Course Name: Fourier Transform and Its Applications

Course Code: S2293042

Semester: 4

Credit: 3

Program: Electronics

Course Module: Optional Courses (Information)

Responsible: Xiangdong Huang

E-mail: liqiang@tju.edu.cn

Department:School of Electrical and Information Engineering, Tianjin University

Time Allocation(1 credit hour = 45 minutes)

Course Description

The course covers the following topics:

• Fourier series, the Fourier transform of continuous and discrete signals and its properties.

• The Dirac delta, distributions, and generalized transforms.

• Convolutions and correlations and applications, probability distributions, sampling theory, filters, and analysis of linear systems.

• The Discrete Fourier transform and the FFT algorithm.

• Multidimensional Fourier transform and use in imaging.

• Further applications to optics, crystallography.

Prerequisite

Signal and Systems,Digital Signal Processing.

Course Objectives

The goals for the course are to gain a facility using the Fourier transform, both specific techniques and general principles, and learn to recognize when, why, and how it is used. Together with a great variety, the subject also has a great coherence, and hopes students come to appreciate both.

Course Syllabus

1. Fundamental

   1. Introductions Periodicity and Fourier series

   2. Fourier series and orthogonality

   3. Fourier series, continued

   4. Applications of Fourier series

   5. Meet the Fourier transform

   6. Fourier transform properties and examples

2. Convolution

   1. Convolution, filters, and differential equations

   2. Convolution and the Central Limit Theorem

3. The Discrete Fourier Transform

   1. Applications and properties of the DFT

   2. The FFT algorithm

4. Linear systems

   1. Linear time invariant systems

   2. Digital Filters

   3. Higher dimensional Fourier transforms

5. Applications

   1. Intro to medical imaging

   2. The Radon transform & medical imaging

Textbooks & References

• Brad Osgood.The Fourier Transform and its Applications (3^rded). Stanford University.

We may also use readings from a few textbooks:

• Ronald Bracewell.The Fourier Transform & Its Applications(3^rded). McGraw-Hill Science, 1999.

Capability Tasks

CT1: To understand basic science, and to have analytical ability and the ability to integrate related knowledge.

CT2: To apply relevant professional knowledge to the field of science and technology: understanding of the basic concepts and its connotation, application of different methods and concepts which have been learned, capability of judging the scope and limitations of such applications.

CT3: To grasp methodologies and engineering tools: identifying, utilizing and solving problems. Even if the students are not familiar with the content, they can turn to computer tools for systematic analysis.

CT4: To carry out experiments in research environment with the abilities to utilize tools, especially for data collection and processing.

CT10: To have the capacity to work in international environment; the capability to master one or more foreign languages and be open to foreign cultures; be able to acclimatize themselves to the international language environment.

Achievements

• To be able to analyze a system or signal with Fourier series or Fourier transform. - Level: M

• To be able to use convolution and FFT in a realistic problem. - Level: M

Students: Electronics, Year 2