ECE351
Issued: April 9, 2010
Assignment # 2
Due: April 16, 2010
Cumulative Reading Assignments:
Kamen & Heck, Chapters 1, 2
Visit textbook web site.
1 System modelling
Problem 2.15 parts (a) and (b) from Kamen & Heck.
n
(Hint: For part (b), you may need
ECE351
Assignment # 2
Solutions
1 Savings account balance
(a) The rst ve quarterly balances are (to the nearest penny):
n
0
1
2
3
y [n]
1000.00
2025.00
3075.63
4152.52
(b) Write out the expressions for y (n) for the rst few n, say n = 1, 2, 3, 4, 5. You w
ECE351
1 K & B - Problem 2.21
Assignment # 1
Solutions
2 (a) K & B - Problem 1.3
(b) K & B - Problem 1.7
3 K & B - Problem 1.16
4 Moving average lter:
This discrete-time system replaces a sequence value by the average of three consecutive
values. Armed wi
ECE351
Issued: April 16, 2010
Assignment # 3
Due: April 23, 2010
Cumulative Reading Assignments:
Kamen & Heck, Chapters 1, 2
Visit textbook web site.
1 System Modeling
Problem 2.15, Parts (c) and (d) from Kamen & Heck.
(Note: Parts (a) and (b) are alrea
ECE351
Issued: April 28, 2010
Assignment # 4
Due: May 7, 2010
Cumulative Reading Assignments:
Kamen & Heck, Chapters 1, 2, 3
Kamen & Heck, Appendix on Complex Numbers
Visit textbook web site.
1 Discretization
Problem 2.27 from Kamen & Heck.
2 Periodic
ECE351
Issued: May 7, 2010
Assignment # 5
Due: May 14, 2010
Cumulative Reading Assignments:
Kamen & Heck, Chapters 1, 2, 3; Section 4.1
Kamen & Heck, Appendix on Complex Numbers
Visit textbook web site.
1 Fourier Series
Problem 3.11, parts (a),(c) and
ECE351
Assignment # 4
1 Continuous time system diagrams: Kamen and Heck 2.27
Solutions
2 Complex Exponential Representation and Amplitude modulation
(a) First, write x(t) as a sum of complex exponentials, reading from the gure left-toright (note 45 degree
ECE351
1 Savings account balance
Assignment # 3
Solutions
2 Continuous-time Convolution: Kamen and Heck 2.29
3 Solution of Dierence Equations by Recursion: Kamen and Heck 2.29
4 Discrete time system examples
The system diagram has the following dierence
ECE351
Issued: May 14, 2010
Assignment # 6
Due: May 21, 2010
Cumulative Reading Assignments:
Kamen & Heck, Chapters 1, 2, 3, 4
Kamen & Heck, Appendix on Complex Numbers
Visit textbook web site.
1 DTFT
Problem 4.4, parts (b), (c), (d) and (g), Kamen & H
ECE351
Issued: May 26, 2010
Assignment # 7
Due: June 4, 2010
Cumulative Reading Assignments:
Kamen & Heck, Chapters 1, 2, 3, 4, 5
Kamen & Heck, Appendix on Complex Numbers
Visit textbook web site.
1 Frequency Response
Problem 5.1, parts (a) and (b), Ka
ECE351
Assignment # 5
1 Fourier Series: Kamen & Heck 3.11
Solutions
2 Fourier Transforms: Kamen & Heck 3.18
3 Fourier Transform Pairs and Properties
X (j ) =
1
j + b
(a) Problem 3.24 (b)
v (t) = t2 x(t)
(1)
This is multiplication by a power of t with n =
ECE351
1 DTFT: Kamen & Heck 4.4
Assignment # 6
Solutions
2 DTFT: Kamen & Heck 4.5
3 IDTFT: Kamen & Heck 4.7
5 Circular convolution
(a) N = 4; x = [1 0 1 0]; X = fft(x,N); v = [1 0 -1 0]; V = fft(v,N); Y
= X.*V; y = ifft(Y,N) y =
0
0
0
0
% compare to linea
ECE351
Review, Final Exam
Modeling: Signals contain information about a phenomenon. They are modeled as functions of independent variables. We focused on 1 dimensional signals.
Signals are categorized into classes such as Continuous-time (CT) /Discrete-t
ECE351
Assignment # 7
Solutions
1 Frequency Response
The ideal lter, H ( ), gives a gain of 1 0 to any frequency component in the band 2 | | 7, and
gives a gain of 0 0 (i.e., innite attenuation) to all other frequency components.
