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
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 #1 SOLUTIONS
Problems:
1. The method to solve this problem is outlines in the lecture notes.
>
>
>
>
>
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
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
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
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
ECE 3050
Signals and Systems
Spring 2015
HOMEWORK ASSIGNMENT #7
Due Fri. Mar. 13, 2015 (in class)
Suggested Reading: Oppenheim, Chapter 5, Sections 5.35.9, pp. 372400.
Problems:
1. (a) Let x(t) = sin(W t) be a continuous time sinc function. Write the cont
ECE 3050
Signals and Systems
Spring 2015
HOMEWORK ASSIGNMENT #4 SOLUTIONS
Problems:
1. (a) From inverse Euler formulas,
1 jt 1 jt
1 j1000t 1 j1000t
e + e
e
+ e
2
2
2
2
1 j1001t 1 j999t 1 j999t 1 j1001t
= e
+ e
+ e
+ e
4
4
4
4
The fundamental frequency is
ECE 3050
Signals and Systems
Spring 2015
HOMEWORK ASSIGNMENT #8
Due Fri. April. 3, 2015 (in class)
Suggested Reading: Oppenheim, Chapter 6, Sections 6.06.6, pp. 423472.
Problems:
1. For each of the following frequency responses, sketch Bode plots (both ma
ECE 3050
Signals and Systems
Spring 2015
HOMEWORK ASSIGNMENT #4 SOLUTIONS
Problems:
1. (a) From inverse Euler formulas,
1 jt 1 jt
1 j1000t 1 j1000t
e + e
e
+ e
2
2
2
2
1 j1001t 1 j999t 1 j999t 1 j1001t
= e
+ e
+ e
+ e
4
4
4
4
The fundamental frequency is
ECE 3050
Signals and Systems
Spring 2015
HOMEWORK ASSIGNMENT #5 SOLUTIONS
Problems:
1. (a) The pulse is 1 for a 2 time-units in every period, T . Hence, the DC value is a0 = 2 /T . For
k = 0,
ak =
T /2
1
T
p (t)ej2kt/T dt
T /2
j2kt/T
1
=
T
e
dt
1
ej2kt/T
ECE 3050
Signals and Systems
Spring 2015
HOMEWORK ASSIGNMENT #6
Due Fri. Mar. 6, 2015 (in class)
Suggested Reading: Oppenheim, Chapter 4, Sections 4.44.8, pp. 314333.
Oppenheim, Chapter 5, Section 5.05.2, pp. 358372.
Problems:
1. Oppenheim, Problem 4.32.
ECE 3050
Signals and Systems
Spring 2015
HOMEWORK ASSIGNMENT #1
Due Fri. Jan. 23, 2015 (in class)
Suggested Reading: Oppenheim, Chapter 1, pp. 156.
Problems:
1. Oppenheim, Problem 1.21, parts (a), (c), and (e).
2. Oppenheim, Problem 1.22, parts (a), (d),
ECE 3050
Signals and Systems
Spring 2015
HOMEWORK ASSIGNMENT #2
Due Fri. Jan. 30, 2015 (in class)
Suggested Reading: Oppenheim, Chapter 2, Sections 2.0 and 2.1, pp. 7490.
Oppenheim, Chapter 2, Section 2.3, pp. 103116.
Problems:
1. Compute the convolution
ECE 3050
Signals and Systems
Spring 2015
HOMEWORK ASSIGNMENT #3
Due Fri. Feb. 6, 2015 (in class)
Suggested Reading: Oppenheim, Chapter 2, Section 2.2, pp. 90103.
Oppenheim, Chapter 2, Section 2.4, pp. 116127.
Oppenheim, Chapter 3, Sections 3.03.2, pp. 177
ECE 3050
Signals and Systems
Spring 2015
HOMEWORK ASSIGNMENT #3 SOLUTIONS
Problems:
1. (a) The desired convolution is
x()h(t )d
y(t) =
t
e e(t) d, where t 0.
=
0
Then,
t ()t
1)
e (e
u(t) =
y(t) =
.
t
te u(t)
= .
(c) The desired convolution is
x()h(t
ECE 3050
Signals and Systems
Spring 2015
HOMEWORK ASSIGNMENT #1 SOLUTIONS
Problems:
1. Solutions are shown in Figure 1.
1.21 (a)
1.21 (c)
1.21 (e)
Figure 1: Solutions to problem 1.
2. Solutions for parts (a) and (d) are shown in Figure 1. For part (e), x[
ECE 3050
Signals and Systems
Spring 2015
HOMEWORK ASSIGNMENT #4
Due Fri. Feb. 13, 2015 (in class)
Suggested Reading: Oppenheim, Chapter 3, Sections 3.33.4, pp. 177202.
Problems:
1. Determine the Fourier series coecients, ak for all k, for the following si
FINAL PILAC Tlce Gugswords
Io . - l L
PT (muoluhm 7“} I I I I if}
_w. _ n.4,. —. -f—. up“
IL) A n. ?‘ T l, t c
gm]: 2’ Mn] = 2 \ :‘nH ogmﬁé r
K30 L10 a i
e ‘ I
at = ? 1176 i
VI 40 f0 ‘l “J 4 5’ 8 3f f n
IQ) lat-H] is A Pafmc/mme 5) VF); If? hhggr pkapé
ECE 3050
Signals and Systems
Spring 2015
HOMEWORK ASSIGNMENT #6 SOLUTIONS
Problems:
1. Note that h(t) = h1 (t 1), where
sin 4t
.
t
The Fourier transform H1 (j) of h1 (t) is as shown in Fig. 1.
h1 (t) =
Figure 1
From the above gure it is clear that h1 (t)
ECE 3050
Signals and Systems
Spring 2015
HOMEWORK ASSIGNMENT #10 SOLUTIONS
Problems:
1. All of these may be found from tables.
(a) X(s) =
1
s+2
+
1
s+5 ,
Recfw_s > 2
> syms t x
> x = exp(-2*t) + exp(-5*t);
> laplace(x)
ans =
1/(s + 2) + 1/(s + 5)
(b) X(s)
ECE 3050: Signals and Systems
Lecture 1: Introduction
Dept. of Electrical and Computer Engineering
Ohio State University
January 9, 2017
Course Information
I
Time: Mon/Wed/Fri 1:50am-2:45pm
I
Location: Scott Lab N048
I
Instructor: Prof. Yuejie Chi (chi.97
ECE 3050: Signal and Systems
Homework 1
Posted: 1/13; Due: 1/23 3pm.
Homework can be submitted in class or to my mailbox outside Dreese 606.
January 10, 2017
1. Complex numbers.
Compute the magnitude and phase of the complex numbers:
(1) 1 j
(2) 2 + j
(3