# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

### lecture17

Course: ECE 313, Fall 2008
School: University College of...
Rating:

Word Count: 920

#### Document Preview

Linear EE313 Systems and Signals Spring 2009 Frequency Response of Discrete-Time Systems Prof. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at Austin Initial conversion of content to PowerPoint by Dr. Wade C. Schwartzkopf Complex Exponentials Complex exponentials have special property when they are input into LTI systems. Output will be same complex exponential weighted...

Register Now

#### Unformatted Document Excerpt

Coursehero >> Puerto Rico >> University College of the Caribbean >> ECE 313

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
Linear EE313 Systems and Signals Spring 2009 Frequency Response of Discrete-Time Systems Prof. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at Austin Initial conversion of content to PowerPoint by Dr. Wade C. Schwartzkopf Complex Exponentials Complex exponentials have special property when they are input into LTI systems. Output will be same complex exponential weighted by H[z] y[ n] = h[ n] f [ n] = h[ n] z n = m = n h[ m] z n m m = =z h[m]z m = z n H [ z] When we specialize the z-domain to frequency domain, the magnitude of H[z] will control which frequencies are attenuated or passed 17 - 2 Frequency Response For continuous-time systems, response to complex e j t H ( j ) e j t sinusoid is frequency response cos( t ) H ( j ) cos( t + H ( j ) ) frequency response For discrete-time systems, response to complex sinusoid is e j k H (e j ) e j k cos( k ) H ( e j ) cos( k + H ( e j ) ) For real-valued impulse response, H(e-j ) = H*(ej ) e j k + e j k H e j e j k + H e j e j k 2 cos( k ) 2 H (e j ) cos( k ) 17 - 3 () () Response to Sampled Sinusoids Start with a continuous-time sinusoid Sample it every T seconds (substitute t = n T) We show discrete-time sinusoid with cos( k ) = cos( n T ) cos( n T ) cos( t ) Resulting in = T Discrete-time frequency is equal to continuoustime frequency multiplied by sampling period 17 - 4 Example Calculate the frequency response of the system given as a difference equation as y[n + 1] 0.8 y[n] = x[n + 1] Assuming zero initial conditions we can take the z-transform of this difference equation Y [ z ]( z 0.8) = X [ z ]z Y [ z] z 1 H [ z] = = = X [ z ] z 0.8 1 0.8 z 1 j Since z = e He [] j 1 1 = = j 1 0.8e 1 0.8( cos j sin ) 17 - 5 Example Group real and imaginary parts He [] j j 1 = (1 0.8 cos ) + j 0.8 sin 1 The absolute value (magnitude response) is He [ ] = (1 0.8 cos ) + j 0.8 sin = 1 (1 0.8 cos ) 2 + ( 0.8 sin ) 2 17 - 6 1 = 1.64 1.6 cos Example The angle (phase response) is H e () j 0.8 sin = 0 tan 1 0.8 cos 1 where 0 comes from the angle of the nominator and the term after comes from the denominator of H ( e j ) Reminder: Given a complex number a + j b the absolute value and angle is given as a + j b = a 2 +b 2 1 b a + j b = tan a 17 - 7 Example We can calculate the output of this system for a sinusoid at any frequency by substituting with the frequency of the input sinusoid. H ( e j ) 5 H ( e j ) 53.13 2 3 17 - 8 2 3 Discrete-time Frequency Response As in previous example, frequency response of a discrete-time system is periodic 2 with Why? Frequency response is function of the complex j j ( + 2 m) exponential which is periodic with 2 : e = e Absolute value of discrete-time frequency response is even and angle is odd symmetric. Discrete-time sinusoid is symmetric around cos( ( + 2m ) n ) = cos( n + 2mn ) = cos n cos( ( x ) n ) = cos( x n ) cos( n ) sin ( x n ) sin ( n ) = cos( x n ) cos( n ) cos( + x ) = cos( x ) 17 - 9 Aliasing and Sampling Rate Continuous-time sinusoid can have a frequency from 0 to infinity By sampling a continuous-time sinusoid, cos( t ) sample t = nT 0 T < 0 < = f s 0 2f < f s 0 f < f s / 2 T We only can represent frequencies up to half of the sampling frequency. Higher frequencies exist would be wrapped to some other frequency in the range. 17 - 10 Discrete-time frequency unique from 0 to cos( n T ) = cos( n ) Effect of Poles and Zeros of H[z] The z-transform of a difference equation can be written in a general form as H [ z ] = bn ( z z1 )( z z2 ) ( z zm ) ( z 1 )( z 2 ) ( z m ) We can think of complex number as a vector in the complex plane. Im Since z and zi are both complex numbers the difference is again a complex number thus a vector in the complex plane. zi z zi z Re 17 - 11 Effect of Poles and Zeros of H[z] Each difference term in H[z] may be represented as a complex number in polar form Magnitude is the distance of the pole/zero to the chosen point (frequency) on unit circle. Angle is the angle of vector with the horizontal axis. r1e j1 r2e j2 rm e jm H ( e j ) = bn d1e j1 d 2e j 2 d m e j m Im 1 d1 d2 r...

Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

University College of the Caribbean - ECE - 382
CHARACTERIZATION OF EMBEDDED WORKLOADSCourse Project Embedded Software SystemsAjay Joshi University of Texas, Austin March 24, 2004MOTIVATIONMarketing RequirementsEmerging ApplicationsTechnology Microprocessor DesignBottlenecks in Existing
University College of the Caribbean - ECE - 382
EE 382C EMBEDDED SOFTWARE SYSTEMS Literature Survey Report Characterization of Embedded Workloads Ajay Joshi March 30, 2004ABSTRACTSecurity applications are a class of emerging workloads that will play a central role in determining the performance
University College of the Caribbean - ECE - 382
Data Word Length Reduction for LowPower DSP SoftwareKyungtae Han March 24, 2004Low-Power Software Portable computing demands minimizing power dissipation due to limited power Minimizing power consumption Reducesupply voltage Decrease switch
University College of the Caribbean - ECE - 382
EE382C: LITERATURE SURVEY, APRIL 2, 20041Data Word Length Reduction for Low-Power DSP SoftwareKyungtae HanAbstract The increasing demand for portable computing accelerates the study of minimizing power dissipation. Most power in processes is co
University College of the Caribbean - ECE - 382
Data Wordlength Reduction for LowPower Signal Processing SoftwareKyungtae Han May 3rd, 2004 The University of Texas at AustinMay 3, 2004Low-Power at Software Level Portable wireless computing demands minimizing power dissipation due to limited
University College of the Caribbean - ECE - 382
EE382C: FINAL REPORT, MAY 13, 20041Data Wordlength Reduction for Low-Power Signal Processing SoftwareKyungtae HanAbstract Reducing power consumption prolongs battery life and increases integration. In digital CMOS designs, switching activity is
University College of the Caribbean - ECE - 382
Distributed Process Network Deadlock Detection &amp; ResolutionAlex OlsonEmbedded Software Spring 20041. What is Process Networks?Process Network (PN) [Kahn74]Concurrent processes communicate only over one-way channels (FIFO queues) Reads block
University College of the Caribbean - ECE - 382
0Distributed Deadlock Detection for Distributed Process NetworksAlex OlsonAbstractThis paper presents a discussion of the Kahn process network (PN) model and the challenges in distributing it onto multiple networked workstations. Compared to a
University College of the Caribbean - ECE - 382
Deadlock Detection for Distributed Process NetworksAlex Olson Embedded Software Spring 2004Problem StatementImplement deadlock detection in a distributed process network (DPN)Deadlock detection required for PN scheduling algorithms Deadlock no
University College of the Caribbean - ECE - 382
0Distributed Deadlock Detection for Distributed Process NetworksAlex Olson Embedded Software SystemsAbstractThe distributed process network (DPN) model allows for greater scalability and performance over a non-distributed process network model
University College of the Caribbean - ECE - 382
Modeling and Simulation of Data Transmission in an ADSL TransceiverEmbedded Software Systems Literature Survey Briefing By Elmustafa Erwa March 24, 2004Overview1 1 1 1 1Introduction to ADSL Technology ADSL Transceiver Architecture Block Diagram
University College of the Caribbean - ECE - 382
Modeling of an ADSL Transceiver Data Transmission SubsystemElmustafa Erwa ABSTRACT Recently, there has been an increase in demand for digital services provided over the public telephone line network. Asymmetric digital subscriber lines (ADSL) transm
University College of the Caribbean - ECE - 382
Modeling and Simulation of Data Transmission in an ADSL TransceiverEmbedded Software Systems Literature Survey Briefing By Elmustafa Erwa May 03, 2004Overview1 1 1 1 1ADSL Transceiver Architecture Problem Statement System Modeling Implementatio
University College of the Caribbean - ECE - 382
Modeling and Simulation of an Asynchronous Digital Subscriber Line Transceiver Data Transmission SubsystemElmustafa Erwa ABSTRACT Recently, there has been an increase in demand for digital services provided over the public telephone line network. As
University College of the Caribbean - ECE - 382
Modeling a Multicarrier Wireless Communication TransceiverEmbedded Software Systems Literature Survey March 24,2004By Hunaid LotiaOverview Multicarrier Modulation Motivation Existing Research OFDM (Orthogonal FrequencyDivision Multiplexing
