Chapter 3
PERIODIC SEQUENCES
Copyright c 1996 by Ali H. Sayed. All rights reserved. These notes are distributed only to the students attending the undergraduate DSP course EE113 in the Electrical Engineering Department at UCLA. The notes cannot be reprodu

1
EE113 Fall 2012 - Homework 3
Problem 5.3 Find the impulse response sequences of the following systems:
1
(a) The relaxed system y (n) = 3 y (n 1) + x(n + 1).
1
(b) The system cfw_y (n) = 3 y (n 1) + x(n + 1), y (1) = 1.
Which system is LTI?
Solution: Th

UCLA
Dept. of Electrical Engineering
EE113
Problem Set 5
Due: 11/08/2012
Reading Assignment: Chapters 12 and 13.
1. Problem 12.1.
2. Problem 12.11.
3. Problem 12.21.
4. Problem 13.4.
5. Problem 13.5.
6. Problem 13.11 part (a) only.
7. Computer Exercise: G

EE113 - Fall 2012 - Quiz 1 - Solution
1. The various parts of this question are independent of one another.
(a) Sampling Consider the discrete-time sequence:
8
Find two dierent continuous-time signals that would produce this sequence if the sampling frequ

UCLA
Dept. of Electrical Engineering
EE113
Quiz 1, Fall 2012
This quiz consists of three problems. Please justify your answers clearly;
a correct answer with no justication will not receive credit. Please write
your name clearly on each page. Good Luck!
1

EE 113 - Fall 2012
Solution for Homework 1
1) Consider the continuous-time signal
sequence
that are obtained by sampling
.
where is in seconds. Plot the samples of the
at multiples of
second over the interval
2) Consider the sequences
a) Plot the samples

1
EE113 Fall 2012 - Homework 2
Problem 3.1 What is the angular frequency of the sequence x(n) = ej 5n/4 ?
Solution: It is 5/4 + 2 = 3/4 by denition.
Problem 3.3 Order the following sequences according to (a) increasing angular frequencies and (b) decreasi

UCLA
Dept. of Electrical Engineering
EE113
Problem Set 1
Due: 10/09/2012
Reading Assignment: Chapters 1 and 2.
1. Problem 1.1.
2. Problem 1.12 (but not part (d).
3. Are the following signals one or multi-dimensional? Are they continuous-time
or discrete-t

UCLA
Dept. of Electrical Engineering
EE113
Problem Set 2
Due: 10/16/2012
Reading Assignment: Chapters 3, 4, and 5
1. 3.1.
2. 3.3. Write down the angular frequency and period for each sequence.
3. 3.7.
4. 3.12 (only the rst 4 parts).
5. 3.26.
6. 4.1.
7. 4.

UCLA
Dept. of Electrical Engineering
EE113
Problem Set 3
Due: 10/23/2012
Reading Assignment: Chapters 5 and 6.
1. Problem 5.3 (parts a and b).
2. Problem 5.9, parts (a), (b), and (c).
3. Problem 5.11, parts (a), (b), and (e).
4. 5.16.
5. 5.25.
6. 6.2.
7.

UCLA
Dept. of Electrical Engineering
EE113
Problem Set 4
Due: 10/30/2012
Reading Assignment: Chapters 9, 10 (except for 10.4 and 10.5), and 11.
1. 9.3.
2. 9.5.
3. 9.15.
4. Parts (a) and (b) of 9.19.
5. 10.1.
6. 10.8.
7. 10.22.
8. Part (a) of 10.23.
9. 11.

Chapter 2
SOME BASIC SEQUENCES
Copyright c 1996 by Ali H. Sayed. All rights reserved. These notes are distributed only to the
students attending the undergraduate DSP course EE113 in the Electrical Engineering Department
at UCLA. The notes cannot be repro

1
EE113 Fall 2012 - Homework 4
Problem 9.3 Let
X (z ) =
1
z 1
+
z 1/4 (z 1/3)2
Describe all sequences x(n) whose z -transform coincide with X (z ).
Solution: By inspection, we have a pole at z = 1/4, two poles at z = 1/3 and two poles at z = 0. The possib

Midterm Review
Why Digital Signal Processing?
Most signals are CT (e.g., speech and
audio). But:
digital computers are fast (real time in
many apps), efficient, and flexible and
Several techniques such as encryption
(for security) and compression techni

Chapter 4
DISCRETE-TIME SYSTEMS
Copyright c 1996 by Ali H. Sayed. All rights reserved. These notes are distributed only to the students attending the undergraduate DSP course EE113 in the Electrical Engineering Department at UCLA. The notes cannot be repr

Chapter 5
THE IMPULSE RESPONSE SEQUENCE
Copyright c 1996 by Ali H. Sayed. All rights reserved. These notes are distributed only to the students attending the undergraduate DSP course EE113 in the Electrical Engineering Department at UCLA. The notes cannot

Chapter 6
LINEAR CONVOLUTION
Copyright c 1996 by Ali H. Sayed. All rights reserved. These notes are distributed only to the students attending the undergraduate DSP course EE113 in the Electrical Engineering Department at UCLA. The notes cannot be reprodu

Chapter 7
HOMOGENEOUS DIFFERENCE EQUATIONS
Copyright c 1996 by Ali H. Sayed. All rights reserved. These notes are distributed only to the students attending the undergraduate DSP course EE113 in the Electrical Engineering Department at UCLA. The notes can

Chapter 12
DISCRETE-TIME FOURIER TRANSFORM
Copyright c 1996 by Ali H. Sayed. All rights reserved. These notes are distributed only to the students attending the undergraduate DSP course EE113 in the Electrical Engineering Department at UCLA. The notes can

Chapter 13
FREQUENCY RESPONSE
Copyright c 1996 by Ali H. Sayed. All rights reserved. These notes are distributed only to the students attending the undergraduate DSP course EE113 in the Electrical Engineering Department at UCLA. The notes cannot be reprod

All-Pass Systems An all-pass system will be defined as a causal and stable LTI system that has unit magnitude response over the entire frequency range [-, ]. The condition of causality means that its impulse response sequence is a right-sided sequence so

Chapter 15
THE DISCRETE FOURIER TRANSFORM
Copyright c 1996 by Ali H. Sayed. All rights reserved. These notes are distributed only to the students attending the undergraduate DSP course EE113 in the Electrical Engineering Department at UCLA. The notes cann

Chapter 2
SOME BASIC SEQUENCES
Copyright c 1996 by Ali H. Sayed. All rights reserved. These notes are distributed only to the students attending the undergraduate DSP course EE113 in the Electrical Engineering Department at UCLA. The notes cannot be repro

EE 113: Digital Signal Processing
Spring 2015
Prof. Mihaela van der Schaar (Instructor)
Homework #2
Solve the following problems from the electronic versions of the chapters of An
Undergraduate Course on Discrete-Time Signal Processing by A.H. Sayed
Probl