Signals and Systems

EI 331, Spring 2019

Instructor: Bo Jiang

TA: Huaying Wu (吴华颖)


When: Tue Thu 10:00-11:40 am
Where: East Middle Hall 4-306 (东中院4-306)
Office Hours: Huaying Wu, Wed 3:00-4:00 pm, SEIEE 1-441; Bo Jiang, by appointment


Overview

This course is about the analysis of linear time-invariant systems. Topics include convolution, Fourier series and transform, sampling, Laplace transform, and Z transform. We will also cover basics of complex analysis.

Requirements: Coursework will include

  • Weekly homework assignments, 40% of course grade.
  • A midterm exam, 25% of course grade.
  • A final exam, 35% of course grade.

Grading policy:

  • ONE late homework submission is allowed without penalty. It should be submitted by the next class after the due date.
  • Late submissions beyond the first one will NOT be accepted.
  • ONE lowest score for the homework assignments will be automatically dropped.

Honor code:

  • You are encouraged to discuss homework assignments with each other, but write up solutions on your own! Sharing or copying a solution will result in a zero score for the relevant assignment for both parties.
  • If a significant part of your solution is due to someone else or from other sources (books, forums, etc), you should acknowledge the source! Failure to do so will result in a zero score for the relevant assignment.

Textbooks

  • [OWN] Signals and Systems, by Oppenheim, Willsky and Nawab, 2nd Edition, 电子工业出版社（英文影印版）
  • [C] 复变函数（第四版），西安交通大学高等数学教研室，高等教育出版社
References (Optional)
  • 信号与系统（第三版），郑君里、应启珩、杨为理，高等教育出版社
  • Fourier Analysis: An Introduction, by Stein and Shakarchi， 世界图书出版公司（影印版）
  • Complex Analysis, 3rd Edition, by Lars V. Ahlfors, 机械工业出版社（英文影印版）
  • 复变函数教程，方企勤，北京大学出版社
  • 几何背景下的数学物理方法，常晋德，高等教育出版社

Homeworks

  1. Homework 1. Released 2/28, due 3/5. (Solutions)
  2. Homework 2. Released 3/7, due 3/14. (Solutions)
  3. Homework 3. Released 3/14, due 3/21. (Solutions)
  4. Homework 4. Released 3/23, due 3/28. (Solutions)
  5. Homework 5. Released 3/29, due 4/4. (Solutions)
  6. Homework 6. Released 4/5, due 4/11. (Solutions)
  7. Homework 7. Released 4/12, due 4/18. (Solutions)
  8. Homework 8. Released 4/18, due 4/23. (Solutions)
  9. Homework 9. Released 5/11, due 5/16. (Solutions)
  10. Homework 10. Released 5/18, due 5/23. (Solutions)
  11. Homework 11. Released 5/23, due 5/30. (Solutions)
  12. Homework 12. Released 5/31, due 6/6. (Solutions)
  13. Homework 13. Released 6/8, will not be collected or graded. (Solutions)
Feel free to use this latex template and style file.

Lecture Schedule

All readings refer to the OWN unless specified otherwise. The schedule may change as the semester progresses.

Week Date Lecture Topics Readings Assignments
1 2/26 Signals and their properties, basic transformations
2/28 Complex numbers, complex exponential, convergence, infinite series
  • HW 1 out
    		•
    2 3/5 Complex exponential, unit impulse and unit step functions
  • HW 1 due
    		•
    3/7 Dirac delta function, systems, properties of systems
  • HW 2 out
    		•
    3 3/12 Linearity, DT LTI systems, convolution sum and its properties
    3/14 CT LTI systems, convolution integral, proprties of LTI systems, systems described by differential equations
  • HW 2 due
  • HW 3 out
    		•
    4 3/19 Systems described by differential equations
    3/21 Systems described by difference equations, singularity functions
  • HW 3 due
  • HW 4 out
    		•
    5 3/26 CT Fourier series
    3/28 Properties of CT Fourier series, mean-square convergence
  • HW 4 due
  • HW 5 out
    		•
    6 4/2 Convergence of CT Fourier series, periodic impulse train, filtering
    4/4 DT Fourier series and its properties
  • HW 5 due
  • HW 6 out
    		•
    7 4/9 FFT, DT filters, CT Fourier transform
    4/11 CT Fourier transform
  • HW 6 due
  • HW 7 out
    		•
    8 4/16 Properties of CT Fourier transform
    4/18 Properties of CT Fourier transform, systems described by linear constant-coefficient ODEs
  • HW 7 due
  • HW 8 out
    		•
    9 4/23 Sampling and reconstruction of CT signals
  • HW 8 due
    		•
    4/25 DT Fourier transform and its properties
    10 4/28 MIDTERM -- in class
    4/30 Properties of DT Fourier transform, systems described by difference equations, DT sampling, DT processing of CT signals
    • 5.4-5.9, Appendix A.3, 7.4-7.6
    • Slides
    5/2 NO CLASS -- rescheduled to 4/28
    11 5/7 Magnitude-phase representation, group delay, uncertainty principle, relations among Fourier representations
    5/9 Complex plane and functions, analytic functions
  • HW 9 out
    		•
    12 5/14 Analytic functions, elementary analytic functions
    5/16 Complex integration, Cauchy's Integral Theorem, Cauchy's Integral Formula
  • HW 9 due
  • HW 10 out
    		•
    13 5/21 Higher order derivatives, harmonic functions, power series
    5/23 Taylor series, Laurent series
  • HW 10 due
  • HW 11 out
    		•
    14 5/28 Residue
    5/30 Z-transform
  • HW 11 due
  • HW 12 out
    		•
    15 6/4 Analysis of DT LTI systems by z-transforms, unilateral z-transform
    6/6 Laplace transform
  • HW 12 due
  • HW 13 out
    		•
    16 6/11 Inverse Laplace transform, analysis of CT LTI systems by Laplace transforms
    6/13 Unilateral Laplace transform, review