ECE 3500 Fundamentals of Signals and Systems (Fall 2019)

Part I: Language of Signals and Systems

Lecture 1 (08/20/2019) (Syllabus, Slides)

  1. Syllabus

  2. Motivations and Basic Concepts

  • What are the signals and systems?

  • Application of signals and systems?

  • What we will learn in ECE 3500?

  • What follows this class?

Lecture 2 (08/22/2019) (lecture note, Lecture Scribe 1, Lecture Scribe 2, Homework 1, Lab 1)

  1. Typs of Signals

  2. Engery and Power of Signals

  • References:

    • Lathi's book: Ch. 1.1-1.2, 1.5, 8.1, 8.4

    • Mitra's book: Ch. 1.1-1.2, 1.4-1.5, 3.1, 7.1-7.2

Lecture 3 (08/27/2019) (lecture note, Lecture Scribe 1, Lecture Scribe 2, Examples on Signal Types and Properties)

  1. Engery and Power of Signals

  2. Basic Signal Operations

  3. Introduction to Periodic Signals

  • References:

    • Lathi's book: Ch. 1.1-1.3, 1.5, 8.1, 8.4

    • Mitra's book: Ch. 3.1-3.4, 7.1-7.4

Lecture 4 (08/29/2019) (Lecture Notes, Lecture Scribe 1, Lecture Scribe 2, Examples, Homework 2)

  1. Periodic Signals

  • References:

    • Lathi's book: Ch. 1.2, 1.4, 8.2, B.1

    • Mitra's book: Ch. 3.1-3.4, 7.1-7.4

Lecture 5 (09/03/2019) (Lecture Notes, Lecture Scribe 1, Lecture Scribe 2, Quiz 1 solutions)

  1. Complex Numbers

  2. Specific Signals

    1. Complex Exponentials

  • Refrences:

    • Lathi's book: Ch. B.1, 1.4, 8.2

    • Mitra's book: Ch. 2.1-2.5, 3.2, 7.3

  • Homework 1 solution: here.

Lecture 6 (09/05/2019) (Lecture Notes, Lecture Scribe 1, Lecture Scribe 2, Homework 3, Lab 2)

  1. Specific Signals

    1. Unit Impluse Signals

    2. Unit Step Signals

  • Refrences:

    • Lathi's book: Ch. 1.4, 8.2

    • Mitra's book: Ch. 3.2, 7.3

Lecture 7 (09/10/2019) (Lecture Notes, Lecture Scribe 1, Lecture Scribe 2, Examples)

  1. System Properties

  • Refrences:

    • Lti's book: Ch. 1.6-1.7, 2.6

    • Mitra's book: Ch. 4.1-4.3, 8.1-8.4

Lecture 8 (09/12/2019) (Lecture Notes, Lecture Scribe 1, Lecture Scribe 2, Convolution Examples (Continuous Time), Convolution Examples (Discrete Time), Homework 4)

  1. System Properties Cont.

  2. Convolution Integral/Sum

  • Refrences:

    • Lathi's book: Ch. 1.6-1.7, 2.6, 2.1-2.5, 9.1-9.5

    • Mitra's book: Ch. 4.1-4.3, 8.1-8.4

  • Homework 2 solution: here.

Lecture 9 (09/17/2019) (Lecture notes, Lecture Slides, Lecture Scribe 1, Lecture Scribe 2 Quiz 2 solutions)

  1. Convolution Examples (Continuous-time)

  • Refrences:

    • Lathi's book: Ch. 2.1-2.5, 9.1-9.5

    • Mitra's book: Ch. 4.1-4.3, 8.1-8.4

Lecture 10 (09/19/2019) (Lecture notes, Lecture slides, Lecture Scribe 1, Lecture Scribe 2, Excercise Exam, Excercise Exam Solutions)

  1. Convolution Examples (Discrete-time)

  2. Convolution Properties

  3. Properties of LTI systems using unit impluse response

  • Refrences:

    • Lathi's book: Ch. 2.1-2.5, 9.1-9.5

    • Mitra's book: Ch. 4.1-4.3, 8.1-8.4

  • Homework 3 solution: here.

Part II: Continous-time Signals and Systems

Lecture 11 (09/26/2019) (Lecture Notes, Lecutre Scribe 1, Lecture Scribe 2)

  1. Frequency Basis and Fourier Series (FS)

    1. Cosine and Sine Fourier Series

  • Refrences:

    • Lathi's book: Ch. 3.1-3.5

    • Mitra's book: Ch. 5.1

  • Homework 4 solutions: here.

Lecture 12 (10/01/2019) (Lecture Notes, Lecture Scribe 1, Lecture Sribe 2. Quiz 3 Solutions)

  1. Complex Exponential Fourier Series

  • Refrences:

    • Lathi's book: Ch. 3.4-3.7

    • Mitra's book: Ch. 5.1

Lecture 13 (10/01/2019) (Lecture Notes, Lecture Scribe 1, Lecture Scribe 2, Homework 5)

  1. Examples of Complex Exponential Fourier Series

  2. Drichlet Conditions

  • Refrences:

    • Lathi's book: Ch. 3.4-3.7

    • Mitra's book: Ch. 5.1

Lecture 14 (10/15/2019) (Lecture Notes, Lecture Scribe 1, Lecture Scribe 2)

  1. Properties of Fourier Series

  • Refrences:

    • Lathi's book: Ch. 3.4-3.7

    • Mitra's book: Ch. 5.1

  • Continuous-time Transform Tables: here.

