# ELEC442 Digital Signal Processing

## Paper Description

Introduces techniques of digital signal processing for deterministic signals. Covers discrete-time and linear time-invariant systems, difference equation description, the Z-transform, and advanced applications such as FIR filter design.

Students gain a working knowledge of discrete-time signals and systems, using a formalism that is natural to those systems. The paper covers discrete-time, linear time-invariant systems, the impulse response and system function, the frequency response, the Nyquist-Shannon sampling theorem, BIBO stability, difference equation description, the Z-transform and its connection to the discrete Fourier transform, and advanced applications.

Prerequisites:
None

This paper consists of 15 lectures and 6 tutorials. There are 3 assignments.

Assesment:
Final Exam 70%, Assignments 30%

Important information about assessment for ELEC442

Course Coordinator:
Associate Professor Colin Fox

After completing this paper students are expected to have achieved the following major learning objectives:

• Understand the consequences of the sampling theorem.
• Convert between continuous-time and discrete-time signals by using sampling theorem.
• Classify discrete-time signals and linear time-invariant systems using difference equations description.
• Apply the Z–transform to discrete-time signals and systems .
• Perform simple manipulations on Z-transforms, in particular find solutions to some simple systems given by their difference equations or their block diagrams.
• Determine the stability of a linear time-invariant system based on its poles and zeros structure.
• Design elementary infinite impulse response (IIR) and finite impulse response (FIR) filters.
• Construct Matlab functions, using the built-in DSP toolbox, corresponding to FIR filter specifications.

• An overall goal is to provide each student with confidence in their ability to describe linear time-invariant systems and discrete-time signals over the time-domain and over the frequency domain.
• Confidence in interpreting block diagram representation of a linear time-invariant system.

Topics:

• Classification of signals/systems
• Sampled waveforms
• Common waveforms
• Sampling theorem
• Signal reconstruction, Quantisation
• Introductions of the Z-transform
• Consequences of the sampling theorem
• Properties of the Z-transform
• Introduction of the system function
• Analysis of a linear time-invariant system over the z domain
• Manipulating the Z-transforms
• Block-diagram representation of linear time-invariant systems
• Causality and stability
• Introduction of digital filters and the two big classes: IIR and FIR filters
• Interpretation of a typical filter specification
• Four classes of linear phase digital filters
• Filter design by windowing technique

# Formal University Information

The following information is from the University’s corporate web site.

## Details

An introduction to techniques of digital signal processing for deterministic signals: discrete-time and linear time-invariant systems, difference equation description, the Z-transform, and advanced applications such as FIR filter design.

Paper title Digital Signal Processing ELEC442 Electronics 0.0833 10 points Second Semester \$653.49 \$2,757.23
Limited to
BSc(Hons), PGDipSci, MSc, MAppSc
Contact
colin.fox@otago.ac.nz
Teaching staff

Course co-ordinator: Associate Professor Colin Fox
Dr Tim Molteno

Textbooks
Textbooks are not required for this paper.
Global perspective, Interdisciplinary perspective, Lifelong learning, Scholarship, Communication, Critical thinking, Information literacy, Research, Self-motivation, Teamwork.
Learning Outcomes
By the end of the module students are expected to be able to:
1. Understand the consequences of the sampling theorem
2. Convert between continuous-time and discrete-time signals by using sampling theorem
3. Classify discrete-time signals and linear time-invariant systems using difference equations description
4. Apply the Z-transform to discrete-time signals and systems
5. Perform simple manipulations on Z-transforms, in particular find solutions to some simple systems given by their difference equations or their block diagrams
6. Determine the stability of a linear time-invariant system based on its poles and zeros structure
7. Design elementary infinite impulse response (IIR) and finite impulse response (FIR) filters
8. Construct Matlab functions using the built-in DSP toolbox corresponding to FIR filter specifications

## Timetable

### Second Semester

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
None

An introduction to techniques of digital signal processing for deterministic signals: discrete-time and linear time-invariant systems, difference equation description, the Z-transform, and advanced applications such as FIR filter design.

Paper title Digital Signal Processing ELEC442 Electronics 0.0833 10 points Second Semester Tuition Fees for 2020 have not yet been set Tuition Fees for international students are elsewhere on this website.
Limited to
BSc(Hons), PGDipSci, MSc, MAppSc
Contact
colin.fox@otago.ac.nz
Teaching staff

Course co-ordinator: Associate Professor Colin Fox
Dr Tim Molteno

Textbooks
Textbooks are not required for this paper.
Global perspective, Interdisciplinary perspective, Lifelong learning, Scholarship, Communication, Critical thinking, Information literacy, Research, Self-motivation, Teamwork.
Learning Outcomes
By the end of the module students are expected to be able to:
1. Understand the consequences of the sampling theorem
2. Convert between continuous-time and discrete-time signals by using sampling theorem
3. Classify discrete-time signals and linear time-invariant systems using difference equations description
4. Apply the Z-transform to discrete-time signals and systems
5. Perform simple manipulations on Z-transforms, in particular find solutions to some simple systems given by their difference equations or their block diagrams
6. Determine the stability of a linear time-invariant system based on its poles and zeros structure
7. Design elementary infinite impulse response (IIR) and finite impulse response (FIR) filters
8. Construct Matlab functions using the built-in DSP toolbox corresponding to FIR filter specifications

## Timetable

### Second Semester

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
None