ECE 360

Signals and Linear Systems

Fall 2002

 

Lectures : M, T, W, F 12:40-1:30 p.m. A155

 

Instructor :  Selin Aviyente, Assistant Professor of Electrical & Computer Engineering

                     2210 Engineering Building

                     355-7649

                     aviyente@egr.msu.edu

           

Office Hours :  MTF 10:00-11:30 am or by appointment

                       

 

Textbook : Analog and Digital Signal Processing, Ashok Ambardar, Brooks/Cole, 2nd Edition.

 

Course Objectives: This course provides a fundamental background in analog and digital signal and linear system theory that is prerequisite to many following courses in signals, systems, and control. The focus of the course is the time and frequency domain analysis of linear time-invariant systems. Fourier, Laplace and z-transforms, and their applications to signal and system analysis will be emphasized.

 

Requirements: There will be two midterm exams, one final exam and weekly homework assignments.

 

  1. Homeworks: Homework assignments will be given every week and will constitute 15 percent of your final grade. The homework questions will be posted on the web with their due dates. Posting of new assignments will be announced in class. You must submit your homeworks during the class period on the due date unless prior permission has been granted to submit otherwise. No late homework assignments will be graded. The lowest homework score will be dropped when computing your average homework grade. Homework solutions must be original copies in the student’s own handwriting. No other submissions will be graded. Solutions must be clear and neatly written to receive credit. Solutions to homework assignments will be put on the web.

 

  1. Exams: There will be two midterm exams (one class period each), and a final exam. The midterm exams will count 50 percent and the final exam will count 35 percent toward your final grade. A makeup exam, which will be given only in legitimate cases of illness or personal emergency which is documented by a physician or other appropriate official, will take place during the last week of the semester. This exam will take the place of any missed midterm and will be comprehensive. A student who finds it necessary to miss a midterm should contact the professor before the exam to explain the circumstances. A student who must miss the final exam should contact the professor as well as the Dean’s Office, according to MSU policy.

 

Midterm exam 1- October 2  12:40-1:30 pm 25%

Midterm exam 2- November 20 12:40-1:30 pm 25%

Final Exam- December 9 12:45-2:45 pm 35%

Homeworks 15%

 

Incomplete grades will be given only in unusual cases of illness or other personal emergency which causes the student to miss a significant amount of the course. This grade cannot be given for any other reason. A student who misses the final exam without satisfactory explanation will receive a failing grade in the course according to MSU policy.

 

Web page : The class web page is http://www.egr.msu.edu/~aviyente/ECE 360.htm. You can get to this web page through the department page, www.egr.msu.edu/ece. Please check the web page frequently for announcements and a list of lecture by lecture topics.

 

  

Course Outline:

 

PART 1: CONTINUOUS-TIME (CT) SIGNAL AND SYSTEM ANALYSIS

 

  1. Introduction to the course

 

  1. Basic CT Signal and System Concepts (Chapters 2 and 4.1, 4.2)
    1. Definition of a CT signal
    2. CT signal properties and operations on signals

                                                               i.      Energy and power signals

                                                             ii.      Periodic vs. aperiodic

                                                            iii.      Operations on signals

    1. Special signals

                                                               i.      Even and Odd signals

                                                             ii.      Harmonic signals and sinusoids

                                                            iii.      Step, ramp, rect, sinc and impulse functions

    1. Definition of a CT system
    2. CT system properties

                                                               i.      Linearity

                                                             ii.      Time invariance

                                                            iii.      Causality

                                                           iv.      Dynamic

                                                             v.      Stability (BIBO)  

 

     II. Time-domain analysis of LTI CT systems (Chapter 4.3- 4.7 and Chapter 6.1-6.4)

A.     Differential equation representation of LTI systems

B.     Time-domain solution of the differential equation ( zero-state response, zero-input response, natural response, forced response)

C.     Impulse response and convolution

D.     Stability in terms of the system modes and in terms of impulse response

 

    III. Laplace Transform (LT) and its use in CT LTI system analysis (Chapter 11)

A.     Definition, existence

B.     Evaluation of LT

C.     Properties

D.     Transfer function, poles and zeros

E.      Inverse LT

F.      Solution of the system differential equation using LT

G.     System analysis (H(s))

1. Use H(s) to find zero-state response

2. Steady-state response to eigensignals, sinusoids

3. Frequency response from pole-zero diagram

H.     LT domain circuit analysis

 

 

  IV. Fourier Series and its use in analyzing CT signals (Chapter 8.1 and 8.4)

A.     Fourier Series (FS)

1. Trigonometric (quadrature) FS

2. Amplitude-phase (polar) FS

3. Complex (exponential) FS

B.     Frequency Spectrum (Line Spectra)

 

  V. Fourier Transform (FT) and its use in CT Signal and System Analysis (Chapter 9.1-9.4)

A.     Definition and existence

B.     Spectra

C.     Relation to LT

D.     Relation to FS and Fourier transform of power signals

E.      Properties

F.      Parseval’s Theorem

G.     Frequency response function and system analysis

H.     Ideal Filters

 

  PART 2: DISCRETE-TIME (DT) SIGNAL AND SYSTEM ANALYSIS

 

  VI. Basic DT Signal and System Concepts (Chapter 3.1-3.6 and 5.1-5.2)

A.     Definition of a DT signal

B.     Sampling Theorem

C.     DT signal properties

1. Energy vs. Power signals

2. Periodic vs. Aperiodic

3. Even and odd signals

4. Operations on signals

D.     Special signals

1. Harmonics

2. Singularity signals

E.      Definition of a DT system

F.      DT system properties

1. Linearity

2. Time invariance

3. Causality

4. Stability (BIBO)

 

  VII. Time domain analysis of LTI DT systems (Chapter 5.3 –5.6 and 7.1-7.2)

A.     Difference equation representation of I/O relationship

B.     Time-domain solution of difference equation

C.     Impulse response and convolution

 

  VIII. The z-transform (ZT) and its use in the analysis of DT LTI Systems (Chapter 17)

A.     Definition, motivation and existence

B.     Evaluation of ZT

C.     Properties

D.     Inverse ZT

E.      Solution of Difference Equations using ZT

F.      System function, H(z)

1. Definition

2. Using H(z) to find zero-state response

3. Poles and zeros and stability

4. Steady-state response

          G. Comments on DTFT