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September 25, 2023


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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)

Course Curriculum

  • Lecture 01 – An Overview of the Course, Periodic Phenomena and the Fourier Series Unlimited
  • Lecture 02 – Fourier Series; Analyzing General Periodic Phenomenon Unlimited
  • Lecture 03 – Fourier Series (cont.); Fourier Coefficients Unlimited
  • Lecture 04 – Fourier Series (cont.); Applications of Fourier Series Unlimited
  • Lecture 05 – Fourier Series and the Heat Equation Unlimited
  • Lecture 06 – Fourier Transform Derivation, Fourier Transform Properties and Examples Unlimited
  • Lecture 07 – Fourier Transform Properties and Examples (cont.) Unlimited
  • Lecture 08 – General Properties of the Fourier Transforms; Convolution Unlimited
  • Lecture 09 – Example of Convolution: Filtering, Interpreting Convolution in the Time Domain Unlimited
  • Lecture 10 – Convolution and Central Limit Theorem Unlimited
  • Lecture 11 – Discussion of the Convergence of Integrals Unlimited
  • Lecture 12 – Generalized Functions, Distributions and the Fourier Transform Unlimited
  • Lecture 13 – The Fourier Transform of a Distribution Unlimited
  • Lecture 14 – Derivative of a Distribution, Examples, Applications to the Fourier Transform Unlimited
  • Lecture 15 – Application of the Fourier Transform: Diffraction Unlimited
  • Lecture 16 – Crystallography Discussion, Fourier Transform of the Shah Function Unlimited
  • Lecture 17 – Sampling and Interpolation, Discussion of the Associated Properties Unlimited
  • Lecture 18 – Sampling, Interpolation and Aliasing Unlimited
  • Lecture 19 – Aliasing Demonstration with Music, The Discrete Fourier Transform Unlimited
  • Lecture 20 – The Discrete Fourier Transform Unlimited
  • Lecture 21 – Properties of the Discrete Fourier Transform Unlimited
  • Lecture 22 – The Fast Fourier Transform (FFT) Algorithm Unlimited
  • Lecture 23 – Linear Systems: Basic Definitions, Eigenvectors and Eigenvalues Unlimited
  • Lecture 24 – Linear Systems (cont.): Impulse Response, Linear Time Invariant Systems Unlimited
  • Lecture 25 – The Relationship between LTI Systems and the Fourier Transforms Unlimited
  • Lecture 26 – The Higher Dimensional Fourier Transform Unlimited
  • Lecture 27 – Higher Dimensional Fourier Transforms (cont.) Unlimited
  • Lecture 28 – Higher Dimensional Fourier Transforms (cont.): Shift Theorem, Stretch Theorem Unlimited
  • Lecture 29 – Shahs, Lattices, and Crystallography Unlimited
  • Lecture 30 – Tomography and Inverting the Radon Transform Unlimited

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