ECE 3050
Signals and Systems
Autumn 2015
MINI-PROJECT #1
Due Mon. Oct. 5, 2015 at 5:00pm
You have just purchased a used speaker. However, once it is set up you realize that the speaker
distorts the sound we wish to hear (it tends to dampen high frequency
ECE 3050
Signals and Systems
Spring 2015
MINI-PROJECT #1 SOLUTIONS
Problems:
1. The method to solve this problem is outlines in the lecture notes.
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Lh = 6;
Xmat_pilot = convmtx(x_pilot, Lh);
Xmat_pilot = Xmat_pilot(Lh:length(x_pilot), :);
y_pilot
ECE 3050
Signals and Systems
Spring 2015
HOMEWORK ASSIGNMENT #7 SOLUTIONS
Problems:
1. (a) From tables, X(j) = 1 if | < W and X(j) = 0 otherwise.
(b) Note that
x[n] = x(t) =
sin(W T n)
.
T n
(1)
From tables, the DTFT of this signal is
cfw_
j
X(e ) =
1
T
0
ECE 3050
Signals and Systems
Spring 2015
FINAL PRACTICE QUESTIONS
Problems:
1. A discrete-time LTI system is known to have impulse response h[n] = [1, 1, 1, 1, 1, 1, 1].
(a) Find the output of this system given an input x[n] = [3, 0, 1].
(b) Find the step
ECE 3050
Signals and Systems
Spring 2015
MINI-PROJECT #2 SOLUTIONS
Problems:
1. (a) From transform tables, the impulse response of an ideal low-pass lter is
h[n] =
where fc =
c
2
sin(c n)
= 2fc sinc(2fc n),
n
is the cuto frequency in Hz.
(b) Since h[n] =
ECE 3050
Signals and Systems
Spring 2015
MINI-PROJECT #2
Due Wed., Mar. 25, 2015 at 5:00pm
Problem description:
Download the audio le audio.wav from Carmen. We can load this le into MATLAB using the
following command:
[x, FS] = audioread(audio.wav);
This
ECE 3050
Signals and Systems
Spring 2015
MIDTERM EXAM #2, REVIEW
Midterm exam #2 will be held on Monday, April 6.
The exam is closed book. Calculators are allowed but internet enabled devices are not allowed.
One page of notes (letter sized, front and b
ECE 3050
Signals and Systems
Spring 2015
MINI-PROJECT #2
Due Wed., Mar. 25, 2015 at 5:00pm
Problem description:
Download the audio le audio.wav from Carmen. We can load this le into MATLAB using the
following command:
[x, FS] = audioread(audio.wav);
This
ECE 3050
Issued: August 30, 2013
Assignment # A2
Due: September 6, 2013
Readings:
All materials are posted to the Carmen web page
Oppenheim & Willsky: sections 2.02.6.
1 Computing the convolution sum
A discrete-time LTI system has the impulse response
ECE3050
Assignment # 1
Solutions & Comments
1 Discrete-time system model example: amortization table
(a) The balance at month n is the output and is denoted y[n]. This balance is the previous
months balance, plus interest accrued on the previous months ba
ECE3050
Homework Set 1
1. For V = 18 V, R1 = 39 k, R2 = 43 k, and R3 = 11 k, use Ohms Law, voltage division,
and current division to solve for V1 , V2 , I1 , I2 , and I3 .
V1 = 18
I1 =
39 k
= 14.7 V
39 k + 43 kk11 k
18
= 376.8 A
39 k + 43 kk11 k
I3 =
V2 =
ECE 3050 Signals and Systems Spring 2015
Ebb.18,2015
MIDTERM EXAMINATION #1
Name:
50L 0 T/oA/S
Instructions:
0 Do not turn over this cover page until instructed to do so.
a You will have 55 minutes to complete this exam.
o Calculators are permitted. Inter
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ECE 3050 Signals and Systems Spring 2015
Apr. 6, 2015
NIIDTERM EXAMINATION #2
Name:
SOLU’THNUS
Instructions:
0 Do not turn over this cover page until instructed to do so.
0 You will have 55 minutes to complete this exam.
0 Calculators are permitted. Inter
ECE 3050
Signals and Systems
Spring 2015
HOMEWORK ASSIGNMENT #5
Due Fri. Feb. 27, 2015 (in class)
Suggested Reading: Oppenheim, Chapter 3, Sections 3.53.6, pp. 202220.
