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

• Examples

  • Fourier Series Examples 1

  • Fourier Series Examples 2

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

• Examples

  • CTFT Examples 1.

  • CTFT Examples 2.

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

• Examples

  • Laplace Transform Examples.

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

• Homework 6 solutions: here.

• Quiz 4 solutions: here.

• Exercise Exam 2: 2017 questions, 2017 solutions, 2018 questions, 2018 soltuions.

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

• Examples:

  • Sampling Examples.

• Homework 8: here.

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

• Homework 9: here.

• Examples:

  • DTFT Examples 1.

  • DTFT Examples 2.

• Discrete Transform Tables: here.

• Midterm 2 Solutions: here.

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:

  • Z-Transform

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

• Homework 8 solutions: here

• Homework 9 solutions: here

• Homework 10: here.

• Exercise Exam 3: 2017 questions, 2017 solutions, 2018 questions, 2018 soltuions.

• Quiz 6 solutions: here

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.