ELEC8501: The Fourier Transform and Its Applications

The Fourier transform as a tool for solving physical problems. Fourier transform of discrete and continuous time signals, generalized transforms, and Fourier series. Convolutions and correlations, impulses and sampling, Fourier transform theorems, and analysis of linear systems. Two-dimensional imaging, Hankel and Abel transforms. Time-frequency analysis. Applications in communications, image processing, and medical imaging.

Prerequisite: Prior exposure to Fourier transforms at an undergraduate level course in Signals and Systems.

• Assessment: 100% continuous assessment

• A: Exceptionally good performance demonstrating a superior understanding of the subject matter, a foundation of extensive knowledge, a skillful use of concepts and/or materials, and ability to analyze and evaluate problems.

• B: Good performance demonstrating capacity to use the appropriate concepts, a good understanding of the subject matter, and an ability to handle the problems and materials encountered in the course.

• C: Adequate performance demonstrating an adequate understanding of the subject matter, an ability to handle relatively simple problems, and adequate preparation for moving on to more advanced work in the field.

• D: Minimally acceptable performance demonstrating at least partial familiarity with the subject matter and some capacity to deal with relatively simple problems, but also demonstrating deficiencies serious enough to make it inadvisable to proceed further in the field without additional work.

• F: Unacceptable performance demonstrating unfamiliarity with the subject matter, and lack of capacity to deal with relatively simple problems, and also demonstrating deficiencies serious enough to make it advisable to retake the course.

• Understand the use of Fourier transform in engineering systems analysis.

• Understand the modeling of engineering problems and tackle through the application of Fourier transform.