Signal Processing:
Module A: Representation Theory
B: Time Series Astrophysical Data
Embedded Files
Announcements:
Announcements:
Semester Test 2 Date: 21 May, Time :11-12
Semester Test 2 Date: 21 May, Time :11-12
Tutorial 3 Resources
Tutorial 3 Resources
Note you will have 15 min each to demonstrate your code befor 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
Audio Basics Python Programs
Course Code MATZ 6814
Course Code MATZ 6814
Lecturer
Lecturer
Jeandrew Brink, BrinkJ2@ufs.ac.za , WWG 109
UFS 16 Credits
UFS 16 Credits
Module A, Representation Theory,.Fourier transform and Wavelets
Module B: Time series data. Application to Pulsar data.
Course Material
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
Lectures and Consultation Hours
Fourier Transforms
Fourier Transforms
Lecture 1: Tuesday 10.10 am -12 am WWG119
Lecture 2: Wed 11:10 .am -12am WWG 119
(Possible Lec 3?)
Consultation: Immediately after any class WWG 109
Module A: Representation Theory
Module A: Representation Theory
Description
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
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
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
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
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.
Slide Videos 2025
Slide Videos 2025
13 Feb Vid SP1 Introduction: Fourier Series ( 93MB 35 min) (Slides Lec SP1)
Video SP5 Image Deconvolution Slides Lec SP5
Slides Lec SP6 Slides Lec SP 7
For Interest Tira Spotted Zebra first observation Tira Spotted Zebra as teenager
Audio Intro in Python
Audio Intro in Python
https://www.youtube.com/watch?v=n2FKsPt83_A
Slides Time Series Data
Slides Time Series Data
Ingrid Daubechies Wavelet Basis Video
Python Programs
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
Problem Sets 2025
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