Phase 3: Advanced Math for AI · ~90 minutes · Python
The Fourier Transform
Every signal is a sum of sine waves. The Fourier transform tells you which ones.
What you will learn
- Implement the DFT from scratch and verify it against the O(N log N) Cooley-Tukey FFT
- Interpret frequency coefficients: extract amplitude, phase, and power spectrum from a signal
- Apply the convolution theorem to perform convolution via FFT multiplication
- Connect Fourier frequency decomposition to transformer positional encodings and CNN convolution layers
Introduction
- Type: Build
- Language: Python
- Prerequisites: Complex Numbers for AI
- Time: ~90 minutes
Objective
Learning objectives
- Implement the DFT from scratch and verify it against the O(N log N) Cooley-Tukey FFT
- Interpret frequency coefficients: extract amplitude, phase, and power spectrum from a signal
- Apply the convolution theorem to perform convolution via FFT multiplication
- Connect Fourier frequency decomposition to transformer positional encodings and CNN convolution layers
Unlock the full lesson
You've read the first 2 sections. The rest of this lesson covers The Problem, The Concept, Build, Check Yourself, Key Terms & Next — plus a hands-on lab, quiz, and project artifact.
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