compression

Monty Montgomery of Xiph.org gives real-time demonstrations of sampling, quantization, bit depth and dither using real audio equipment, including both digital analysis tools and vintage analog bench gear. It shows that sampled audio is not stair-stepped and corrects common misconceptions about digital audio.

Reducible's visual walkthrough of the Fast Fourier Transform, motivated by polynomial multiplication. It shows how the FFT's key ideas can be discovered by asking the right questions.

3Blue1Brown introduces Fourier series, from the heat equation to drawing arbitrary shapes with rotating circles. It builds a visual intuition for decomposing functions into sine waves.

3Blue1Brown's discovery-oriented introduction to error correction codes, building up Hamming codes from the puzzle of locating a flipped bit. It explains the parity-check idea and why it is so efficient.

Veritasium tells the story of the Fast Fourier Transform, from its use in detecting nuclear tests to Cold War politics, and how it could have changed the arms race. It includes a short, intuitive explanation of what the Fourier transform does.

3Blue1Brown uses Wordle as an excuse to teach information theory and entropy, building a solver that picks guesses by expected information and incorporating word frequencies.

GoldenSound publishes music on Tidal to test MQA, a deep dive into the format's claims and problems including its leaky filter. Testing begins around the 5:45 mark.

Mathologer explains epicycles and complex Fourier series, inspired by an animation of Homer Simpson drawn with epicycles. It covers the shape of the Moon's orbit around the Sun and how to make your own epicycle drawings.

Veritasium builds a QR code by hand to explain how it works. It covers the history of Morse code and barcodes, how QR codes encode data, why damaged codes still scan, and how safe they are.

A step-by-step animated explanation of how SHA-256 works, from padding and message schedule to the compression function and final hash, with source code for the animations.