Fourier Analysis
Calculus & Analysis
Master Fourier series, the Fourier transform, DFT/FFT, signal processing, distributions, and wavelet analysis — the mathematics of frequency and signal decomposition.
Learning Objectives
- Compute Fourier series and apply Parseval's theorem
- Work with the Fourier transform and convolution theorem
- Understand the FFT algorithm and its applications
- Solve PDEs using Fourier methods
- Work with Dirac delta and tempered distributions
- Apply wavelet transforms for multi-resolution analysis
Lessons
1
Fourier Series: Orthogonality & Parseval's Theorem
35 min
2
The Fourier Transform on $\mathbb{R}$
35 min
3
Discrete Fourier Transform & FFT
35 min
4
Applications to Differential Equations
35 min
5
Distributions & the Dirac Delta
35 min
6
Signal Processing: Sampling, Filtering & Modulation
35 min
7
Wavelets & Time-Frequency Analysis
35 min
Quick Practice
Test your knowledge with a quick interactive challenge from this module.
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Key Concept Flashcards
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