University College of the Caribbean - ECE - 382
EE382C: EMBEDDED SOFTWARE SYSTEMS LITERATURE SURVEYModeling a Multicarrier Wireless Communication TransceiverHunaid LotiaAbstract The objective of this work is to develop a model for the simulation of a multicarrier wireless communication trans
University College of the Caribbean - ECE - 382
EE382C: EMBEDDED SOFTWARE SYSTEMS FINAL REPORTModeling a Multicarrier Wireless Communication TransceiverHunaid LotiaAbstractThe objective of this work is to develop a model for the simulation of a multicarrier wireless communication transceiv
University College of the Caribbean - ECE - 382
Cooperative Diversity in Wireless NetworksAlex IcazaUniversity of Texas at AustinEmbedded Software Systems Spring 2004Overview Overview Problem Statement &amp; Objective Diversity in Wireless Systems (Background) Spatial Diversity Temporal Dive
University College of the Caribbean - ECE - 382
EE382C-9 Embedded Software Systems (Spring 2004)Literature SurveyModeling Cooperative Diversity in a Wireless Relay ChannelAlejandro Icaza Department of Electrical and Computer Engineering The University of Texas at Austin icaza@ece.utexas.edu
University College of the Caribbean - ECE - 382
Modeling Cooperative Diversity in a Wireless Relay ChannelAlex IcazaThe University of Texas at AustinEmbedded Software Systems Spring 2004Overview Problem Statement &amp; Objectives Background Cooperative Diversity Modeling with Demonstration
University College of the Caribbean - ECE - 382
EE382C-9 Embedded Software Systems (Spring 2004)Final ReportModeling Cooperative Diversity in a Wireless Relay ChannelAlejandro IcazaDepartment of Electrical and Computer Engineering The University of Texas at Austin icaza@ece.utexas.eduAbst
University College of the Caribbean - ECE - 382
Modeling In-Network Processing and Aggregation in Sensor NetworksAjay Mahimkarmahimkar@ece.utexas.edu The University of Texas at Austin March 24, 2004Sensor Networks Goals &amp; ChallengesDistributed Sensing of physical phenomenaEstablish path
University College of the Caribbean - ECE - 382
1Modeling In-Network Processing and Aggregation in Sensor NetworksAjay Mahimkar Department of Electrical and Computer Engineering The University of Texas at Austin, TX 78713, USA mahimkar@ece.utexas.eduAbstract The rapid advances in processor, m
University College of the Caribbean - ECE - 382
Modeling In-Network Processing and Aggregation in Sensor NetworksAjay Mahimkar EE 382C Embedded Software Systems Prof. B. L. Evans May 5, 2004Sensor NetworksMonitor physical environment from remote locations Challenges Battery is the most pressi
University College of the Caribbean - ECE - 382
1Modeling In-Network Processing and Aggregation in Sensor NetworksAjay Mahimkar mahimkar@ece.utexas.eduAbstract The rapid advances in processor, memory and radio technology have enabled the development of distributed networks of sensor nodes cap
University College of the Caribbean - ECE - 382
Modeling of a Humanoid and Multi-agent System (MAS)EE 382C.9 Embedded Software Systems Spring 2004 Literature Survey Briefing byYuklai SuenMarch 24th, 2004ObjectiveMAS Project Develop MAS for research and educationalpurpose, e.g. RoboCup
University College of the Caribbean - ECE - 382
Modeling of a Humanoid and Multi-agent SystemEE382C: Embedded Software Systems Literature Survey Yuklai Suen Dept. of Electrical and Computer Engineering The University of Texas at AustinAbstract. This survey briefly describes the project to imple
University College of the Caribbean - ECE - 382
Modeling of Humanoid and Multi-agent SystemEE 382C.9 Embedded Software Systems Spring 2004 Final Presentation byYuklai SuenMay 5th, 2004Project DescriptionObjectivedevelop a network deployment algorithm for sensor network Humanoid Multi-agent
University College of the Caribbean - ECE - 382
A Genetic-Algorithm Based Mobile Sensor Network Deployment Algorithm EE382C: Embedded Software Systems Final Report Yulai Suen Department of Electrical and Computer Engineering The University of Texas at AustinAbstract. This paper describes a genet
University College of the Caribbean - ECE - 382
MPEG-4 Structured AudioMihir Anandpara EE 382C Embedded Software SystemsOverview Motivation MPEG-4Structured Audio formats Decoder/Synthesizer Implementations Project ObjectivesMotivation and Background MPEG-4standard Traditional aud
