CHAPTER 23 / 40
Fourier Analysis and Tensor Algebra
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Chapter lessons
3 lessons
Why this matters in ML
Fourier turns audio into the spectrograms Whisper and AudioLM eat; einsum and tensor algebra are the literal grammar of every transformer attention block.
- FFT / spectrograms
- Whisper
- multi-head attention
- tensor parallelism
- Step 98~10m13
Fourier Series and the Frequency Domain
Any reasonable periodic function can be written as a sum of sines and cosines — the Fourier series. This single change of basis powers JPEG,…
Open lesson - Step 99~10m13
The Discrete Fourier Transform and FFT
The DFT is the matrix that turns N time samples into N frequency coefficients. The FFT computes it in O(N log N) instead of O(N²) — a differ…
Open lesson - Step 100~10m13
Tensor Algebra and Einsum
Modern deep learning is tensor algebra. Einstein summation gives you a single notation for matrix multiply, batched attention, outer product…
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