(a) Problem 5.1(a). For x
ECE 351, Systems I
OSU, Autumn 2009
Oct. 28, 2009
MIDTERM I
NAME:
The duration of the exam is 48 minutes. The exam consists of 2 questions
with multiple parts each. Questions carry dierent weights, which are noted
next to the question number.
The problems
ECE 351, Systems I
OSU, Autumn 2009
Nov. 23, 2009
MIDTERM II
NAME (5 points):
The duration of the exam is 48 minutes. The exam consists of 3 questions
with multiple parts each. Questions carry dierent weights, which are noted
next to the question number.
ECE351
Issued: April 2, 2010
Assignment # 1
Due: April 9, 2010
Reading Assignments:
Visit the textbook webpage: http:/users.ece.gatech.edu/bonnie/book3/
Read Kamen & Heck, Chapter 1
First, system modelling:
1 Problem 2.21 from Kamen & Heck.
Second, some
ECE 352
Solution to Midterm 1 Practice
1 Given the linear constant coecient dierential equation
d2
d
d
y (t) + 3 y (t) + 2y (t) = x(t) + 3x(t)
2
dt
dt
dt
(i) Find the zero input response for initial conditions y (0) = 1 and y (0) = 2.
(ii) Write the trans
ECE 351, Systems I OSU, Winter 2009
Jan. 12, 2009 Due: Jan. 21, 2009
Problem Set 1 Reading Assignments: Visit the textbook webpage: http:/users.ece.gatech.edu/bonnie/book3/ Read Kamen & Heck, Chapter 1 and 2
Problem 1 (MATLAB Exercise) (a) Problem 1.3 (pa
ECE 351, Systems I OSU, Winter 2009 Problem Set 2 Problem 1 (a) Write the difference equation for the following system
x[n] b0 y[n]
Jan. 21, 2009 Due: Feb. 2, 2009
-a1
-a2
-a3
(b) Draw a system diagram for the following difference equation using only thre
ECE 351, Systems I OSU, Winter 2009
Feb. 2, 2009 Due: Feb. 11, 2009
Problem Set 3 Problem 1 Problem 2.29, Parts (a),(d), and (e) from Kamen & Heck. Problem 2 Let x(t) be given by 1 x(t) = -1 0
x(t) 1 t
0t<1 1<t 2. else
Find the zero state response, y(t),
ECE 351, Systems I OSU, Winter 2009
Feb. 13, 2009 Due: Feb. 23, 2009
Problem Set 4 Problem 1 For each of the following statements, answer True if the statement is always true, and answer False otherwise. If you answered True, provide a brief argument (e.g
ECE 351, Systems I OSU, Winter 2009
Mar. 2, 2009 Due: Mar. 9, 2009
Problem Set 6 Problem 1 If a band-limited signal x(t) has Fourier transform that is nonzero only for |f | < 8 kHz, what is the minimum required sampling rate for the signal y(t) = x 2 (t)
ECE 351, Systems I OSU, Winter 2009 Problem Set 7 - not to be turned in Reading Assignments: Read Kamen & Heck, Sections 4.1, 4.2, 5.5.
Mar. 9, 2009
Problem 1 Consider the LTI system with the frequency response H(j) depicted in the following magnitude and
ECE 351, Systems I OSU, Winter 2009 Solutions - Problem Set 1 Problem 1 (a)
Jan. 21, 2009
1
(b)
2
Problem 2
Problem 3 This discrete-time system replaces a sequence value by the average of three consecutive values. Armed with frequency analysis tools, we'l
ECE 351, Systems I OSU, Winter 2009 Solutions - Problem Set 2 Problem 1 (a) The system diagram has the following difference equation: y(n) = -a1 y(n - 1) - a2 y(n - 2) - a3 y(n - 3) + b0 x(n)
Feb. 2, 2009
(b) The two figures provided are equivalent system
ECE 351, Systems I OSU, Winter 2009 Solutions - Problem Set 3 Problem 1
Feb. 11, 2009
1
Problem 2
x(t) h(t) = x(2-t)
1
1
0
1
2
t
*
0
1
2
t
-1
-1
The graph of this convolution is given below.
2
0, t 1 -1 d = -t, 0 t-1 1 1 1 d + t-1 1 -1 d + 0 y(t) = x(t)