University College of the Caribbean - ECE - 382
1MPEG-4 Structured Audio SystemsMihir Anandpara The University of Texas at Austin anandpar@ece.utexas.eduAbstract The MPEG-4 standard has been proposed to provide high quality audio and video content over the Internet. This content is represented
University College of the Caribbean - ECE - 382
MPEG-4 Structured AudioMihir Anandpara EE 382C Embedded Software SystemsOverview StructuredAudio Systems Audio Synthesis and Effects processing in MPEG-4 AudioBIFS layer in MPEG-4 Software Implementation and Results Conclusions and Future
University College of the Caribbean - ECE - 382
1MPEG-4 Structured Audio SystemsMihir Anandpara The University of Texas at Austin anandpar@ece.utexas.eduAbstract The MPEG-4 standard has been proposed to provide high quality audio and video content over the Internet. This content is represented
University College of the Caribbean - ECE - 6713
EE345S: Real Time DSP Lab Tasks TransmitterObjective:Lab 6: Quadrature Amplitude Modulation (QAM)This lab deals with implementation of a Quadrature amplitude modulation (QAM) transmitter system, used for digital data transmission over bandpass
University College of the Caribbean - ECE - 6713
EE345S: Real Time DSP Lab TasksObjective:Lab 5: Pulse Amplitude Modulation (PAM)This lab deals with implementation of a baseband pulse amplitude modulation (PAM) system, used for digital data transmission.Lab slides:All the slides referr
University College of the Caribbean - ECE - 313
EE313 Linear Systems and SignalsSpring 2009Laplace TransformProf. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at AustinInitial conversion of content to PowerPoint by Dr. Wade C. SchwartzkopfForward Lapl
University College of the Caribbean - ECE - 313
EE 313 Linear Systems and SignalsSpring 2009System State and Differential EquationsProf. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at AustinInitial conversion of content to PowerPoint by Dr. Wade C. Sch
University College of the Caribbean - ECE - 313
EE313 Linear Systems and SignalsSpring 2009System RealizationProf. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at AustinInitial conversion of content to PowerPoint by Dr. Wade C. SchwartzkopfPassive Cir
University College of the Caribbean - ECE - 313
EE313 Linear Systems and SignalsSpring 2009Inverse Laplace TransformProf. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at AustinInitial conversion of content to PowerPoint by Dr. Wade C. SchwartzkopfInve
University of Texas - M - 408
1 Letter of Intent Transforming Calculus Education: A Systemic Approach A Joint Proposal by the Department of Mathematics and the Division of Continuing and Innovative Education Background with Statement of Need and Significance In 2000, the Texas Hi
University College of the Caribbean - MA - 408
1 Letter of Intent Transforming Calculus Education: A Systemic Approach A Joint Proposal by the Department of Mathematics and the Division of Continuing and Innovative Education Background with Statement of Need and Significance In 2000, the Texas Hi
University of Texas - CS - 341
Name: 1 2a b 3 4a b c d 5a b c 6 7 8a b c Total 10 5 10 10 15 15 15 15 5 15 15 15 15 5 5 5 175 CS 341 First Midterm Exam Practice 1. Use extra paper to determine your solutions then neatly transcribe them (including intermediate steps) onto these she
University College of the Caribbean - CS - 341
Name: 1 2a b 3 4a b c d 5a b c 6 7 8a b c Total 10 5 10 10 15 15 15 15 5 15 15 15 15 5 5 5 175 CS 341 First Midterm Exam Practice 1. Use extra paper to determine your solutions then neatly transcribe them (including intermediate steps) onto these she
University of Texas - CS - 341
Name: 1 2a b 3 4a b c d 5a b c 6 7 8a b c Total 10 5 10 10 15 15 15 15 5 15 15 15 15 5 5 5 175 CS 341 First Midterm Exam Practice 1. Use extra paper to determine your solutions then neatly transcribe them (including intermediate steps) onto these she
University College of the Caribbean - CS - 341
Name: 1 2a b 3 4a b c d 5a b c 6 7 8a b c Total 10 5 10 10 15 15 15 15 5 15 15 15 15 5 5 5 175 CS 341 First Midterm Exam Practice 1. Use extra paper to determine your solutions then neatly transcribe them (including intermediate steps) onto these she
University of Texas - CS - 341
Name: 1a b c d 2 3a b c 4a b 5a b 6 Total 15 15 15 15 15 8 8 8 5 15 8 8 20 155CS 341 Second Midterm Exam PracticeUse extra paper to determine your solutions then neatly transcribe them onto these sheets. You may use any claim we proved in class as
