PHYSICS 7007 - Fourier Techniques & Applications

North Terrace Campus - Semester 1 - 2022

An introduction to statistical and Fourier techniques, with applications to experimental design and data analysis.

  • General Course Information
    Course Details
    Course Code PHYSICS 7007
    Course Fourier Techniques & Applications
    Coordinating Unit School of Physical Sciences
    Term Semester 1
    Level Postgraduate Coursework
    Location/s North Terrace Campus
    Units 3
    Contact Up to 2 hours per week
    Available for Study Abroad and Exchange Y
    Assessment Examination, assignments
    Course Staff

    Course Coordinator: Professor Gavin Rowell

    Course Timetable

    The full timetable of all activities for this course can be accessed from Course Planner.

  • Learning Outcomes
    Course Learning Outcomes

    1. Have an understanding of how to derive FT analytically and generate new FTs using various rules.

    2. Develop confidence in solving problems in the appropriate domain, including numerical solutions FT of data and applications to power spectra.

    3. Understand how to be able to apply FT to analysis of linear systems.

    4. Understand the relationship between how the instrument response function limits resolution and its relationship to convolution.

    5. Understand the relationship between the FTs and wave phenomena such as diffraction and scattering from three dimensional objects
    University Graduate Attributes

    This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

    University Graduate Attribute Course Learning Outcome(s)

    Attribute 1: Deep discipline knowledge and intellectual breadth

    Graduates have comprehensive knowledge and understanding of their subject area, the ability to engage with different traditions of thought, and the ability to apply their knowledge in practice including in multi-disciplinary or multi-professional contexts.


    Attribute 2: Creative and critical thinking, and problem solving

    Graduates are effective problems-solvers, able to apply critical, creative and evidence-based thinking to conceive innovative responses to future challenges.


    Attribute 4: Professionalism and leadership readiness

    Graduates engage in professional behaviour and have the potential to be entrepreneurial and take leadership roles in their chosen occupations or careers and communities.


    Attribute 8: Self-awareness and emotional intelligence

    Graduates are self-aware and reflective; they are flexible and resilient and have the capacity to accept and give constructive feedback; they act with integrity and take responsibility for their actions.

  • Learning Resources
    Recommended Resources

    Bracewell, R. N., The Fourier Transform and its Applications, McGraw-Hill

    Champeny, D. C. Fourier Transforms and their Physical Applications, AP

    James, J. F., “A Students Guide to Fourier Transforms”, CUP
  • Learning & Teaching Activities
    Learning & Teaching Modes
    The method of delivery depends on modules selected by students.

    The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

    A student enrolled in a 3 unit course, such as this, should expect to spend, on average 12 hours per week on the studies required. This includes both the formal contact time required to the course (e.g., lectures and practicals), as well as non-contact time (e.g., reading and revision).
    Learning Activities Summary

    One-dimensional FT and applications, including convolution and wavelets
    - Introduction to Fourier transforms of real variables, symmetry relations Application of Fourier Transforms to linear systems with emphasis on circuits, including transfer function and the impulse response
    - Convolution in physical systems, including the Instrument Response
    - The Convolution Theorem and its use in digital filtering and correction for limited instrument response
    - Application of Modulation Rule and Shift Theorem in physical systems
    - Application of Fourier theory in pulse amplifiers, including Comb Filters and signal averaging.
    - The Sampling Theorem and Aliasing
    - Discrete Fourier transforms and the FFT
    - Power spectra
    - Auto and Cross- correlation functions with discrete and continuous variables
    - The Wiener-Khintchine Theorem
    - Fourier Transform spectroscopy

    Two-dimensional FT and applications, including diffraction and antennas
    - Extension to complex functions
    - processing of images
    - Application of W-K theorem to diffraction, including angular spectra and aperture synthesis in radio astronomy
    - Applications of 2-D FT to antennas including broadside arrays and formation of grating lobes

    Three-dimensional FT and applications to weak scattering
    - Three-D Fourier transforms
    - Wave scattering in 3-D (Born approximation), Ewald sphere and reciprocal space.
    - Applications to radiowave scattering from the atmosphere
    - Wavelets and their use.
  • Assessment

    The University's policy on Assessment for Coursework Programs is based on the following four principles:

    1. Assessment must encourage and reinforce learning.
    2. Assessment must enable robust and fair judgements about student performance.
    3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
    4. Assessment must maintain academic standards.

    Assessment Summary
    Written Examination 70%

    Assignments 30%
    Assessment Detail

    The standard assessment consists of 3 assignments. This may be varied by negotiation with students at the start of the semester.

    Final exam
    One 3 hour exam is used to assess the understanding of and ability to use the material.
    If an extension is not applied for, or not granted then a penalty for late submission will apply. A penalty of 10% of the value of the assignment for each calendar day that is late (i.e. weekends count as 2 days), up to a maximum of 50% of the available marks will be applied. This means that an assignment that is 5 days or more late without an approved extension can only receive a maximum of 50% of the mark.
    Course Grading

    Grades for your performance in this course will be awarded in accordance with the following scheme:

    M10 (Coursework Mark Scheme)
    Grade Mark Description
    FNS   Fail No Submission
    F 1-49 Fail
    P 50-64 Pass
    C 65-74 Credit
    D 75-84 Distinction
    HD 85-100 High Distinction
    CN   Continuing
    NFE   No Formal Examination
    RP   Result Pending

    Further details of the grades/results can be obtained from Examinations.

    Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

    Final results for this course will be made available through Access Adelaide.

  • Student Feedback

    The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

    SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy ( course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.

  • Student Support
  • Policies & Guidelines
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