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AI From Scratch/Phase 01/Lesson 20/~90 minutes

The Fourier Transform

BuildNo prerequisites

Every signal is a sum of sine waves. The Fourier transform tells you which ones.

Back to phaseMath Foundations Next lessonGraph Theory for Machine Learning

Phase 01

Math Foundations

01Linear Algebra Intuition 02Vectors, Matrices & Operations 03Matrix Transformations 04Calculus for Machine Learning 05Chain Rule & Automatic Differentiation 06Probability and Distributions 07Bayes' Theorem 08Optimization 09Information Theory 10Dimensionality Reduction 11Singular Value Decomposition 12Tensor Operations 13Numerical Stability 14Norms and Distances 15Statistics for Machine Learning 16Sampling Methods 17Linear Systems 18Convex Optimization 19Complex Numbers for AI 20The Fourier Transform 21Graph Theory for Machine Learning 22Stochastic Processes

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Phase 01

Math Foundations

01Linear Algebra Intuition 02Vectors, Matrices & Operations 03Matrix Transformations 04Calculus for Machine Learning 05Chain Rule & Automatic Differentiation 06Probability and Distributions 07Bayes' Theorem 08Optimization 09Information Theory 10Dimensionality Reduction 11Singular Value Decomposition 12Tensor Operations 13Numerical Stability 14Norms and Distances 15Statistics for Machine Learning 16Sampling Methods 17Linear Systems 18Convex Optimization 19Complex Numbers for AI 20The Fourier Transform 21Graph Theory for Machine Learning 22Stochastic Processes

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Resources

Cooley & Tukey: An Algorithm for the Machine Calculation of Complex Fourier Series (1965)Reading 3Blue1Brown: But what is the Fourier Transform?Reading Lee-Thorp et al.: FNet: Mixing Tokens with Fourier Transforms (2021)Reading Smith: The Scientist and Engineer's Guide to Digital Signal ProcessingReading Vaswani et al.: Attention Is All You Need (2017)Reading Radford et al.: Whisper (2022)Reading