ECE 3500 Fundamentals of Signals and Systems (Fall 2022)

Part I: Language of Signals and Systems

Lecture 1 (08/23/2022) (Syllabus, Slides)

1. Syllabus

2. Motivations and Basic Concepts

   1. What are the signals and systems?

   2. Application of signals and systems?

   3. What we will learn in ECE 3500?

   4. What follows this class?

• In-person lecture video: here.

• Online lecture video: here.

Lecture 2 (08/25/2022) (Lecture Note, Lecture Review Slides)

1. Types of Signals

2. Energy 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

• In-person lecture video: here.

• Online lecture video: here.

• Homework 1: Here, Solutions.

• Lab 1: Instruction, Video: here.

Lecture 3 (08/30/2022) (lecture Note, Lecture Review Slides)

1. Energy 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

• In-person lecture video: here.

• Online lecture video: here.

• Examples of Signal Types and Properties: here.

Lecture 4 (09/01/2022) (Lecture Notes, Lecture Review Slides)

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

• In-person lecture video: here.

• Online lecture video: Youtube: here.

• Examples of Periodic Signals: here.

• Homework 2: here, solutions.

• Quiz 1: here, solutions.

• Quiz 1 and Homework 2 Video: here.

Lecture 5 (09/06/2022) (Lecture Notes, Lecture Review Slides)

1. Complex Numbers

2. Specific Signals

   1. Complex Exponentials

• References:

  • Lathi's book: Ch. B.1, 1.4, 8.2

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

• In-person lecture video: here.

• Online lecture video: here.

Lecture 6 (09/08/2022) (Lecture Notes, Lecture Review Slides)

1. Specific Signals

   1. Unit Impluse Signals

   2. Unit Step Signals

• References:

  • Lathi's book: Ch. 1.4, 8.2

  • Mitra's book: Ch. 3.2, 7.3

• In-person lecture video: here.

• Online lecture video: here.

• Homework 3: here, video, solutions.

Lecture 7 (09/13/2022) (Lecture Notes, Lecture Review Slides)

1. System Properties

• Refrences:

  • Lathi's book: Ch. 1.6-1.7, 2.6

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

• In-person lecture video: here.

• Online lecture video: here.

• Lab 2: Instruction, Video: here.

Lecture 8 (09/15/2022) (Lecture Notes, Lecture Review Slides)

1. System Properties Cont.

2. Convolution Integral/Sum

• References:

  • 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

• In-person lecture video: here.

• Online lecture video: here.

Lecture 9 (09/20/2022) (Lecture Notes, Lecture Review Slides)

1. Convolution Examples (Continuous-time)

• References:

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

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

• In-person lecture video: here.

• Online lecture video: here.

• Quiz 2: here, video, solutions

• Homework 4: here, video, solutions.

• Examples:

  • Systems Examples 1: here.

  • Systems Examples 2 (LTI continuous): here.

  • Systems Examples 3 (LTI discrete): here.

Lecture 10 (09/22/2022) (Lecture Notes, Lecture Review Slides, Lecture 10 review for Part I of the course)

1. Convolution Examples (Discrete-time)

2. Convolution Properties

3. Properties of LTI systems using unit impulse response

• References:

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

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

• In-person lecture video: here.

• Online lecture video: here.

• Video of the review of Part I of the course: here.

• Quiz 3: here, solutions

Part II: Continous-time Signals and Systems

Lecture 11 (09/27/2022) (Lecture Notes, Lecture Review Slides)

1. Frequency Basis and Fourier Series (FS)

   1. Cosine and Sine Fourier Series

• References:

  • Lathi's book: Ch. 3.1-3.5

  • Mitra's book: Ch. 5.1

• In-person lecture video: here.

• Online lecture video: Dropbox: here.

Lecture 12 (09/29/2022) (Lecture Notes, Lecture Review Slides)

1. Complex Exponential Fourier Series

• References:

  • Lathi's book: Ch. 3.4-3.7

  • Mitra's book: Ch. 5.1

• In-person lecture video: TBD.

• Online lecture video: here.

• Homework 5: here, video, solutions.

• Lab 3: instruction, video.

Lecture 13 (10/04/2022) (Lecture Notes, Lecture Review Slides)

1. Examples of Complex Exponential Fourier Series

2. Drichlet Conditions

• References:

  • Lathi's book: Ch. 3.4-3.7

  • Mitra's book: Ch. 5.1

• Online lecture video: here.

• Examples

  • Fourier Series Examples 1

  • Fourier Series Examples 2

Lecture 14 (10/06/2022) (Lecture Notes,Lecture Review Slides)

1. Properties of Fourier Series

• References:

  • Lathi's book: Ch. 3.4-3.7

  • Mitra's book: Ch. 5.1

• Online lecture video: here.

• Continuous-time Transform Tables: here.

