EE 341
Discrete-Time Linear Systems Week 10
Spring 2011
A Final Exam Example Problem 1 (Multiple Choice QuestionsCircle the Single Best
Answer and Justify it.)
a) It is desired to build a sampling system which takes a recorded orchestral music signal s (t
EE341, Winter 2014
Problem Set #7
Due: 5 March 14
Problem 1 is from the text by Oppenheim, Willsky & Nawab, and problems 2-4 are adapted
from the text by Phillips, Parr & Riskin.
1. 5.55(b)
2. Consider two length-4 discrete time signals:
x[n] = ej
2n
4
h[
Spring 2011
Clark
EE 341
Lab 3: The DFT and Digital Filtering
Due: In your discussion section May 11-13
When using a digital computer, frequency analysis and filtering requires that we use
the Discrete Fourier Transform (DFT). In this lab we spend some ti
Spring 2011
EE 341
Lab 1
Lab 1: Elementary Music Synthesis
Due: In your discussion section 4/13 (Sec. AA and Sec. AD), 4/14 (Sec. AB),
or 4/15 (Sec. AC). The hard copy report is to be turned in to your TA just
before the above discussion begins. In additi
EE341, Winter 2014
HW #1 Solutions
Due: 15 January 14
1. A discrete-time signal is shown in Figure P1.22. Sketch and label carefully each of the
following signals:
Figure P1.22
(d) x[3n + 1]
(e) x[n]u[3 n]
(f) x[n 2][n 2]
Solution
(d) Since x[n] is non-ze
EE 341
Spring 2010
Prof. Atlas
Final Exam
June 9, 2010
Your Name:
Solutions
Exam Instructions:
1. Open book and notes. But as listed in our course syllabus: No turned-on
electronic devices (calculators, laptops, ipods, cell phones, beepers, etc.)
are allo
EE 341
Spring 2009
Prof. Atlas
Final Exam
June 10, 2009
Your Name:
Solutions
Exam Instructions:
1. Open book and notes. But as listed in our course syllabus: No electronic
devices (calculators, laptops, netbooks, PDAs, cell phones, beepers, etc.)
are allo
EE 341
Summer 2011
Discrete Time Linear Systems
Midterm
Your Name:
Exam Instructions:
1. Open book and notes. No electronic devices (calculators, laptops, ipods, cell phones,
etc.)
Please turn all devices o now.
2. Do not open the exam until 1:10.
3. Jus
EE 341
Autumn 2010
Discrete Time Linear Systems
Midterm
Your Name:
Exam Instructions:
1. Open book and notes. No electronic devices (calculators, laptops, ipods, cell phones,
etc.)
Please turn all devices o now.
2. Do not open the exam until 2:30.
3. Jus
EE 341 Lab 2 Report
Assignment 1
In this part I use imread command to store an image into a 3D matrix, and then use the command
rgb2grey to convert the image into the grey scale stored as a 2D matrix in Matlab. Next I
convolve edge detector with the 2D ma
University of Washington Bothell
Electrical Engineering Program
BEE 341 Discrete-time Linear Systems
Homework 1
Instruction: Work out the problems and show all steps of your solutions. When plotting graphs, put label
on all axes. Write neatly and legibly.
BEE 341 Discrete-Time Linear Systems
Lesson Week 4: The Discrete-Time Fourier
Transform (Part I)
The Discrete-Time Fourier Transform (DTFT):Definition
The DTFT (Discrete-Time Fourier Transform) is a representation of discretetime sequences (signals) in te
BEE 341 Discrete-Time Linear Systems
Lesson Week 2: Characteristics of Discrete-Time
Signals and Discrete-Time Systems
Tadesse Ghirmai
Learning Goals
After completing this lecture students will be able to
Classify discrete-time signal based on properties
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University of Washington Bothell
Electrical Engineering Program
BEE 341 Discrete-time Linear Systems
Homework 2
Instruction: Work out the problems and show all steps of your solutions. When plotting graphs, put label
on all axes. Write neatly and legibly.
BEE 341 Discrete-Time Linear Systems
Lesson Week 6: Discrete Fourier Transform (DFT)
The Discrete Fourier Transform
Recall that DTFT is calculated from a discrete-time signals, x[n], and the
resulting function X(ej) is a continuous function, and, therefor
BEE 341 Discrete-Time Linear Systems
Lesson Week 1: Introduction to Discrete-Time Signals
Tadesse Ghirmai
Learning Goals
After completing this lecture students will be able to
Describe the difference between continuous-time and discrete-time
signals
Repre
BEE 341 Discrete-Time Linear Systems
Lesson Week 3: LTI Systems (Continuation)
Tadesse Ghirmai
Learning Goals
After completing this lecture students will be able to
Determine the output of an LTI system from its impulse response using
convolution.
Determi
HW 2 Solutions
EE 341 Autumn 2011
Problem 1
Part a)
Part a)
Alternatively, could use Method 1
Part b)
Part c)
Part c)
Alternatively could use Method 1
Part d)
Problem 2
Part a)
And for xo[n]
Part b)
Part c)
Part d)
Part e)
Problem 3
Problem 4: Book 1.26
P
HW 8 Solutions
EE341
Autumn 2011
Problem 1
Design fft algorithm for DFT length 4: I chose
Decimation in time radix 2, like in class.
SOLUTION
Let the 4 point DFT of x[n] be defined as X[k], and we note that:
X[k] =
3
X
kn
x[n]W4
n=0
We can first try and b
4/25/2017
EE 341:Discrete time linear signals and
systems
Lecture #16
UWEE TC Chen
DISCRETE TIME SIGNAL CONVOLUTION
Example: Find = [], where = [] and
= [ + 2], where .
First way: flip []
2, two functions starts to overlap.
The summation range is from 0
5/3/2017
EE 341:Discrete time linear signals and
systems
Lecture #21
UWEE TC Chen
STABILITY AND THE NATURAL
RESPONSE
1
5/3/2017
STABILITY AND THE NATURAL RESPONSE
Recall the Natural Solution was
= 1 1 + 2 2 + +
Roots, , of the characteristic equation ca
5/2/2017
EE 341:Discrete time linear signals and
systems
Lecture #20
UWEE TC Chen
COMPLEMENTARY/NATURAL RESPONSE
The Complementary (Natural) Response [] is the solution to the
homogeneous equation:
[ ] = 0 (where 0 0)
=0
Solving the Natural Response:
3)
4/26/2017
EE 341:Discrete time linear signals and
systems
Lecture #17
UWEE TC Chen
DISCRETE TIME SIGNAL CONVOLUTION
Example: Find = [], where = [ + 2] and
Use:
= [], where < 1.
[]
+1
=
First way: flip []
1
=
2, two functions overlap.
The summation ran
5/1/2017
EE 341:Discrete time linear signals and
systems
Lecture #19
UWEE TC Chen
TESTING PROPERTIES OF LTI SYSTEMS
Example #1: Is =
1
3
[] BIBO stable? YES
[] =
=
0
1
3
=
1
1
1
3
<
Example #2: Is = [] BIBO stable? NO
[] = 1 =
=
0
Example #3: Is = 3 []
5/5/2017
SUMMARY: FIR AND IIR FILTER
FIR / IIR filter
FIR
> Inherently BIBO (bounded-input, bounded-output) stable
> Nonzero pole does not exist in its transfer function
> Easy to implement
> Can be designed to have linear phase property
IIR (analog fil