw y(t) and identify the type of distortion

caused by the channel. If more than one pulse is to be transmitted over this transmission line,

should these pulses be multiplexed in time or in frequency? Justify your answer. What kind of

fading is observed over this transmission line?

g(t) | H(w)| = 1 + cos (w T)

- 2πB 2πB

Θh(ω) = -ωtd – k sin (ω T)

Question 2

By using properties find the Fourier transform of the following signals.

6 rect ( (t-5) / 2)

sinc ( π t) ej10t

δ ( t+5) + δ (t-5)

Question 3

Signals g1(t) = 104

rect (104) and g2(t) = δ (t) are applied at the inputs of the ideal low pass filters

H1 (ω) = rect ( ω / 40,000 π) and H2(ω) = rect ( ω/ 20,000 π) . The outputs y1(t) and y2(t) of these

filters are multiplied to obtain the signal y(t) = y1(t) y2(t).

a) Sketch G1 (ω) and G2 (ω).

b) Sketch H1 (ω) and H2 (ω).

c) Sketch Y1 (ω) and Y2 (ω).

d) Find the bandwidths of y1(t), y2(t) and y(t).

g1(t) y1(t)

y(t) = y1(t) y2(t)

g2(t) y2(t)

H1(ω)

H2(ω)

Question 4

Using the properties find the inverse Fourier transform of the following spectra.

G( ω)

3

ω

-8 -2 2 -8

G (ω)

3

-5 -3 3 5 ω

Question 5

Calculate the Fourier transform for the following signals.

g( t)

8 g (t)

4

3 6 t -4 -2 0 2 4 t

Question 6

Given are the certain modulated signals with carrier cos(20t). Find the Fourier transforms of each

of them.

2

π 2π t

3

π 3π t

Question 7

Determine the maximum bandwidth of a signal that can be transmitted through the low pass RC

filter with R= 1 kohm and C= 10-9

if over this bandwidth the amplitude response variation is to

be within 6 % and he time delay variation is to be within 3%.