# InfoCoBuild

## 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)

 An Overview of the Course

 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 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

 References EE 261 - The Fourier Transform and its Applications Instructors: Professor Brad Osgood. Handouts. Assignments. Exams. 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.