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The Discrete Fourier Transform (DFT)
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Classroom Contents
Data-Driven Science and Engineering
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- 1 Singular Value Decomposition (SVD): Overview
- 2 Singular Value Decomposition (SVD): Mathematical Overview
- 3 Singular Value Decomposition (SVD): Matrix Approximation
- 4 Singular Value Decomposition (SVD): Dominant Correlations
- 5 SVD: Image Compression [Matlab]
- 6 SVD: Image Compression [Python]
- 7 The Frobenius Norm for Matrices
- 8 SVD Method of Snapshots
- 9 Matrix Completion and the Netflix Prize
- 10 Unitary Transformations
- 11 Unitary Transformations and the SVD [Matlab]
- 12 Unitary Transformations and the SVD [Python]
- 13 Linear Systems of Equations, Least Squares Regression, Pseudoinverse
- 14 Least Squares Regression and the SVD
- 15 Linear Systems of Equations
- 16 Linear Regression
- 17 Linear Regression 1 [Matlab]
- 18 Linear Regression 2 [Matlab]
- 19 Linear Regression 1 [Python]
- 20 Linear Regression 2 [Python]
- 21 Linear Regression 3 [Python]
- 22 Principal Component Analysis (PCA)
- 23 Principal Component Analysis (PCA) [Matlab]
- 24 Principal Component Analysis (PCA) 1 [Python]
- 25 Principal Component Analysis (PCA) 2 [Python]
- 26 SVD: Eigenfaces 1 [Matlab]
- 27 SVD: Eigenfaces 2 [Matlab]
- 28 SVD: Eigenfaces 3 [Matlab]
- 29 SVD: Eigenfaces 4 [Matlab]
- 30 SVD: Eigen Action Heros [Matlab]
- 31 SVD: Eigenfaces 1 [Python]
- 32 SVD: Eigenfaces 2 [Python]
- 33 SVD: Eigenfaces 3 [Python]
- 34 SVD and Optimal Truncation
- 35 SVD: Optimal Truncation [Matlab]
- 36 SVD: Optimal Truncation [Python]
- 37 SVD and Alignment: A Cautionary Tale
- 38 SVD: Importance of Alignment [Matlab]
- 39 SVD: Importance of Alignment [Python]
- 40 Randomized Singular Value Decomposition (SVD)
- 41 Randomized SVD: Power Iterations and Oversampling
- 42 Randomized SVD Code [Matlab]
- 43 Randomized SVD Code [Python]
- 44 Fourier Analysis: Overview
- 45 Fourier Series: Part 1
- 46 Fourier Series: Part 2
- 47 Inner Products in Hilbert Space
- 48 Complex Fourier Series
- 49 Fourier Series [Matlab]
- 50 Fourier Series [Python]
- 51 Fourier Series and Gibbs Phenomena [Matlab]
- 52 Fourier Series and Gibbs Phenomena [Python]
- 53 The Fourier Transform
- 54 The Fourier Transform and Derivatives
- 55 The Fourier Transform and Convolution Integrals
- 56 Parseval's Theorem
- 57 Solving the Heat Equation with the Fourier Transform
- 58 The Discrete Fourier Transform (DFT)
- 59 Computing the DFT Matrix
- 60 The Fast Fourier Transform (FFT)
- 61 The Fast Fourier Transform Algorithm
- 62 Denoising Data with FFT [Matlab]
- 63 Denoising Data with FFT [Python]
- 64 Computing Derivatives with FFT [Matlab]
- 65 Computing Derivatives with FFT [Python]
- 66 Solving PDEs with the FFT [Matlab]
- 67 Solving PDEs with the FFT [Python]
- 68 Solving PDEs with the FFT, Part 2 [Matlab]
- 69 Solving PDEs with the FFT, Part 2 [Python]
- 70 The Spectrogram and the Gabor Transform
- 71 Spectrogram Examples [Matlab]
- 72 Spectrogram Examples [Python]
- 73 Uncertainty Principles and the Fourier Transform
- 74 Wavelets and Multiresolution Analysis
- 75 Image Compression and the FFT
- 76 Image Compression with Wavelets (Examples in Python)
- 77 Image Compression with the FFT (Examples in Matlab)
- 78 Image Compression and Wavelets (Examples in Matlab)
- 79 Image Compression and the FFT (Examples in Python)
- 80 The Laplace Transform: A Generalized Fourier Transform
- 81 Laplace Transforms and Differential Equations
- 82 Laplace Transform Examples
- 83 Sparsity and Compression: An Overview
- 84 Data-driven Modeling of Traveling Waves
- 85 Machine Learning for Fluid Mechanics
- 86 Data-Driven Resolvent Analysis
- 87 Data-driven nonlinear aeroelastic models of morphing wings for control
- 88 Model Predictive Control
- 89 Robust Principal Component Analysis (RPCA)
- 90 Deep Learning of Hierarchical Multiscale Differential Equation Time Steppers
- 91 Reinforcement Learning: Machine Learning Meets Control Theory
- 92 Deep Reinforcement Learning: Neural Networks for Learning Control Laws
- 93 Deep Reinforcement Learning for Fluid Dynamics and Control
- 94 Overview of Deep Reinforcement Learning Methods
- 95 Reinforcement Learning Series: Overview of Methods
- 96 Model Based Reinforcement Learning: Policy Iteration, Value Iteration, and Dynamic Programming
- 97 Q-Learning: Model Free Reinforcement Learning and Temporal Difference Learning
- 98 Nonlinear Control: Hamilton Jacobi Bellman (HJB) and Dynamic Programming
