PHYSICS 7007 - Fourier Techniques & Applications
North Terrace Campus - Semester 1 - 2019
General Course Information
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 Course Description An introduction to statistical and Fourier techniques, with applications to experimental design and data analysis.
Course Coordinator: Professor Gavin Rowell
The full timetable of all activities for this course can be accessed from Course Planner.
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) Deep discipline knowledge
- informed and infused by cutting edge research, scaffolded throughout their program of studies
- acquired from personal interaction with research active educators, from year 1
- accredited or validated against national or international standards (for relevant programs)
1,3,4,5 Critical thinking and problem solving
- steeped in research methods and rigor
- based on empirical evidence and the scientific approach to knowledge development
- demonstrated through appropriate and relevant assessment
1-5 Career and leadership readiness
- technology savvy
- professional and, where relevant, fully accredited
- forward thinking and well informed
- tested and validated by work based experiences
1-5 Self-awareness and emotional intelligence
- a capacity for self-reflection and a willingness to engage in self-appraisal
- open to objective and constructive feedback from supervisors and peers
- able to negotiate difficult social situations, defuse conflict and engage positively in purposeful debate
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 ModesThe 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.
The University's policy on Assessment for Coursework Programs is based on the following four principles:
- Assessment must encourage and reinforce learning.
- Assessment must enable robust and fair judgements about student performance.
- Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
- Assessment must maintain academic standards.
Assessment SummaryWritten Examination 70%
The standard assessment consists of 3 assignments. This may be varied by negotiation with students at the start of the semester.
One 3 hour exam is used to assess the understanding of and ability to use the material.
SubmissionIf 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.
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.
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 (http://www.adelaide.edu.au/policies/101/) 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.
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