Signals and Systems
Sharif University of Technology
Ali Soltani Farani
April 19, 2013
CE 40-242
Date Due: Ordibehesht 16, 1392
Homework 6 (Chapter 7)
Problems
1. (a) Consider the system as shown in below:
And let H(Ω) and X(ω) be as given in below:
Sketch X(Ω) and Y (Ω).
(b) Suppose we replace the system in (a) with this system:
Find G(ω) such that z[n] = y[n].
2. Consider the system as shown in below and T0 = 0.01:
(a) If X(ω) is as shown in below, find Y (Ω).
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(b) If Y (Ω) is as shown in below, find Y (ω).
3. Consider that discrete-time sequence x[n] is given and xd [n] and xp [n] is given as:
x[n], n is even
xp [n] =
0,
n is odd
xd [n] = x[2n]
Sketch Xp (Ω) and Xd (Ω) if X(Ω) is as shown below:
4. Suppose we have a system and its input as given in below. Find H(Ω) such that y[n] = x[n].
(For all possible values of N)
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5. Suppose a system that the relation between its input and output is:
y[n] =
x[3n] + x[3n + 1] + x[3n + 2]
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Express this system as a combination of filtering and decimation.
6. Consider the system shown below:
Suppose x(t) = sin(10t) and s(t) and H(ω) is as shown in below. Find y(t). (T =
3
2π
90 )
Practical Assignment
1. We have a continuous signal c(t). With a frequency for preventing aliasing, sample this signal:
c(t) = cos(Ωc (t) + θc ) = cos(2πFc (t) + θc )
0≤t≤3
π
Fc = 10Hz, θc = radians
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2. If sampled signal in (1) is cn [n], plot CN (Ω).
3. We want to work with sound in MATLAB. Create a ’.wav’ file and read it in MATLAB. (Hint:
You can use this function: wavread(’path of .wav file in your PC’)) Now you have a continuous
signal. You can play it by using this function: sound(c,fs).
Read a .wav file, sample the signal and play it.
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