ECE 455: Digital Signal Processing

Digital signal processing (DSP) is the mathematical manipulation of a discrete-domain information signal to enhance or simply modify it in some way. The objective of this course is to introduce students to fundamental concepts of digital signal processing including sampling and reconstruction, the z-Transform, discrete-time Fourier transforms and their implementations, FIR and IIR digital filtering, multirate signal processing and digital media. The purpose of the tutorials is to help elucidate lecture concepts and problem set assignments while the labs aim to provide more hands-on-experience of DSP concepts.


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, Prentice-Hall, 2007. ISBN-13: 9780131873742.

The following topics and text book sections are covered in this course.

  • Review of ECE355 Concepts: Signal classes, sampling theorem, overview of analog-to-digital and digital to-analog conversion. (Text, §1.1-1.4). Discrete-time signals and systems. (Text, §2.1-2.5). Discrete-time Fourier transform and analysis. (Text, §4.1-4.4, 5.4).
  • DFT and FFT: Discrete Fourier Transform, complexity of filtering, radix-2 fast Fourier transform (Text, §7.1, 7.2, 7.3, 8.1, 8.4).
  • The z-Transform: definition, properties, rational z-transforms, inverse of z-transform, analysis of LTI systems in the z-domain. (Text, §3.1-3.4).
  • Design of Digital Filters: Design of FIR, IIR filters from analog filters, frequency transformations. (Text, §10., 10.2, 10.3, 10.4).
  • Applications to audio, image and video processing. (supplementary notes).
  • Multirate digital signal processing: integer decimation and interpolation, rater conversion by a rational factor. (Text, portions of §11.1-11.4).


Lecture Notes and Related Handouts


Problem Sets and Solutions

Problem Set Questions Solutions
1 1.1, 1.7, 1.8, 1.9, 1.15 PDF
2 2.2, 2.3, 2.4, 2.7, 2.10, 2.11, 2.23, 2.29, 2.35, 2.37, 2.38, 2.41
3 2.31, 2.44, 2.46, 2.49, 2.52
4 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
5 5.1, 5.3, 5.4(a,b,c,d,n), 5.9, 5.11, 5.23
6 7.1, 7.2, 7.3, 7.7, 7.8, 7.11, 7.13(a), 7.14, 7.23(a,b,c,h), 7.25, 7.28
7 8.1, 8.3, 8.4, 8.8, 8.11, 8.13, 8.16, 8.19, 8.20, 8.25, 8.35 PDF
8 3.1, 3.3, 3.5, 3.6, 3.7, 3.9
9 3.12, 3.13, 3.14(a,i,j), 3.15, 3.18, 3.23, 3.24, 3.25, 3.28, 3.32, 3.36, 3.37, 3.39, 3.40, 3.41, 3.51, 3.53
10 11.5, 11.9, 11.12, 11.13


Note: Problem set solutions are courtesy of Jin Wei , Eman Hammad , Wael Louis and Xingyu Li, past and present TAs for this course.



The Lab webpage courtesy of Mr. Bruno Korst is at: Please note that the labs will be made available by Mr. Korst (i.e., their links will work) at least two weeks before the associated lab day.



Course Policies

  • The course will make use of Blackboard ( for important course announcements. All students must register on Blackboard and check it regularly.
  • All tests and the final exam make use of a non-programmable (Type 2) calculator. No programmable calculators are allowed. The final exam is Type C (candidates may prepare, bring to the exam and use a single standard aid sheet supplied by the registrar’s office).
  • The Faculty’s policy on Petition for Consider in Course Work will be employed for missed tests and late assignments. Official supporting documentation must be provided and the completed petition must be filed with the EngSci Office. How To Deal with Missed Course Credit Due to Illness:
  • Questions regarding marking must be formally written on a piece of paper and submitted along with the associated test/assignment to the cognizant TA. There is a 48-hour limit (excluding weekends and holidays) from the time the test/assignment is first returned in which you may request a recheck.
  • Please note that late assignments (e.g., lab write-ups) will be deducted 15% per business day.
  • Academic integrity is of utmost important. Any issues of plagiarism and inappropriate collaboration will be taken seriously and reported to the appropriate higher authority.
  • Students with diverse learning styles and needs are welcome in this course. In particular, if you have a disability/health consideration that may require accommodations, please feel free to approach me and/or Accessibility Services at (416) 978 8060;