EEE393 Basic Electrical Engineering
20 Mar 2007, Tuesday (bring to class)
HOMEWORK 3
1. The frequency spectrum of two signals p(t) and q(t)
are given in the figures as P(ω) and Q(ω), respectively.
p(t) is modulated (multiplied) by cos(200t) and q(t) is
multiplied by cos(300t), and then the two are summed.
a) Draw the spectrum of p(t)⋅cos(200t) and the spectrum
of q(t)⋅cos(300t) .
b) Draw the combined signal p(t)⋅cos(200t) +
q(t)⋅cos(300t) .
c) How can you get p(t) from the above combined signal?
2. Magnitude of the frequency response of a system, |H(ω)|, is given in the figure.
Magnitude of the frequency spectrum of the input to the system, |X(ω)| is also given.
Draw the magnitude of the frequency spectrum of the system output.
3. a) Assume x(t) can be expressed as a sum of N cosine signals with different
amplitudes Ai, different frequencies ωi, and different phases φi. Write the expression that
shows x(t) as a sum of N such cosines.
b) Convert the sum into a sum of complext exponentials instead of cosines (using
Euler’s identity).
4. For each of the following: What is the phasor? What is the value of ω?
a) tj
jee 50
3
100
π
b) )
2
60(
220
π
−tj
e c) tj
e30
110
5. The magnitude of the spectrum (Fourier transform) of
x(t) is given in the figure.
a) What is the Fourier transform of y(t) = x(t-10)?
Draw |Y(ω)|.
b) What is the Fourier transform of y(t) = x(t/2)?
Draw |Y(ω)|.
|P(
ω
)|
ω
50 -50
|R(
ω
)|
50 -50
|X(
ω
)|
ω
100 -100
100 |H(
ω
)|
50 -50
1
ω
|X(
ω
)|
ω
10 -10
10
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