COURSE INFORMATION

 

EN157: Linear System Analysis

Fall 2004

MWF 13:00-14:00 (Barus & Holley 455)

 

 

Instructor: David B. Cooper

Barus & Holley room 318

Tele. 863-2601

E-mail: cooper@lems.brown.edu


 

Short Course Description

Analysis of discrete and continuous time electrical signals and systems in both time and frequency domains.  Convolution, sampling, spectral analysis, analog and digital filtering, image and speech filtering, system stabilization through feedback.  Discrete and continuous time Fourier and Laplace transforms, and the state-space approach.  The goals of this course are:

1) Understanding of various types of systems and how they apply to a wide range of problems in electrical and computer engineering (and elsewhere).

2) Understanding at theoretical and intuitive levels, a number of fundamental representations in the time and frequency domains for signals and their use in the analysis of systems operating on such signals.

3) Introductory understanding of linear filter design for 1-dimensional time signals and 2-dimensinoal images.

This course is the gateway to digital and analog signal processing for: filtering, system analysis, and control; digital and analog communications; image, video, and speech processing; pattern recognition; computer vision; speech recognition; medical image-analysis; robotics and intelligent systems.

 

Course Outline

Chapter 1.  Introductory material on: a number of continuous-time and discrete-time signals of interest, signal properties, energy and power in signals, transformations of signals; examples of a number of important continuous-time and discrete-time systems, concept of a system as a transformation or operator which takes an input signal and produces an output signal, types of systems, system properties.

 

Introduction to MATLAB

 

Chapter 2.  Discrete-time and continuous-time linear time-invariant (LTI) systems in the time-domain: convolution sums and integrals, properties of LTI systems, impulse and step responses, block diagrams, state-variable descriptions, important examples.

 

MATLAB Project 1 on image processing.

 

Chapter 3. Approximating signals by sums of simple signals having nice properties; orthogonal bases for linear vector spaces; signal-space dimensionality (i.e., complexity).  Fourier analysis: continuous-time and discrete-time Fourier series and Fourier transform representations of signals.  Properties of Fourier transforms.  Fourier analysis of linear continuous and discrete time-invariant systems.  Filtering. 

 

Chapter 4.  Sampling: Reconstruction of continuous-time signal from their samples.  Discrete-time processing of continuous-time signals.

 

Chapter 6 and 7.  Brief introduction to Laplace transforms and Z-transforms.

 

Chapter 8.  Application to filters.

 

MATLAB Project 2 on speech signal filtering and spectral analysis. 

 

Chapter 5.  Brief introduction to modulation for communications, and to the detection of signal buried in noise (e.g., cellular communications).

 

Chapter 9.  Brief introduction to linear system stabilization.

 

MATLAB Project 3 on use of feedback to stabilize an unstable system.

 

Text

“Signals & Systems”, 2nd edition, S. Haykin, B. Van Veen, John Wiley and Sons.

 

Useful references: “Signals and Systems”, 2nd edition, Willsky, Oppenheim, Nalwab, Prentice Hall; “Signal Processing First”, J. McClellan, R. Schafer, M. Yoder, Prentice Hall; “Structure and Interpretations of Signals and Systems”, E. Lee, P. Vavaiya, Addison Wesley.

Course Requirements

Two 1-hour exams: mid-October, 3rd week of November; Final Exam.

 

3 graded MATLAB projects: 1. Image deblurring and noise suppression; 2. Speech filtering and spectral analysis; 3. Use of feedback to stabilize an unstable system.

 

7 required (but not graded) homework assignments which include a few introductory MATLAB exercises

 

3    15-minute graded quizzes on assigned homework problems. 

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