EE431: Discrete-Time Signal Processing

Introduction to the fundamentals of discrete-time signals and systems including the representation of discrete-time and digital signals, analysis of linear discrete-time signals and systems, frequency response, discrete Fourier transform, Z transform, and sampled data systems. The design and analysis of digital filters are examined. The laboratory emphasizes practical considerations involved with the implementation of DSP algorithms. MATLAB will be used for digital signal generation, plotting and the implementation and analysis of DSP operations. Prerequisite: EE230. (2 lecture hours, 2 lab hours, 3 credit hours)

Lecture Schedule

In the following table, the readings and homework are assigned on the day listed and due at the start of the following lesson. The readings are taken from the custom-printed class textbook unless otherwise noted. This semester, as we struggle with COVID restrictions, join me virtually at our classroom Zoom site here. ** = HW is collected at the start of the following class (or in the metal folder outside the ECE Department if you are unable to attend class). CP problems due but not collected.

You can purchase a hardcopy of the textbook at the bookstore, or an electronic version using this link.

You can use/install/download MATLAB four different ways as described here.

#	Date	Title	Read	Homework & Handouts
1	30 Aug	Introduction to DSP	Chap 1	Syllabus, video, PS1, PS1_ecg.txt (r-click, save link as...)
2	4 Sep	Discrete time signals overview	2.1-2.1.2	CP2, CP2 Solutions, More Problems, More Solutions Overview.mp4 (4 min) Representation of Signals.mp4 (8 min) Sequence Lengths.mp4 (12 min) Intro to Sampling.mp4 (7 min) Operations.mp4 (14 min) whiteboards for above
3	11	Symmetry	2.1.3	PS3 CP3, CP3Solutions 01 Up and Downsampling (10 min) 02 Even and Odd Symmetry (6 min) 03 Complex Conjugate Symmetry (6 min) 04 PCS, PCA Symmetry Definition (10 min) 05 PCS, PCA Symmetry Example (15 min) 06 Other Signal Descriptors (12 min) whiteboards for above
4	13	Common sequences, sampling	2.3	CP4, CP4 Solutions Video link Whiteboards for above
5	18	DT Systems, examples and types	2.4	PS5 and solutions 01 Sampling Review (7 min) 02 Sampling Quz (3 min) 03 DT System Representation (9 min) 04 DT System Characterization (7 min) Whiteboards for above
6	20*	Class is asynchronous (view videos) Convolution	2.5.1	CP6, CP6 Solutions 01 DT Math (8 min) 02 DT Properties (3 min) 03 MATLAB (8 min) 04 Graphical (10 min) Whiteboards for above MATLAB convolution demo
7	25	Review for Test 1: signals and systems in the time domain		Test 1 study guide Sample test, solutions 01 Sequences (12 min) 02 Sequences (4 min) 03 Block Diagrams (12 min) 04 Symmetry (4 min) 05 Symmetry (8 min) 06 Convolution (13 min) Whiteboards for above Extra block diagram to DE problem (5 min)
8	27	Test 1: DT Signals & Systems in the Time Domain
9	2 Oct*	Class is asynchronous (view videos) DTFT - intuition and math	3.1	PS9**, CP and Solutions 01 Frequency Domain Overview (8 min) 02 Intuition (6 min) 03 Math (6 min) 04 Example (5 min) 05 MATLAB (4 min) 06 Euler's Identities (5 min) Whiteboard for above
10	4	DTFT - tables, properties	3.1	CP10, CP10 Solutions, PS10, DTFT Tables (also lab due in the afternoon) Video Whiteboards for above
11	9	DFT - intuition, math, and Matlab	3.2	PS11/12, due at start of lecture 13, CP, CP Solutions 01 Intuition (13 min) 02 Math (3 min) 03 Math Example 1 (6 min) 04 Real World Example; MP3 (7 min) 05 MATLAB (4 min) 06 Math Example 2 (5 min) Whiteboards for above
12	11	Changing between the DTFT, DFT	3.3	2 lesson HW assignment 01 Review (19 min) 02 Zero Padding (9 min) 03 DFT to DTFT (8 min) 04 k vs. w vs. f (5 min) 05 Summary (6 min) Whiteboards for above
13	16	DFT properties, linear convolution w/ DFT	3.4, 3.6	PS13, PS Solution, CP and solutions, DTFT Tables 01 Circular Shifting (11 min) 02 Linear Convolution Review (5 min) 03 Circular Convolution (5 min) 04 Linear Convolution with DFTs (15 min) Whiteboards for above
14	18	Z transform - math, intuition, properties	3.7-3.8	PS14**, CP, CP Solutions Z transform tables, notation handout (also lab due in the afternoon) 01 Big Picture (7 min) 02 Math (11 min) 03 Tables (4 min) 04 Z vs. DTFT (8 min) 05 Notation (5 min) 06 Visualizing (5 min) 07 Example (4 min) Whiteboards for above
15	23	Inverse Z transform by PFD	3.9	PS15, student notes, Z-plane app, CP, CP Solutions 01 Big Picture (11 min) 02 Partial Fraction Decomposition (15 min) 03 Residuez (MATLAB) (5 min) 04 Long Division (3 min) 05 Filter (MATLAB) (2 min) 06 Example I (old HW) (16 min) 07 Example II (Investment) (15 min) Whiteboards for above
16	25	Review Test 2: signals in the freq domain		Test 2 study guide, example test, example test solutions 01 Comparison of DTFT, DFT, Z (12 min) 02 DTFT Review (9 min) 03 DFT Review (8 min) 04 Z Transform Review (10 min) Whiteboard for above exoplanet.m A short script that shows how the DFT might be used to detect an exoplanet
17	30	Test 2: Signals in the frequency domain		In-person in NEB427/NEB428
18	1 Nov	Transfer function: 3 perspectives	notes	no HW! Filter demo (also lab due in the afternoon)
19	6	Steady-state vs causal responses	notes	PS19**, CP, CP Solutions, Class Notes Video example (14 min) Whiteboard for above 01 Steady State Review (11 min) 02 Causal Input Response (12 min) Raw video 1 (starts with above, contains more) Raw video 2 (on easy filter design method) Whiteboards for above lessons
20	8	Geometric interpretation of pole/zero plots		PS20, Solutions, Class Notes Raw, unedited video Whiteboard for above
21	13	FIR filters: Ideal and realizable LP, HP		no HW! Student Notes 01 Review Geometric Interpret of H(z) (9 min) 02 FIR Filters (5 min) 03 Zero Phase Filters (9 min) 04 Linear Phase Filters (5 min) 05 Nonlinear Phase Filters (3 min) 06 New FIR Notation (4 min) 07 Classification of Systems (4 min) 08 Classifications of FIR Filters (4 min) Whiteboards for above
22	15	FIR and IIR filters, C code		PS22**, c-code outline
23	27	Filter design using Matlab		PS23** (includes class notes), in-class minilab
24	29	Sampling of CT signals in the freq domain	4.1,2	Work on Lab 6
25	4 Dec	DSP site visit		(lab presentations due in afternoon)
26	6	Modern Topics in DSP
27	11	Final exam review - Test 1, course admin		Final exam study guide Practice Exam Block 1 Practice Exam Block 1 Solutions
28	13	Final exam review - Test 2		Practice Exam Block 2 Practice Exam Block 2 Solutions
	19	Final Exam		Tue, 19 Dec 0830-1130

