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EE 261: The Fourier Transform and its Applications

EE 261: The Fourier Transform and its Applications (Stanford Univ.). Instructor: Professor Brad Osgood. The Fourier transform is a tool for solving physical problems. In this course the emphasis is on relating the theoretical principles to solving practical engineering and science problems. Topics include: The Fourier transform as a tool for solving physical problems. 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. (from see.stanford.edu)

Lecture 21 - Properties of the Discrete Fourier Transform

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Lecture 01 - An Overview of the Course, Periodic Phenomena and the Fourier Series

Lecture 02 - Fourier Series; Analyzing General Periodic Phenomenon

Lecture 03 - Fourier Series (cont.); Fourier Coefficients

Lecture 04 - Fourier Series (cont.); Applications of Fourier Series

Lecture 05 - Fourier Series and the Heat Equation, Transition from Fourier Series to Fourier Transforms

Lecture 06 - Fourier Transform Derivation, Fourier Transform Properties and Examples

Lecture 07 - Fourier Transform Properties and Examples (cont.)

Lecture 08 - General Properties of the Fourier Transforms; Convolution

Lecture 09 - Example of Convolution: Filtering, Interpreting Convolution in the Time Domain

Lecture 10 - Convolution and Central Limit Theorem

Lecture 11 - Discussion of the Convergence of Integrals

Lecture 12 - Generalized Functions, Distributions and the Fourier Transform

Lecture 13 - The Fourier Transform of a Distribution

Lecture 14 - Derivative of a Distribution, Examples, Applications to the Fourier Transform

Lecture 15 - Application of the Fourier Transform: Diffraction

Lecture 16 - Diffraction (cont.), Crystallography Discussion, Fourier Transform of the Shah Function

Lecture 17 - Sampling and Interpolation, Discussion of the Associated Properties

Lecture 18 - Sampling, Interpolation and Aliasing

Lecture 19 - Aliasing Demonstration with Music, The Discrete Fourier Transform

Lecture 20 - The Discrete Fourier Transform

Lecture 21 - Properties of the Discrete Fourier Transform

Lecture 22 - The Fast Fourier Transform (FFT) Algorithm

Lecture 23 - Linear Systems: Basic Definitions, Eigenvectors and Eigenvalues

Lecture 24 - Linear Systems (cont.): Impulse Response, Linear Time Invariant Systems

Lecture 25 - The Relationship between LTI Systems and the Fourier Transforms

Lecture 26 - The Higher Dimensional Fourier Transform

Lecture 27 - Higher Dimensional Fourier Transforms (cont.)

Lecture 28 - Higher Dimensional Fourier Transforms (cont.): Shift Theorem, Stretch Theorem

Lecture 29 - Shahs, Lattices, and Crystallography

Lecture 30 - Tomography and Inverting the Radon Transform