Explore the fundamental concepts of Fast Fourier Transforms (FFT) and their application to audio processing in this comprehensive lecture from the Engineering Mathematics course at the University of Washington. Delve into topics such as Discrete Fourier Transform, the differences between DFT and NFT, and the historical context of FFT. Learn how to implement FFT using MATLAB, analyze noise in audio signals, and apply filtering techniques. Gain hands-on experience with practical examples, including playing sounds, loading music files, and creating spectrograms. Access accompanying lecture notes and MATLAB code examples to reinforce your understanding of these essential signal processing concepts.