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Introduction and Course Overview,Introduction 1 1,Signals and Systems What for 1 1. Course Perspective From Here to There 1 3,Course Syllabus 1 4. Computer Tools 1 6, Introduction to Mathematical Modeling of Signals and Systems 1 8. Mathematical Representation of Signals 1 8,Mathematical Representation of Systems 1 10. Thinking About Systems 1 12,The Next Step 1 13,Review of Sine and Cosine Functions 2 2.
Sinusoidal Signals 2 6,Relation of Frequency to Period 2 7. Phase Shift and Time Shift 2 9,Sampling and Plotting Sinusoids 2 13. Complex Exponentials and Phasors 2 16,Review of Complex Numbers 2 16. Complex Exponential Signals 2 23,The Rotating Phasor Interpretation 2 24. Phasor Addition 2 28,Phasor Addition Rule 2 28,Summary of Phasor Addition 2 32.
Physics of the Tuning Fork 2 33,Equations from Laws of Physics 2 34. General Solution to the Differential Equation 2 35. Listening to Tones 2 38,Time Signals More Than Formulas 2 39. Spectrum Representation,The Spectrum of a Sum of Sinusoids 3 1. A Notation Change 3 6,Beat Notes 3 7,ECE 2610 Signals and Systems iii. Beat Note Spectrum 3 7,Beat Note Waveform 3 9,Multiplication of Sinusoids 3 10.
Amplitude Modulation 3 10,Periodic Waveforms 3 13,Nonperiodic Signals 3 14. Fourier Series 3 17,Fourier Series Analysis 3 18,Fourier Series Derivation 3 18. Orthogonality Property 3 20,Summary 3 22,Spectrum of the Fourier Series 3 22. Fourier Analysis of Periodic Signals 3 24,The Square Wave 3 24. Spectrum for a Square Wave 3 26,Synthesis of a Square Wave 3 27.
Triangle Wave 3 31,Triangle Wave Spectrum 3 33,Synthesis of a Triangle Wave 3 35. Convergence of Fourier Series 3 36,Time Frequency Spectrum 3 37. Stepped Frequency 3 38,Spectrogram Analysis 3 39,Frequency Modulation Chirp Signals 3 42. Chirped or Linearly Swept Frequency 3 42,Summary 3 45. Sampling and Aliasing,Sampling 4 1,Sampling Sinusoidal Signals 4 4.
The Concept of Aliasing 4 6,The Spectrum of a Discrete Time Signal 4 12. The Sampling Theorem 4 14,Ideal Reconstruction 4 16. Spectrum View of Sampling and Reconstruction 4 19,The Ideal Bandlimited Interpolation 4 20. FIR Filters,Discrete Time Systems 5 2,The Running Moving Average Filter 5 2. The General FIR Filter 5 5,iv ECE 2610 Signals and Systems.
The Unit Impulse Response 5 8,Convolution and FIR Filters 5 12. Using MATLAB s Filter Function 5 16,Convolution in MATLAB 5 17. Implementation of FIR Filters 5 18,Building Blocks 5 19. Block Diagrams 5 20,Linear Time Invariant LTI Systems 5 24. Time Invariance 5 25,Linearity 5 26,The FIR Case 5 28.
Convolution and LTI Systems 5 29,Derivation of the Convolution Sum 5 30. Some Properties of LTI Systems 5 32,Cascaded LTI Systems 5 33. Filtering a Sinusoidal Sequence with a Moving Average Filter 5 37. Frequency Response of FIR Filters,Sinusoidal Response of FIR Systems 6 1. Superposition and the Frequency Response 6 6,Steady State and Transient Response 6 10. Properties of the Frequency Response 6 14, Relation to Impulse Response and Difference Equation 6 14.
Periodicity of 6 16,Conjugate Symmetry 6 16, Graphical Representation of the Frequency Response 6 18. Cascaded LTI Systems 6 22,Moving Average Filtering 6 24. Plotting the Frequency Response 6 26,Filtering Sampled Continuous Time Signals 6 27. Interpretation of Delay 6 32,z Transforms,Definition of the z Transform 7 1. The z Transform and Linear Systems 7 3,The z Transform of an FIR Filter 7 3.
Properties of the z Transform 7 6,The Superposition Linearity Property 7 6. The Time Delay Property 7 7,A General z Transform Formula 7 8. ECE 2610 Signals and Systems v,The z Transform as an Operator 7 8. Unit Delay Operator 7 8,Convolution and the z Transform 7 10. Cascading Systems 7 12,Factoring z Polynomials 7 13.
