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

Lecture 05 - Fourier Series and the Heat Equation

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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