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Math · Advanced

Fourier Series

In 1807, Joseph Fourier made a bold claim: any repeating signal, even one with sharp corners, can be built by adding up sine waves. Mix waves to match targets, watch a square wave emerge, discover why a violin and a flute sound different, learn the trick that finds the recipe, draw shapes with spinning circles, and see how smoothness controls everything.

7 lessons~35 min0/7 complete
1

Adding Waves

Sines as building blocks.

  1. Mixing SinesHarmonics and their amplitudes
  2. Building a Square WaveCorners from smooth curves
2

Using Fourier

Sound, coefficients and compression.

  1. The Sound of HarmonicsWhy instruments sound different
  2. Finding the RecipeOrthogonality and integrals
  3. Fourier EverywhereHeat, compression and more
3

Circles and Corners

Drawing with epicycles, and how smoothness controls convergence.

  1. Drawing with CirclesSpinning arrows trace any shape
  2. Corners and SmoothnessHow fast do the harmonics fade?

Courses that build on this

Ready for more? These courses use what you learn in Fourier Series.

Math · Advanced

Sampling & Digital Signals

How smooth sound becomes numbers, why wheels spin backwards on film, filters, the FFT, and how MP3s shrink music.

7 lessons3 chapters