## 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.

**Additional outcomes:**

- 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 |
---|---|

Paper code | ELEC442 |

Subject | Electronics |

EFTS | 0.0833 |

Points | 10 points |

Teaching period | Second Semester |

Domestic Tuition Fees (NZD) | $640.66 |

International Tuition Fees (NZD) | $2,676.93 |

- 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.
- Graduate Attributes Emphasised
- Global perspective, Interdisciplinary perspective, Lifelong learning, Scholarship,
Communication, Critical thinking, Information literacy, Research, Self-motivation,
Teamwork.

View more information about Otago's graduate attributes. - Learning Outcomes
- By the end of the module students are expected to be able to:
- 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