Explore an in-depth 8-hour video series on Fourier Analysis, covering a wide range of topics from basic concepts to advanced applications. Begin with an overview of Fourier series and progress through complex Fourier series, Fourier transforms, and their applications in solving differential equations. Dive into practical implementations using both MATLAB and Python, including examples of denoising data, computing derivatives, and solving partial differential equations. Examine the Discrete Fourier Transform (DFT) and the Fast Fourier Transform (FFT) algorithm, along with their applications in signal processing. Investigate advanced topics such as spectrograms, the Gabor transform, wavelets, and multiresolution analysis. Apply Fourier techniques to real-world problems like image compression, and explore the relationship between Fourier and Laplace transforms. Gain a comprehensive understanding of Fourier analysis and its practical applications in various fields of science and engineering.
Overview
Syllabus
Fourier Analysis: Overview.
Fourier Series: Part 1.
Fourier Series: Part 2.
Inner Products in Hilbert Space.
Complex Fourier Series.
Fourier Series [Matlab].
Fourier Series [Python].
Fourier Series and Gibbs Phenomena [Matlab].
Fourier Series and Gibbs Phenomena [Python].
The Fourier Transform.
The Fourier Transform and Derivatives.
The Fourier Transform and Convolution Integrals.
Parseval's Theorem.
Solving the Heat Equation with the Fourier Transform.
The Discrete Fourier Transform (DFT).
Computing the DFT Matrix.
The Fast Fourier Transform (FFT).
The Fast Fourier Transform Algorithm.
Denoising Data with FFT [Matlab].
Denoising Data with FFT [Python].
Computing Derivatives with FFT [Matlab].
Computing Derivatives with FFT [Python].
Solving PDEs with the FFT [Matlab].
Solving PDEs with the FFT [Python].
Solving PDEs with the FFT, Part 2 [Matlab].
Solving PDEs with the FFT, Part 2 [Python].
The Spectrogram and the Gabor Transform.
Spectrogram Examples [Matlab].
Spectrogram Examples [Python].
Uncertainty Principles and the Fourier Transform.
Wavelets and Multiresolution Analysis.
Image Compression and the FFT.
Image Compression with Wavelets (Examples in Python).
Image Compression with the FFT (Examples in Matlab).
Image Compression and Wavelets (Examples in Matlab).
Image Compression and the FFT (Examples in Python).
The Laplace Transform: A Generalized Fourier Transform.
Laplace Transforms and Differential Equations.
Laplace Transform Examples.
Taught by
Steve Brunton
