# San José State University Department of Electrical Engineering EE 112, Linear Systems, Spring 2010

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1 San José State University Department of Electrical Engineering EE 112, Linear Systems, Spring 2010 Instructor: Robert H. Morelos-Zaragoza Office Location: ENGR 373 Telephone: (408) Office Hours: TuW 14:30-17:00 Class Days/Time: MW 18:00-19:15 Classroom: Clark Building 234 Prerequisites: EE98 with a grade of C or better, EE101, Math133A Course Description Advanced study of linear discrete-time and continuous-time systems. Laplace transforms and Z transforms. Convolution. System functions and frequency response, Fourier series and Fourier transforms. Discrete and fast Fourier transforms. Course Goals and Student Learning Objectives This course provides an introduction to linear time-invariant (LTI) systems. It introduces signals and systems, both discrete and continuous, for representing and manipulation in the time domain. Laplace and Z-transforms are covered as analytical tools to solve linear systems using a characterization in the frequency domain as well as for computing time-domain responses to input signals. Fourier series and the Fourier transform are covered, to understand the relationship between the time-domain and the frequency-domain representation of LTI systems. GE/SJSU Studies Learning Outcomes (LO) Upon successful completion of this course, students will be able to: LO1 Demonstrate an understanding of the fundamentals of Electrical Engineering, including its mathematical and scientific principles, analysis and design. LO2 Demonstrate the ability to apply the practice of Engineering in real-world problems. Course Content Learning Outcomes Upon successful completion of this course, students will be able to: LO3 Analyze a system and determine if it is linear, time-variant, causal, and/or stable (a) LO4 Perform convolution in the time domain to compute the response of an LTI system (c) LO5 Apply the Laplace transform to solve linear differential equations (a, k) LO6 Apply Z-transform to solve linear difference equations (a, k) LO7 Analyze a periodic signal, using the Fourier series, to determine its frequency content (a, k)

2 LO8 Analyze a signal, using the Fourier transform, to determine its frequency content (a, k) LO9 Analyze a linear system transfer function using its poles and zeros (a, k) LO10 Determine the frequency response of a system (a, k) LO11 Use MATLAB to analyze a system both in the time and in the frequency domains, to do convolution for time domain response of a system, determine frequency response of a system, and analyze a signal in terms of its frequency content (k) ABET outcomes The letters in parentheses in each of the course learning objectives above refer to ABET (Accreditation Board for Engineering and Technology) criterion 3 outcomes satisfied by the objective. These are listed below as a reference: (a) An ability to apply knowledge of mathematics, science, and engineering (b) An ability to design and conduct experiments, as well as to analyze and interpret data (c) An ability to design a system, component, or process to meet desired needs (d) An ability to function on multi-disciplinary teams (e) An ability to identify, formulate, and solve engineering problems (f) An understanding of professional and ethical responsibility (g) An ability to communicate effectively (h) The broad education necessary to understand the impact of engineering solutions in a global and societal context (i) A recognition of the need for, and an ability to engage in life-long learning (j) A knowledge of contemporary issues (k) An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice (l) Specialization in one or more technical specialties that meet the needs of companies (m) Knowledge of probability and statistics, including applications to electrical engineering (n) Knowledge of advanced mathematics, including differential and integral equations, linear algebra, complex variables, and discrete mathematics (o) Basic sciences, computer science, and engineering sciences necessary to analyze and design complex electrical and electronic devices, software, and systems containing hardware and software components Required Texts/Readings Textbook Haykin and Van Veen, Signals and Systems, 2nd Ed., John Wiley, Other readings Lathi, Linear Systems and Signals, Oxford, 2004.

4 Table 1 Course Schedule (Subject to change with fair notice as announced in class) Week Date Topics, Readings, Assignments, Deadlines 1 1/28 Introduction to signals and systems. 2 2/1 Classification of signals, signal operations and elementary signals. (Chapter 1) 3 2/8 Systems and their properties. Using Matlab (Chapter 2) 4 2/17 Convolution sum and integral (Chapter 2) 5 2/24 LTI systems, impulse and step response, system representation using differential and difference equations, block diagrams (Chapter 2) 6 3/1 Midterm exam 1 (Monday 3/1) 7 3/8 Laplace transform (Chapter 6) 8 3/15 Transfer function, poles and zeros and frequency response (Chapter 6) 9 3/22 Fourier Series (Chapter 3) 10 4/5 Fourier transform (Chapter 3) 11 4/12 Discrete-time Fourier transform and FFT (Chapter 4) 12 4/19 Midterm exam 2 (Wednesday 4/21) 13 4/26 Z transform (Chapter 7) 14 5/3 Applications in filters (Chapter 8) 15 5/10 Final Exam Applications in control and communication Systems (Chapters 9 and 5) 5/24 Comprehensive final exam. 17:15-19:30 Other Notes: MATLAB will be used to demonstrate some of the concepts discussed in class and also to solve some homework problems. Students are responsible for self-learning and purchasing the software if necessary. The Student Version of MATLAB and the Signal Processing Toolbox are available from the bookstore or directly from the Mathworks, Inc. ( MATLAB and many toolboxes are also available on many PCs in rooms ENG387 and ENG405. MATLAB has a good help facility that the student can invoke to learn more about specific commands or functions.

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