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Fourier Analysis & Epicycles

Discover how any function can be expressed as a sum of sine waves through 27 interactive demonstrations. Draw shapes with rotating circles, visualize audio frequencies, and see Fourier transforms in action.

See also: Complex Analysis for residues and contour integration of Fourier integrals, Real Analysis for convergence of Fourier series, and Differential Equations for solving heat and wave equations by spectral decomposition.

  1. 01

    Introduction to Waves

    Sine waves, superposition, and the building blocks of Fourier analysis

    3 demos
  2. 02

    Fourier Series

    Decompose any periodic function into sines and cosines

    3 demos
  3. 03

    Epicycles & Drawing

    Draw any shape with rotating circles - the magic of complex Fourier series

    3 demos
  4. 04

    Fourier Transform

    Convert between time and frequency domains

    3 demos
  5. 05

    Audio Visualization

    See sound as waves and frequencies with real-time spectrograms

    3 demos
  6. 06

    Signal Filtering

    Low-pass, high-pass, and convolution - shaping signals

    3 demos
  7. 07

    2D Fourier Transform

    Image frequency analysis, edge detection, and compression

    3 demos
  8. 08

    Heat Equation

    Fourier's original application - watch heat diffuse

    2 demos
  9. 09

    Applications Gallery

    MP3, JPEG, MRI, and more - Fourier in the real world

    4 demos

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