Announcements:

Intro Slides for Planetary Motion

Tutorial 3 Musical Tut Due 7 May

Music file for Musical Tut Tr7Short.wav

See Python Programs heading below for example Starter programs using Audio files

Check out the International Pulsar Timing Array workshop.

If interested please preregister to ensure you become eligable for funding

Mainly the Student week will be useful for you at this time

https://ipta4gw.org/meetings/2026/

Tutorial Two Due 19 March in class

Tutorial One Due 2 March in class

Course Code MATZ 6814

Lecturer

Jeandrew Brink, BrinkJ2@ufs.ac.za , WWG 109

UFS 16 Credits

Module A, Representation Theory,.Fourier transform and Wavelets
Module B: Time series data. Application to Pulsar data.

Course Material

Notes, articles assignments posted on this webpage.

Notes by C Venter/ HCoetzer on Fourier Transforms.!!!

Ten Lectures of Wavelets by Ingrid Daubechies

Digital Image Processing 4th edition, 2018 by R. C. Gonzalez and R. E. Woods. (GW)

Handbook of Pulsar Astronomy Duncan Lorimer Micheal Kramer (2004) ISBN-13 978-0521828239

Pulsar Searching Software PRESTO Scott Ransom (Thesis) and references at the bottom of PRESTO Software Github

Images: Intensity data for Pulsar J0737 -3029A taken with MeerKAT Radio Telescope. L Band.

Lectures and Consultation Hours

Fourier Transforms

Lecture 1 :Monday 11.10 am -13 am WWG119

Lecture 2: Thurs 8:10 .am -10am WWG 119

(Consultation: Immediately after any class WWG 109

Module A: Representation Theory

Signal Processing:

Module A: Representation Theory

B: Time Series Astrophysical Data

Description

In modern society we often make a digital representation of the world a round us. For example, we may take a photograph on an object with optical, infrared or x-ray sensors (such as CCD cameras) or record a time series of intensity data with a optical or radio telescope. This module explores the mathematical techniques of storing, manipulating, transforming and extracting useful information of these digital representations of reality.

Topics that will be covered are Discrete Fourier Transforms, Cosine transforms and Wavelets. Theorems and characteristics that govern these transforms will be explored in detail

Filtering techniques to enhance images and reduce noise in frequency domain (high, low and band pass filter) or physical domain (Point transformations, convolution).

Alternate representations of data and transforms such as Haar and Daubechies Wavelets.

This is a sub module has several applications in either:

The Digital image Processing: specifically with applications to medical imaging and photography or the
Signal analysis for analysing time series data from astrophysical transients or pulsar data.

Evaluation for Module A

Module A will be evaluated with one semester test counting 50 % of the mark for the module.

The two tutorial assignments will make up the remaining 50 %.

The semester test provisional schedule

Semester Test 1 ~ Thursday 26 March 11:00-13:00 In class, closed book

Grading Policy

No tutorials will be accepted after the due date. Hard copies must be handed in for grading.

In the unfortunate circumstance of missing a semester test, the lecturer must be notified within 24 h. In the case of illness, a doctors certificate must be provided. A make up / special test, may be oral and/or written and will cover all the semesters work.

Great emphasis is placed on original, creative work. Collaboration on homework sets is allowed provided collaborators are given credit and the person handing in the answer can provide all the steps in obtaining the answer and defend the reasoning. If other sources are used, such as, books, articles, web etc they must be referenced. Should plagiarism be suspected, a student will be asked to solve a similar problem on the blackboard during a consultation session, to obtain the marks for the tutorial.

Computing

Any programming language can be used to do the exercises. (Matlab Python3, C++, Mathematica.)

Examples will be given in the form of Python notebooks.

Module B: Time Series Data, Application Pulsar Science MATZ

This Module specifically looks at the techniques for analyising time series astrophysical data. Ultimately focusing on the searching and timing techniques for pulsar timing. Aspects from the Handbook of Pulsar Astronomy will be examined. The pulsar search algorithms will be introduced using approach followed by Scott Ransom who wrote PRESTO, one of the dominant search algorithms used in the Pulsar Community. The application of other transforms to pulsar data in particular the data of J0737 will also be explored.

Simulation of Pulsar J0737

Pulse Profile measured with MeerKAT

Search Collaboratory Manuals

Slide Videos 2025

13 Feb Vid SP1 Introduction: Fourier Series ( 93MB 35 min) (Slides Lec SP1)

Vid SP2 Python Basics

Slides Lec SP2 Slides Lec SP3

Slides Lec SP4

Video SP5 Image Deconvolution Slides Lec SP5

Slides Lec SP6 Slides Lec SP 7

Slides Lec SP89

For Interest Tira Spotted Zebra first observation Tira Spotted Zebra as teenager

Slides Lec SP10 Video Lec 10

Audio Intro in Python

https://www.youtube.com/watch?v=n2FKsPt83_A

Slides Time Series Data

TS2024Lec1

TS2024Lec2

TS2024Lec3

Ingrid Daubechies Wavelet Basis Video

TS2024Lec4_5

TS2024Lec5_6

TS2024Lec7

Lecture notes on Audio Signals

TSdataL8

TSdataL9

TSdataL10

Python Programs

Fourier1.ipynb Open with Google Colaboratory when connected to the internet

Fourier2.ipynb Complex examples of a Fourier Series

FourierDFT_Ex1.ipynb Code to perform the Discrete Fourier Transform and work out the convolution between two functions

Fast Fourier Transform 2D Example FFT2D_Ex1.ipynb

FFT 2D Example 2 Sine waves and a gaussian FFT2D_Ex2.ipynb

How to split a color image into constituent parts and make a grayscale image FirstPicsZebraBaby_Ex1.ipynb make sure you first download the image zebra-baby.jpg and place it in the working directory where python is running.

Audio Basics Python Programs

Making sounds AudioExBasicSound.ipynb

Loading a .wav file starter pack AudioExStarterPack.ipynb

Example .wav file Download this file into your working directory PiratesTr6Short.wav

Problem Sets 2025

Tutorial 1

Tutorial 2

Tutorial 3 .... Start Early to enable time for Coding !!!!!

Note you will have 15 min each to demonstrate your code before the class an discuss some of the results and answer a few question from me.

20 out of 100 marks will be awarded for this presentation. The remainder on the plots and written discussion you hand in.

Audio Basics Python Programs

Making sounds AudioExBasicSound.ipynb

Loading a .wav file starter pack AudioExStarterPack.ipynb

Example .wav file Download this file into your working directory PiratesTr6Short.wav

Tutorial 4

Page updated

Google Sites

Report abuse