Deconvolution Inverse Filtering 7 14, Relationship Between the z Domain and the Frequency Domain 7 16. The z Plane and the Unit Circle 7 16,The Zeros and Poles of H z 7 17. The Significance of the Zeros of H z 7 19,Nulling Filters 7 19. Graphical Relation Between z and 7 22,Useful Filters 7 24. The L Point Moving Average Filter 7 24,A Complex Bandpass Filter 7 26.
A Bandpass Filter with Real Coefficients 7 26,Practical Filter Design 7 26. Properties of Linear Phase Filters 7 26,The Linear Phase Condition 7 26. Locations of the Zeros of FIR Linear Phase Systems 7 27. IIR Filters,The General IIR Difference Equation 8 1. Block Diagram 8 2,Time Domain Response 8 2,Impulse Response of a First Order IIR System 8 3. Linearity and Time Invariance of IIR Filters 8 4, Step Response of a First Order Recursive System 8 6.
System Function of an IIR Filter 8 9,The General First Order Case 8 11. System Functions and Block Diagram Structures 8 12. The Transposed Structures 8 14,Relation to the Impulse Response 8 15. Poles and Zeros 8 16,Poles or Zeros at the Origin or Infinity 8 17. Pole Locations and Stability 8 18,Frequency Response of an IIR Filter 8 20. 3D Surface Plot of 8 23,The Inverse z Transform and Applications 8 23.
A General Procedure for Inverse z Transformation 8 24. Steady State Response and Stability 8 33,Second Order Filters 8 36. vi ECE 2610 Signals and Systems,Poles and Zeros 8 36. Impulse Response 8 39,Frequency Response 8 43,Example of an IIR Lowpass Filter 8 45. Continuous Time Signals and LTI Systems,Continuous Time Signals 9 1. Two Sided Infinite Length Signals 9 1,One Sided Signals 9 3.
Finite Duration Signals 9 4,The Unit Impulse 9 5,Sampling Property of the Impulse 9 7. Operational Mathematics and the Delta Function 9 8. Derivative of the Unit Step 9 9,Continuous Time Systems 9 11. Basic System Examples 9 11,Linear Time Invariant Systems 9 12. Time Invariance 9 12,Linearity 9 13,The Convolution Integral 9 13. Properties of Convolution 9 15,Impulse Response of Basic LTI Systems 9 15.
Integrator 9 16,Ideal delay 9 16,Convolution of Impulses 9 16. Evaluating Convolution Integrals 9 16,Step and Exponential 9 16. Square Pulse Input 9 19,Properties of LTI Systems 9 20. Cascade and Parallel Connections 9 20, Differentiation and Integration of Convolution 9 21. Stability and Causality 9 22,Frequency Response, The Frequency Response Function for LTI Systems 10 1.
Response to Real Sinusoid Signals 10 4,Symmetry of 10 5. Response to a Sum of Sinusoids 10 5,Periodic Signal Inputs 10 5. Ideal Filters 10 5,Simulation of Circuit Implementations 10 6. ECE 2610 Signals and Systems vii,viii ECE 2610 Signals and Systems. Introduction,Signals and systems what for,Course perspective.
Course syllabus,Instructor policies,Computer tools. Introduction to mathematical modeling of signals and sys. Signals and Systems What for, Electronics for audio iPod and wireless devices cell. phones wireless local area networking are all around us. What are some others, Signals and systems are an integral part of making these. devices perform their intended function, Signals convey information from one point to another. They may be generated by electronic means or by some. natural means such as talking walking your heart beating. an earthquake the sun heating the sidewalk,ECE 2610 Signal and Systems 1 1.
Chapter 1 Introduction and Course Overview, Systems process signals to produce a modified or transformed. version of the original signal, The transformation may be as simple a microphone con. verting a sound pressure wave into an electrical waveform. The four campuses of the University of Colorado are often. termed the CU System, In this class systems are specialized primarily to those that. process signals of an electrical nature, If we do not have an electrical signal directly we may use a. transducer to obtain one e g a thermistor to sense the. temperature of the heat sink in a computer power supply. In the traditions of electrical engineering signals and systems. means the mathematical modeling of signals and systems to. assist in the design and development of electronic devices. 1 2 ECE 2610 Signals and Systems,Intro to Logic Rhetoric Electron I Circuits.