University College of the Caribbean - CS - 341
Name: 1a b c d 2 3a b c 4a b 5a b 6 Total 15 15 15 15 15 8 8 8 5 15 8 8 20 155CS 341 Second Midterm Exam PracticeUse extra paper to determine your solutions then neatly transcribe them onto these sheets. You may use any claim we proved in class as
University of Texas - CS - 341
Name: 1a b c d 2 3a b c 4a b 5a b 6 Total 15 15 15 15 15 8 8 8 5 15 8 8 20 155CS 341 Second Midterm Exam PracticeUse extra paper to determine your solutions then neatly transcribe them onto these sheets. You may use any claim we proved in class as
University College of the Caribbean - CS - 341
Name: 1a b c d 2 3a b c 4a b 5a b 6 Total 15 15 15 15 15 8 8 8 5 15 8 8 20 155CS 341 Second Midterm Exam PracticeUse extra paper to determine your solutions then neatly transcribe them onto these sheets. You may use any claim we proved in class as
University of Texas - CS - 341
Name: CS 341 Practice Final Exam 1. Please write neatly. You will lose points if we cannot figure out what you are saying. 2. Whenever you answer a question with a machine or a grammar, add comments to help us figure out what you are trying to do. 3.
University College of the Caribbean - CS - 341
Name: CS 341 Practice Final Exam 1. Please write neatly. You will lose points if we cannot figure out what you are saying. 2. Whenever you answer a question with a machine or a grammar, add comments to help us figure out what you are trying to do. 3.
University of Texas - CS - 341
Name: CS 341 Practice Final Exam 1. Please write neatly. You will lose points if we cannot figure out what you are saying. 2. Whenever you answer a question with a machine or a grammar, add comments to help us figure out what you are trying to do. 3.
University College of the Caribbean - CS - 341
Name: CS 341 Practice Final Exam 1. Please write neatly. You will lose points if we cannot figure out what you are saying. 2. Whenever you answer a question with a machine or a grammar, add comments to help us figure out what you are trying to do. 3.
University of Texas - CS - 341
Coloring Grid Points, without Rabbits and Snakes Jayadev Misra 12/18/96 Problem: The following verbatim description is from Dijkstra, EWD-1248.Show that, for any finite set of grid points in the plane, we can colour each of the points either red or
University College of the Caribbean - CS - 341
Coloring Grid Points, without Rabbits and Snakes Jayadev Misra 12/18/96 Problem: The following verbatim description is from Dijkstra, EWD-1248.Show that, for any finite set of grid points in the plane, we can colour each of the points either red or
University of Texas - PHR - 452
Prof. Patrick J. DavisDrug MetabolismProf. Patrick Davis Basic Medicinal Chem Principles PHR 143M Fall-04Prof. Patrick J. DavisImportance of Drug Metabolism The basic premise: Lipophilic Drugs -&gt; Hydrophilic Metabolites (Not Excreted) (Excret
University of Texas - PHR - 452
Phase-1 Oxidations: Cytochrome P-450Prof. Patrick Davis Basic Med Chem Principles PHR 143M Fall-04Patrick J. DavisProf. Patrick J. DavisCytochrome(s) P-450 [CYP-450] Heme enzymes Enzyme family: ~50 isoforms (not isozymes) Binds CO -&gt; 450 nm
University of Texas - PHR - 452
Phase-2 Drug MetabolismProf. Patrick Davis Basic Med Chem Principles PHR 143M Fall-04Prof. Patrick J. DavisPhase-2 (Conjugation) Reactions Glucuronidation - Most Important Huge supply of glucuronic acid Reacts with many functional groups Ver
University of Texas - PHR - 452
Factors Affecting Drug MetabolismProf. Patrick J. DavisProf. Patrick Davis Basic Med Chem Principles PHR 143M Fall-04Factor Affecting Drug Metabolism The Big PictureProf. Patrick J. DavisFactor Affecting Drug Metabolism The Simple View Con
University College of the Caribbean - ECE - 382
UT Austin, ECE VLSI Design 1. IntroductionGoals of this CourseEE 382M (#16675) VLSI ISpring 2009 David Z. Pan Electrical and Computer Engineering The University of Texas at Austin Learn to design and synthesize state-of-theart digital Very Larg
University College of the Caribbean - ECE - 382
VLSI-ISpring 2009 (Prof. David Pan) Homework #0: Assigned Jan. 20, Due Jan. 22 in class1. Name:2. Please give a brief description of your background (relevant courses, work experiences, etc.) and interest in the course. Whats your expectation fro