Oppenheim, Chapter 4, Section 4.04.3, pp. 284314.
Problems:
1. (a) For some positive co
ECE 3050
Signals and Systems
Spring 2015
HOMEWORK ASSIGNMENT #9
Due Fri. April. 17, 2015 (in class)
Suggested Reading: Oppenheim, Chapter 7, Sections 7.07.4, pp. 514541.
Problems:
1. Determine the Nyquist rate for each of the following signals.
(a) y(t) =
ECE 3050
Signals and Systems
Spring 2015
HOMEWORK ASSIGNMENT #9 SOLUTIONS
Problems:
1. (a) The maximum frequency in this signal is 300 or 150 Hz, thus the Nyquist rate is 300
samples/sec.
(b) The CTFT of sin(3t) is a rectangular pulse from 3 to 3. The CTF
ECE 3050
Signals and Systems
Spring 2015
HOMEWORK ASSIGNMENT #10
Due Mon. April. 27, 2015 (in class)
Suggested Reading: Oppenheim, Chapter 9, Sections 9.09.3, pp. 654674.
Oppenheim, Chapter 9, Section 9.59.9, pp. 682720.
Problems:
1. Determine the Laplace
ECE 3050
Signals and Systems
Spring 2015
HOMEWORK ASSIGNMENT #8 SOLUTIONS
Problems:
1. Bode plots are shown in Fig. 1.
2. (a) Running the following in MATLAB,
omega = 0.001:0.001:1000;
H = (i*omega + 100).*(100*i*omega + 1)./(10*(i*omega + 10).*(10*i*omeg
ECE 3050
Signals and Systems
Autumn 2015
BONUS ASSIGNMENT
Due Mon. Dec. 14, 2015 at 6:30pm
This assignment is optional, but highly recommended. If you turn it in, your score (out of 10) times 0.2
will be added to your overall grade (for a maximum of 2 poi
ECE 3050
Signals and Systems
Spring 2015
MINI-PROJECT #1
Due Mon. Feb. 16, 2015 at 5:00pm
Consider a wireless communications system in which a transmitter sends a message signal, x[n], this
message is distorted as it passes through a communication channel
ECE 3050
Signals and Systems
Spring 2015
MINI-PROJECT #3
Due Fri., May 1, 2015 at 5:00pm
Problem description:
In this project, we study the sampling system illustrated in Fig. 1. This system is comprised of three
parts: a plant that distorts the input sig
ECE 3050
Signals and Systems
Spring 2015
MINI-PROJECT #3 SOLUTIONS
Problems:
1. Since this is a rst order system, we know that
H(j) =
b0 + b1 j
.
1 + a1 j
From the Bode plot, we can see that we have a high-pass ler with phase starting at 90 degrees,
so we
ECE 3050
Signals and Systems
Autumn 2015
HOMEWORK ASSIGNMENT #4
Due Fri. Sep. 25, 2015 (in class)
Suggested Reading: Oppenheim, Chapter 2, Section 2.2, pp. 90103.
Oppenheim, Chapter 2, Section 2.4, pp. 116127.
Problems:
1. The following functions are the
ECE 3050
Signals and Systems
Autumn 2015
HOMEWORK ASSIGNMENT #5
Due Mon. Oct. 12, 2015 (in class)
Suggested Reading: Oppenheim, Chapter 3, Sections 3.03.5, pp. 177211.
Oppenheim, Chapter 4, Sections 4.04.2, pp. 284300.
Problems:
1. In this problem, we exa