Lecture 15 (10/18/2022) (Lecture Notes, Lecture Review Slides)

1. Continuous-time Fourier Transform

• References:

  • Lathi's book: Ch. 4.1-4.3

  • Mitra's book: Ch. 5.3

• In-person lecture video: here.

• Online lecture video: here.

• Homework 6: here, here, solutions.

Lecture 16 (10/20/2022) (Lecture Notes, Lecture Review Slides)

1. Magnitude and Phase of CTFT

2. Uniform Convergence Conditions (Dirichlet Conditions)

• References:

  • Lathi's book: Ch. 4.1-4.3

  • Mitra's book: Ch. 5.3

• In-person lecture video: here.

• Online lecture video: here.

• Examples

  • Fourier Transform Examples 1

  • Fourier Transform Examples 2.

Lecture 17 (10/25/2022) (Lecture Notes, Lecture Review Slides)

1. Uniform Convergence Conditions (examples)

2. Properties of CTFT

• References:

  • Lathi's book: Ch. 4.3-4.7

  • Mitra's book: Ch. 5.3-5.5

• In-person lecture video: here.

• Online lecture Video: here.

• Quiz 4: here, solutions.

• Exercise Midterm: here, solutions, video.

Lecture 18 (10/27/2022) (Lecture Notes, Lecture Review Slides)

1. Properties of CTFT

2. Applications: Amplitude Modulations (AM)

• References:

  • Lathi's book: Ch. 4.3-4.7

  • Mitra's book: Ch. 5.3-5.5

• In-person lecture video: here.

• Online lecture video: here.

• Video for the review of Part II of the course: here.

• Slides for the review of Part II: here.

• Homework 7: here, video, solutions.

Lecture 19 (11/03/2022) (Lecture Notes, Lecture Review Slides)

1. Laplace Transform

• References:

  • Lathi's book: Ch. 6.1-6.4

  • Mitra's book: Ch. 5.6

• Online lecture video: here.

Lecture 20 (11/08/22) (Lecture Notes, Lecture Review Slides)

1. Inverse Laplace Transform

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

• References:

  • Lathi's book: Ch. 6.7, 7.1-7.2

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

• In-person lecture video: TBD.

• Online lecture video: here.

• Homework 8: here, video, solutions.

• Laplace Transform Example: here.

• Lab 4: instruction, video.

Part III: Discrete-time Signals and Systems

Lecture 21 (11/10/2022) (Lecture Notes, Lecture Review Slides)

1. Sampling

• References:

  • Lathi's book: Ch. 5.1-5.2, 8.3

  • Mitra's book: Ch.7.1, 7.5

• In-person lecture video: here.

• Online lecture video: here.

• Quiz 5: here, solutions, video.

Lecture 22 (11/15/2022) (Lecture Notes, Lecture Review Slides)

1. Sampling

2. Nyquist Sampling Theorem and Aliasing

3. Anti-Aliasing Filter

• References:

  • Lathi's book: Ch. 5.1-5.2, 8.3

  • Mitra's book: Ch.7.1, 7.5

• Online lecture video: here.

• Sampling Examples: here.

Lecture 23 (11/17/2022) (Lecture Notes, Lecture Review Slides)

1. Discrete-Time Fourier Transform (DTFT)

• References:

  • Lathi's book: Ch. 10.1-10.4

  • Mitra's book: Ch.9.2

• In-person lecture video: here.

• Online lecture video: here.

• Discrete Transform Tables: here.

• Lab 5: here.

• Homework 9: here, video, solutions.

Lecture 24 (11/22/2022) (Lecture Notes, Lecture Review Slides, Circular_Convolution_slides)

1. DTFT Properties

2. DTFT Applications

3. DTFT Existence Conditions

• References:

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

  • Mitra's book: Ch.9.2-9.3, 9.8

• In-person lecture video: here.

• Online lecture video: here.

• DTFT Examples:

  • DTFT Example 1, Example 2.

• Homework 10: here, video. solutions.

Lecture 25 (11/29/2022) (Lecture Notes, Lecture Review Slides)

1. Z-Transform Examples

2. Inverse Z-Transform

3. Applications of Z-Transform

• References:

  • Lathi's book: Ch. 11.1-11.3

  • Mitra's book: Ch. 9.8-9.10

• Online lecture video: here.

• Examples:

  • Z-Transform Example.

• Quiz 6: here, video, solutions.

Lecture 26 (12/01/2022) (Lecture Notes, Lecture Review Slides)

1. Resampling (Downsampling, Upsampling)

• References:

  • Lathi's book: 8.4, 10.4

  • Mitra's book: N/A.

• In-person lecture video: here.

• Online lecture video: here.

• Examples:

  • Resampling Example.

• Quiz 7: here, video, solutions.

• Homework 11: here, solutions.

Lecture 27 (12/06/2022) (Lecture Notes, Lecture Review Slides)

• Video for Review of Part III: here.

• Videos for Homework 11: here.

Lecture 28 (12/08/2022)

• Exercise Final Exam: here, solution.

• video: here.