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The Discrete Fourier Transform - Most Important Algorithm Ever?

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Overview

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This course develops an intuitive derivation of the Discrete Fourier Transform from first principles. It uses signal sampling, cosine and sine wave analysis, linear algebra, and complex exponentials to explain frequency decomposition and the phase problem.

Syllabus

Intro
Sampling Continuous Signals
Shannon-Nyquist Sampling Theorem
Frequency Domain Representations
Defining Ideal Behavior
Measuring SImilarity
Analysis Frequencies
Cosine Wave Analysis Frequency Transform
A Linear Algebraic Perspective
Sponsored Segment
Testing our "Fake Fourier Transform"
Phase Problems
Solving the Phase Problem
Defining the True DFT
DFT Recap/Outro

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