# ECE 362: Digital Signal Processing

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).

### Problem Sets and Solutions

 Tutorial (Date) Problem Set Questions Solutions 1 (Jan 17) 1.1, 1.3, 1.4, 1.5 PDF 2 (Jan 24) 1.7, 1.15, 2.2, 2.3, 2.4, 2.7. PDF 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. PDF 4 (Feb 7) TEST 1 PDF 5 (Feb 14) 3.1, 3.3, 3.5, 3.6 PDF 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 PDF 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 PDF 8 (Mar 14) — — 9 (Mar 21) 5.1, 5.3, 5.4(a,b,c,d,n), 5.9, 5.11, 5.23, 5.31, 5.65 PDF 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 PDF 11 (Apr 4) TEST 2 PDF 12 (Apr 11) 11.5, 11.9, 11.12, 11.13 PDF

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/