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 in the metal wall folder outside the ECE office before the following 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 25 Jan Introduction to DSP Chap 1 Syllabus, video, PS1, PS1_ecg.txt (r-click, save link as...)
2 27 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 1 Feb Symmetry 2.1.3 PS3 and solutions
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 3 Common sequences, sampling 2.3 CP4, CP4 Solutions
Video link
Whiteboards for above
5 8 DT Systems, examples and types 2.4 PS5 and solutions
Video link
Whiteboards for above
6 10 Convolution 2.5.1  CP6, CP6 Solutions
Video link
Whiteboards for above
MATLAB convolution demo
7 15
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 17 Test 1: DT Signals & Systems in the Time Domain    
9 22 DTFT - intuition and math 3.1 PS9**, CP and Solutions
Video link
Whiteboard for above
10 24 DTFT - tables, properties 3.1 CP10, CP10 Solutions, PS10, PS10 Solutions, DTFT Tables (also lab due in the afternoon)
Whiteboards for above
11 1 Mar 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 3 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 8 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 10 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 15 Inverse Z transform by PFD 3.9 PS15, PS Solutions, 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 17 Review Test 2: signals in the freq domain   Test 2 study guide, example test, example test solutions
Whiteboard for above
exoplanet.m A short script that shows how the DFT might be used to detect an exoplanet (goes along with a question I fielded by Jeremiah/Brahn - do not worry about it if you were not present for it)
17 22 Test 2: Signals in the frequency domain
  In-person in NEB427/NEB428
18 26 Transfer function: 3 perspectives notes no HW!  Filter demo (also lab due in the afternoon)
19 29 Steady-state vs causal responses notes PS19**, CP, CP Solutions, Class Notes
Video example (14 min)
Whiteboard for above
20 31 Geometric interpretation of pole/zero plots   PS20, Solutions, Class Notes
21 5 Apr 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 7  FIR and IIR filters, C code   PS22**, c-code outline
23 15 Filter design using Matlab PS23** (includes class notes), in-class minilab
24 19 Sampling of CT signals in the freq domain 4.1,2 Work on Lab 6
25 21 DSP site visit   (lab presentations due in afternoon)
26 26 Modern Topics in DSP    
27 28 Final exam review - Test 1, course admin   Final exam study guide
Practice Exam Block 1
Practice Exam Block 1 Solutions
28 3 May Final exam review - Test 2   Practice Exam Block 2
Practice Exam Block 2 Solutions
  6 Final Exam 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  


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.