# MATH 7019 Mathematics of Signal Processing

Credit Points 10

Legacy Code 301440

Coordinator Paul Hurley Opens in new window

Description This subject teaches students to abstract and develop algorithms, in Python, for analysing and processing deterministic and stochastic data/signals. Students are taught strategies in developing solutions that are optimal and efficient to implement. They learn how to analyse signals under the Fourier transform and under different bases, allowing for an appreciation of how lossy compression works, and how to formulate and solve some convex optimisation algorithms. This subject will be undertaken at Parramatta City - Hassall St campus.

School Computer, Data & Math Sciences

Discipline Mathematics

Student Contribution Band HECS Band 1 10cp

Check your fees via the Fees page.

Level Postgraduate Coursework Level 7 subject

Restrictions

Students must be enrolled in a postgraduate program

Assumed Knowledge

Students should know and understand basic linear algebra. Basic programming skills are necessary. Familiarity with Python notebooks is helpful but not mandatory.

## Learning Outcomes

On successful completion of this subject, students should be able to:

1. Explain mathematical formulations of signal processing algorithms
2. Demonstrate mastery of tools for tackling advanced signal and data processing problems
3. Analyse advanced signal and data processing algorithms using numerical python programming
4. Design applications as advanced signal and data processing algorithms
5. Appraise applications of mathematical signal processing

## Subject Content

1.Motivation - what is mathematics of signal processing, etc.
2.Linear algebra and Hilbert spaces
Examples ? neural networks
Basis and frames
3.Fourier Transforms
Continuous Fourier series, Fast Fourier transforms
Convolution
4.Sampling and interpolation
1D, 2D (sphere/manifold)
5.Filtering
Finite Impulse Response (FIR) filters, Infinite Impulse Response (IIR) filters
6.Approximation and compression
Wavelets
Time-frequency analysis
7.Inverse problems and optimisation
Compressed sensing
LASSO
8.Random signals
Probabilistic modelling
Wiener filter, etc.
Max likelihood / EM
9.Event-driven sampling/filtering
Sampling in time vs sampling in amplitude
Filtering in asynchronous time
10.Array signal processing
Beamforming

## Assessment

The following table summarises the standard assessment tasks for this subject. Please note this is a guide only. Assessment tasks are regularly updated, where there is a difference your Learning Guide takes precedence.

Type Length Percent Threshold Individual/Group Task Mandatory
Quiz 30 minutes (per Quiz) 20 N Individual Y
Applied Project 16 hours 30 N Individual Y
Practical Exam 1.5 hours 20 Y Individual Y
Practical Exam 2 hours 30 Y Individual Y

Teaching Periods

## Autumn (2024)

### Parramatta City - Macquarie St

#### On-site

Subject Contact Paul Hurley Opens in new window

View timetable Opens in new window