Lecture 15 (10/17/2019) (Lecture Notes, Lecture Scribe 1, Lecture Scribe 2, Homework 6, Lab 4)

  1. Continuous-time Fourier Transform

  • Refrences:

    • Lathi's book: Ch. 4.1-4.3

    • Mitra's book: Ch. 5.3

Lecture 16 (10/22/2019) (Lecture Notes, Lecture Scribe 1, Lecture Scrib 2)

  1. Magnitude and Phase of CTFT

  2. Uniform Convergence Conditions (Dirichlet Conditions)

  • Refrences:

    • Lathi's book: Ch. 4.1-4.3

    • Mitra's book: Ch. 5.3

Lecture 17 (10/24/2019) (Lecutre Notes, Lecture Scribe 1, Lecture Scribe 2)

  1. Uniform Convergence Conditions (examples)

  2. Properties of CTFT

  • Refrences:

    • Lathi's book: Ch. 4.3-4.7

    • Mitra's book: Ch. 5.3-5.5

Lecture 18 (10/29/2019) (Lecture Notes, Lecture Scribe 1, Lecture Scribe 2, Homework 7)

  1. Properties of CTFT

  2. Applications: Amplitude Modulations (AM)

  • Refrences:

    • Lathi's book: Ch. 4.3-4.7

    • Mitra's book: Ch. 5.3-5.5

  • Midterm 1 Solutions: here.

  • Homework 5 solutions: here.

Lecture 19 (10/31/2019) (Lecture Notes, Lecture Scribe 1, Lecture Scribe 2)

  1. Laplace Transform

  • Refrences:

    • Lathi's book: Ch. 6.1-6.4

    • Mitra's book: Ch. 5.6

Lecture 20 (11/05/2019) (Leture Notes, Lecture Scribe 1)

  1. Inverse Laplace Transform

  2. Applications of Laplace Transform: Determine System Properties (causal and BIBO stable), Analog Filter Design

  • Refrences:

    • Lathi's book: Ch. 6.7, 7.1-7.2

    • Mitra's book: Ch. 5.7-5.9, 6.1-6.4

Part III: Discrete-time Signals and Systems

Lecture 21 (11/07/2019) (Review Slides, Lecture Notes, Lecture Scribe 1, Lecture Scribe 2, Lecture Scribe 3)

  1. Review of Part II

  2. Sampling

  3. Nyquest Sampling Theorem and Aliasing

  • Refrences:

    • Lathi's book: Ch. 5.1-5.2, 8.3

    • Mitra's book: Ch.7.1, 7.5

  • Quiz 5 solutions: here.

  • Homework 7 solutions: here.

  • Lab 5: here.

Lecture 22 (11/14/2019) (Lecture Notes, Lecture Scribe 1, Lecture Scribe 2)

  1. Sampling

  2. Nyquest Sampling Theorem and Aliasing

  3. Anti-Aliasing Filter

  • Refrences:

    • Lathi's book: Ch. 5.1-5.2, 8.3

    • Mitra's book: Ch.7.1, 7.5

Lecture 23 (11/19/2019) (Lecture Notes, Overview Slides, Lecture Scribe 1, Lecture Scribe 2)

  1. Discrete-Time Fourier Transform (DFT)

  • Refrences:

    • Lathi's book: Ch. 10.1-10.4

    • Mitra's book: Ch.9.2

Lecture 24 (11/21/2019) (Lecture Notes, Lecture Scribe 1, Lecture Scribe 2, Lecture Scribe 3)

  1. DTFT Properties

  2. DTFT Applications

  3. DTFT Existence Conditions

  4. Z-Transform

  • Refrences:

    • Lathi's book: Ch. 10.1-10.4, 11.1-11.3

    • Mitra's book: Ch.9.2-9.3, 9.8

  • Examples:

Lecture 25 (11/26/2019) (Lecture Notes, Lecture Scribe 1, Lecture Scribe 2, Lecture Scribe 3, Lecture Scribe 4)

  1. Z-Transform Examples

  2. Inverse Z-Transform

  3. Applications of Z-Transform

  • Refrences:

    • Lathi's book: Ch. 11.1-11.3

    • Mitra's book: Ch. 9.8-9.10

Lecture 26 (12/03/2019) (Lecture Notes, Part III Review Slides, Lecture Scribe 1, Lecture Scribe 2, Lecture Scribe 3)

  1. Resampling (Downsampling, Upsampling)

  • Refrences:

    • Lathi's book: 8.4, 10.4

    • Mitra's book: None.

  • Homework 10 solutions: here.

  • Homework 11: here.

  • Homework 11 solutions: here.

  • Midterm 3 solutions: here.