Lab Schedule

In the following table the lab occurs on the given date, the prelab is due on that date, and the lab report is due on the following lesson. More information on lab policies are in the syllabus.

#	Date	Title	Handouts
1	27 Jan	Matlab Review I	Lab 1 kit
2	3 Feb	Matlab Review II
3	10	Time Domain Signals I	Lab 2 kit
4	17	Time Domain Signals I
5	24	Time Domain Systems I	Lab 3 kit
6	3 Mar	Time Domain Systems II
7	10	Frequency Domain DTFT I	Lab 4 kit
8	17	Frequency Domain DTFT II
9	26	Frequency Domain DFT I	Lab 5 kit
10	31	Frequency Domain DFT II
11	7 Apr	Project Lab prep	Lab 6 instructions
12	14	Project Lab prep
13	21	Project Presentations
14	28	Lab cleanup

Other

Mitra text errata You may want to update your Mitra text with these before the first lesson.

FE Reference Handbook. This printed book is an authorized reference in all my exams. You can download a free pdf version (not authorized for my exams unless you print the entire text) directly from the NCEES website, and it is a good general reference for homework (especially for integral equations).

Z-Plane Simulator Free software I wrote that lets one drag poles and zeros around the z-plane. It plots the resulting frequency response and time response to an impulse, step, or sinuosoid.