 Digital signal processing is the mathematical manipulation of a discrete-domain information signal to modify or improve it in some way. This course provides an introduction to fundamental concepts in digital signal processing. Topics include sampling and reconstruction, discrete-time signals and linear time-invariant systems, the z-Transform, discrete-time Fourier transform, fast Fourier transform, and discrete-time filters. Applications to audio, image, video and communications signal processing are provided throughout. |
Course Syllabus
This course makes use of the following text:
John G. Proakis and Dimitris G. Manolakis, Digital Signal Processing: Principles, Algorithms, and Applications, 4th edition, 2007.
The following topics and text book sections are covered in this course:
- Introduction: Review of signal classes and the sampling theorem, overview of analog-to-digital and digital-to-analog conversion.
(Text, §1.1, 1.2, 1.3, 1.4) - Discrete-Time Signals and Systems: Analysis of discrete-time linear time-invariant (LTI) systems, difference equations, implementation.
(Text, §2.1, 2.2, 2.3, 2.4, 2.5) - The z-Transform: definition, properties, rational z-transforms, inverse of z-transform, analysis of LTI systems in the z-domain.
(Text, §3.1, 3.2, 3.3, 3.4) - Frequency-Domain Analysis: Discrete-time Fourier transform, frequency response of LTI systems, frequency selective filters, inverse systems and deconvolution
(Text, §4.1, 4.2, 4.3, 4.4, 5.1, 5.2, 5.4, 5.5) - DFT and FFT: Discrete Fourier Transform, complexity of filtering, radix-2 fast Fourier transform
(Text, §7.1, 7.2, 8.1) - Applications to audio, image and video processing.
(supplementary notes and Text, §11.2, 11.3, 11.4).
Lecture Notes and Related Handouts
LEC 01: Mondays 9:00 am – 10:00 am GB 120, Wednesdays 1:00 pm – 2:00 pm GB 220, Thursdays 4:00 pm – 5:00 pm BA 1210
- Course Information Sheet/Syllabus
- Introduction to Digital Signal Processing
- Discrete-Time System Properties
- Difference Equations and Implementation
- The z-Transform and Its Applications
- Test 1 Review
- Rational z-Transform and Its Inverse
- Continuous-Time Frequency Analysis
- Frequency Analysis of Discrete-Time Systems courtesy of Eman Hammad
- Properties of the Discrete-Time Fourier Transform courtesy of Eman Hammad
- Frequency Domain Characteristics of LTI Systems courtesy of Eman Hammad
- Fourier Update and Review
- Frequency Domain Analysis of LTI Systems
- The Discrete Fourier Transform
- The Fast Fourier Transform
- FFT Decimation Animation courtesy of Eman Hammad
- Digital Audio
- Audio Special Effects
- Introduction to Image Processing <– Warning this file is over 30MB.
- Introduction to Video Processing and Edge Detection
- Course Review
Problem Sets and Solutions
| Tutorial (Date) | Problem Set Questions | Solutions | |
| 1 (Jan 17) | 1.1, 1.3, 1.4, 1.5 | ||
| 2 (Jan 24) | 1.7, 1.15, 2.2, 2.3, 2.4, 2.7. | ||
| 3 (Jan 31) | 2.10, 2.11, 2.23, 2.29, 2.31, 2.35, 2.37, 2.38, 2.41, 2.44, 2.46, 2.49, 2.52. | ||
| 4 (Feb 7) | TEST 1 | ||
| 5 (Feb 14) | 3.1, 3.3, 3.5, 3.6 | ||
| X (Feb 21) | READING WEEK | ||
| 6 (Feb 28) | 3.7, 3.9, 3.12, 3.13, 3.14(a,i,j), 3.23, 3.28, 3.32, 3.40, 3.51 | ||
| 7 (Mar 7) | 4.4,4.5,4.6(b,d,f),4.7(a),4.8,4.10(b,c),4.12,4.14,4.17,4.18,4.19,4.22 | ||
| 8 (Mar 14) | — |
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| 9 (Mar 21) | 5.1, 5.3, 5.4(a,b,c,d,n), 5.9, 5.11, 5.23, 5.31, 5.65 | ||
| 10 (Mar 28) | 7.1, 7.3, 7.7, 7.13(a), 7.23(a,b,c,h), 7.25, 7.28, 8.1, 8.3, 8.4, 8.8, 8.11, 8.25 | ||
| 11 (Apr 4) | TEST 2 | ||
| 12 (Apr 11) | 11.5, 11.9, 11.12, 11.13 |
Note: Problem set solutions are courtesy of Jin Wei and Eman Hammad, TAs for this course.
Labs
The Lab webpage courtesy of Mr. Bruno Korst is at: http://www.comm.utoronto.ca/~bkf/ECE362/