GPGN 404 — Digital Analysis

Mathematical analysis and processing of digital signals, for seniors and graduate students at Mines.

Summary

We live in a digital world. Speech, image, video, almost any signals worth recording today are sampled functions of time, space, or both. In this course, we learn the special characteristics of these digital signals, and how to analyze and enhance them with computers.

We will focus on four aspects of digital signal processing:

  • Convolutional (FIR - finite impulse response) filters
  • Recursive (IIR - infinite impulse response) filters
  • Sinc interpolation of bandlimited signals
  • Discrete Fourier transforms

For each aspect, we will study existing industrial-strength computer programs, write simpler programs ourselves, and then use these programs to process various digital signals.

Time and place

Mondays, Wednesdays, and Fridays, 10:00-10:50 am; GC 215/297

Text

Discrete-Time Signal Processing, 3rd Edition, by Oppenheim and Schafer. Available from amazon.com and other bookstores.

Grading

Your grade is based on

  • 10%: classwork
  • 15%: homework and labs
  • 50%: midterm exams (two)
  • 25%: final exam

Homework and labs are discussed, graded and returned promptly, and only work submitted on time will be accepted for grading. Assistance from others on labs and homework is permitted under the following conditions: (1) those providing assistance must not share their computer programs or solutions, and (2) recipients must acknowledge any assistance in all work submitted.

Schedule

Week Dates Subjects
0 08/20-08/22 Discrete-time signals and systems (2.0-2.2)
1 08/25-08/29 Linear time-invariant systems and difference eqns (2.3-2.6)
2 09/01-09/05 Fourier transforms and symmetries (2.7-2.9)
3 09/08-09/12 Z-transforms and regions of convergence (3.0-3.2)
4 09/15-09/19 Z-transform properties and theorems (3.3-3.5)
5 09/22-09/26 Review and 1st midterm exam
6 09/29-10/03 Sampling theory (4.0-4.1)
7 10/06-10/10 Reconstructing bandlimited signals (4.2-4.3)
8 10/15-10/17 Processing and resampling (4.4-4.6, Fall Break)
9 10/20-10/24 Frequency responses of LTI systems (5.0-5.1)
10 10/27-10/31 SEG meeting (no classes)
11 11/03-11/07 Frequency responses for rational systems (5.2-5.3)
12 11/10-11/14 Review and 2nd midterm exam
13 11/17-11/21 The discrete Fourier transform (8.0-8.5)
14 11/24 DFT wrapup (Thanksgiving holiday)
15 12/01-12/03 Review for final exam (Dead Day)