Text: Signals & Systems, 2nd ed., M. J. Roberts, McGraw Hill, 2012. References: [
1] Continuous Signals and Systems with MATLAB, 2nd ed., T. S. ElAli & M.
EO2402 Introduction to Linear Systems (4-1) Instructor:
Monique P. Fargues, Span 456, Monterey, CA (PST)
[email protected], 831.656.2859 office hours: posted or by appointment
Text: Signals & Systems, 2nd ed., M. J. Roberts, McGraw Hill, 2012. References: [1] Continuous Signals and Systems with MATLAB, 2nd ed., T. S. ElAli & M. Karim, CRC Press, 2008. [2] Signals and Systems using MATLAB, L. Chaparro, Academic Press, 2011. [3]: MathWorks MATLAB tutorials: http://www.mathworks.com/academia/student_center/tutorials/launchpad.html
[4]: Signal Processing for Communications, P. Brandoni & M. Vetterli, http://www.sp4comm.org/readers.html Description: This course is an introduction to linear system concepts for students in non-electrical engineering curricula. The course is designed to provide students with knowledge needed for the following EC3402 course and provide an introduction to the principles of continuous-time and discrete-time systems. PREREQUISITES: Ability to program in a higher level language like MATLAB. Grades: 3 tests, each worth 25%, 1 comprehensive final, worth 25% Class Notes: I teach from partially filled-in notes and fill in material during the lectures. Notes will be made available electronically before they are needed on the SAKAI course site for you to use during lecture viewing. I will post filled-in versions of the slides after lecture times.
HWs: A few problems will be assigned on a regular basis to apply the various concepts covered in the classroom. Hws will not be collected; however they constitute an essential part of the learning process for the course. You are responsible for working on the problems as they get assigned to facilitate the understanding of the concepts covered in class. Solutions will be made available. Office Hours: I will be available after scheduled class time for questions if needed, and other times by appointment. VTC appointments can be also arranged if needed.
Exams: -
Tests will be take homes and some parts may require the use of MATLAB. Take homes will follow the following protocol: “This is a take-home exam. Open books/notes. You may not discuss this test via any form of communication (written, oral, or computer), or exchange any type of information related to this test with anyone, except the instructor. By turning in your test, you acknowledge having read, agreed to, and followed the above instructions. Violations of this protocol are violations of the Honor Code and will be processed as such.”
Course Management System (Sakai): This course will use Sakai to make course content available to the student. Resources including course notes, lists of weekly concepts, homework assignments/solutions, test material, and Matlab programs (if any needed) will be available through the Sakai utility. https://cle.nps.edu/. You will be expected to upload your test materials using either .doc or .pdf file formats in SAKAI. No other formats will be accepted. E-mailed tests will not be accepted.
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Detailed List of Topics Covered: Section 1: Introduction to Systems Systems definition Signal types (analog vs. discrete, deterministic vs. random) Complex / Real and Complex arithmetic Section 2: Continuous-time Signals Basic signal types Continuous-time signal properties Signal operations Energy and power signals
Section 3: Discrete-time Signals Discrete-Time Signal Description Sampling, Discrete sinusoidal signal, Discrete exponential signal, Unit impulse function, Unit sequence function, Signum function, Unit ramp signal, Periodic impulse function , Even/Odd, Products of Even and Odd Signals Symmetric Finite Summation Periodic Signal Energy & Power Signals Section 4: System Analysis Continuous-time Systems System Representation System Classification: Static / Dynamic, Dumped / Distributed, Active / Passive, With Memory /Without Memory, Causal / Non Causal, Stable, Feedback Continuous-Time Systems Building Blocks: Ideal Delay, Integrator, Differentiator Linear System Invertible System Time-Invariant System Representation of Systems by Differential Equations How to Solve Differential Equations / Homogeneous Equation (zero-input response) How to Solve Differential Equations / Non-Homogeneous Equation (zero-state response) Differential Equation Examples System Stability from the Differential Equation Information Differential Equation Circuit Examples Representing Systems: From Block Diagrams to Differential Equations Representing Systems: From Differential Equations to Block Diagrams Discrete-time Systems Basic Discrete Time System Characteristics Solving Difference Equations Discrete-time System Properties
Section 5: System Analysis Continuous-Time Systems System Representation Convolution Integral and LTI Systems – Concept of Impulse Response Convolution Properties Impulse Response from System Differential Equation Evaluating a Convolution using Equations Convolution Examples Graphical Convolution Step Response for a LTI System
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Complex Exponential Excitation to a LTI System – Concept of Transfer Function and Frequency Response Frequency Response Plots (Using MATLAB) Combination of Complex Exponential Excitations as Input to a LTI System Cosine Signal Excitation as Input to a LTI System Frequency Response Plots (Using MATLAB) Interconnection of LTI Systems: Cascade, Parallel, Feedback System Stability LTI System Causality
Discrete Time Systems Introduction DT LTI System Impulse Response (options 1 & 2) DT LTI System Response Convolution DT LTI System Stability DT System Transfer Function Frequency Response
Section 6: Fourier Series Decomposition & Fourier Transform Introduction: Conceptual Idea behind the Fourier Series (FS) Decomposition Periodic Input to LTI System – Review Fourier Series (FS) Decomposition of a Periodic Signal FS Decomposition examples (No Integration Required) FS Decomposition examples (Integration Required) Line Spectrum of Periodic Signals Parseval’s Theorem Properties of Line Spectra Trigonometric Fourier Series Convergence of the Fourier Series (Gibbs’ Phenomenon) Basic FS Properties Summary Trigonometric FS Properties Evaluating Complex FS Coefficients Using MATLAB Numerical Computation of FS Coefficients From the FS Decomposition to the Fourier Transfer The Generalized FT FT for Periodic Signals Example: FT of Cosine & Sine Functions Basic FT Property: Linearity Basic FT Property: Time – Shifting Property Basic FT Property: Frequency – Shifting Property Basic FT Property: Scaling Property Taking Advantage of FT Properties FT Modulation: Application to AM Modulation FT Modulation: Application to Frequency Division Multiplexing FT and Frequency Response FT Applied to Combinations of LTI Systems Parseval’s Theorem FT Convolution Property Applied to LTI System Numerical Computations of the FT System Analysis Using the FT
Section 7: Discrete Fourier Transform 3
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