Physics I Calculus I,Robotics Circuits I Writing I Lab Systems II. Computer Logic uCmp Sys Technical Communic Communic. Physics II Calculus II,Modeling Circuits II uP Lab Writing Lab Systems I. ECE 2610 Signals and Systems,Signals uComputer Embedded Computer Prob Communic. Physics III Calculus III Systems System Lab Sys Design Arch Design Statistics Systems II. Physical Prob Circuits,Electronics Statistics Systems I. Senior Circuits Semicond Electron I Advanced Feedback Circuits Prob. Seminar Systems II Devices I Lab Dig Des Ctrl Lab Systems II Statistics. Senior Electron II VLSI Circ Rapid Proto Multivar Electron I Modern. Emag II ADD Lab,Design Lab Design type FPGA Control I Lab DSP.
EM Theory Microwave CMOS RF Analog IC Semocond VLSI Signal Real Time. Apps Meas Lab IC Design Design Devices II Processing Process Lab DSP. Mixed Sig VLSI Fab,IC Design Lab,Course Perspective From Here to There. Course Perspective From Here to There,Chapter 1 Introduction and Course Overview. Course Syllabus g y,Spring Semester 2011, Instructor Dr Mark Wickert Office EB 292 Phone 255 3500. wickert eas uccs edu Fax 255 3589,http www eas uccs edu wickert ece2610. Office Hrs M W 12 45 1 15am M W 3 05pm 4 00pm others by appointment. Required James McClellan Ronald Schafer and Mark Yoder Signal Processing First. Text Prentice Hall New Jersy 2003 ISBN 0 13 090999 8. Optional The student version of MATLAB 7 x available under general software in the. Software UCCS bookstore Other specific programming tools will be discussed in class. Grading 1 Graded homework worth 20,2 Quizzes worth 15 total.
3 Laboratory assignments worth 20 total,4 Mid term exam worth 15. 5 Final MATLAB project worth 10,6 Final exam worth 20. Topics Text Weeks,1 Course Overview and Introduction 1 1 1 4 0 5. 2 Sinusoids 2 1 2 9 1 0,3 Spectrum Representation 3 1 3 9 1 0. 4 Sampling and Aliasing 4 1 4 6 1 0,5 FIR filters 5 1 5 9 1 5.
6 Frequency response of FIR filters 6 1 6 9 1 5 exam. 7 z Transforms 7 1 7 10 1 0,8 IIR Filters 8 1 8 12 2 0. 9 Continuous Time Signals and Systems 9 1 9 10 1 5. 10 Frequency Response 10 1 10 6 0 5, 11 Continuous Time Fourier Transform 11 1 11 11 1 5. 12 Filtering Modulation and Sampling 12 1 12 4 1 5 project. Note that topics 9 12 will most likely only be overviewed at the end of the. 1 4 ECE 2610 Signals and Systems,Course Syllabus,Instructor Policies. Homework papers are due at the start of class, If business travel or similar activities prevent you from. attending class and turning in your homework please inform. me beforehand, Grading is done on a straight 90 80 70 scale with curving.
below these thresholds if needed, Homework solutions will be placed on the course Web site. in PDF format with security password required hints pages. may also be provided,ECE 2610 Signals and Systems 1 5. Chapter 1 Introduction and Course Overview,Computer Tools. Through out this semester we will be using MATLAB for. modeling and simulation of signals and systems, MATLAB is a very powerful vector matrix oriented pro. gramming language, If features an integrated graphics visualization engine.
MATLAB has and integrated source code editor and debug. ging environment, There are specialized toolboxes available for signal process. ing communications image processing and may other engi. neering applications, The text for this course includes a collection of MATLAB. functions specialized for the signal processing taught in this. The laboratory portion of this course will focus on the use of. MATLAB to explore signals and systems,A very brief introduction to MATLAB follows. We will be learning shortly that a signal in mathematical. terms can be as simple as a function of time say a trigono. metric function like, where we call the amplitude the frequency in cycles. per second and is the independent variable,1 6 ECE 2610 Signals and Systems.
Computer Tools, MATLAB operates from a command window similar to a. calculator, On the first line we create a time axis vector running from. 0 to 2 seconds with time step 0 01 seconds, The second line we fill a vector with functional values. that correspond in this case to the sum of two sinusoids. What are the amplitudes and frequencies of these sinu. Finally we plot the signal using the function,Sum of Two Sinusoids Signal. 0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 2,Time in seconds.
Signals and systems are an integral part of making these devices perform their intended function Signals convey information from one point to another They may be generated by electronic means or by some natural means such as talking walking your heart beating an earthquake the sun heating the sidewalk 2 3 4 Chapter 1 Introduction and Course Overview 1 2 ECE 2610