TEACHING ARCHIVESTIEI
Course Description (for 2014)
Course Description
Tianjin International Engineering Institute
Course Name(Chinese): 傅立叶变换及其应用
(English):Fourier Transform and Its Applications
Course Name: Fourier Transform and Its Applications
Course Code:
Semester: 2
Credit:
Programme: Electronic
Course Module: Specialized Subjects
Responsible: Li Qiang
E-mail: liqiang@tju.edu.cn
Department:School of Electronic Information Engineering
Time Layout (1 credit hour = 45 minutes)
Practice
Lecture
Lab-study
8
16
8
Project
Internship(days)
Personal Work
10
Course Resume
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.
Pre-requirements
Signal and Systems; Digital Signal Processing
Course Objectives
The goals for the course are to gain a facility with using the Fourier transform, both specific
techniques and general principles, and learning to recognize when, why, and how it is used.
Together with a great variety, the subject also has a great coherence, and the hope is students
come to appreciate both.
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TEACHING ARCHIVESTIEI
Course Description (for 2014)
Course Syllabus
1. Fundamental
1.1 Introductions Periodicity and Fourier series
1.2 Fourier series and orthogonality
1.3 Fourier series, continued
1.4 Applications of Fourier series
1.5 Meet the Fourier transform
1.6 Fourier transform properties and examples
2 .Convolution
2.1 Convolution, filters, and differential equations
2.2 Convolution and the Central Limit Theorem
3 .The Discrete Fourier Transform
3.1 Applications and properties of the DFT
3.3 The FFT algorithm
4 .Linear systems
4.1 Linear time invariant systems
4.2 Digital Filters
4.3 Higher dimensional Fourier transforms
5 .Applications
5.1 Intro to medical imaging
5.2 The Radon transform & medical imaging
Text Book & References
Textbook: Brad Osgood, The Fourier Transform and its Applications(3ed), Stanford University..
We may also use readings from a few textbooks: Ronald Bracewell, The Fourier Transform & Its
Applications(3ed), McGraw-Hill Science 1999.
Capability Tasks
CT1
CT2
CT3
CT4
CT10
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: Electronic year 2
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