The fast Fourier transform

This lecture covers the history of the Fourier transform, from Gauss to the Cooley-Tukey FFT algorithm. It explains the concept of small DFT matrices, the divide-and-conquer approach for DFT, and the analysis of Decimation-in-Time FFT. The lecture demonstrates the matrix factorization view of DFT for different sizes, emphasizing the efficiency of the algorithm. It concludes with practical applications in image processing and the significant reduction in computational complexity compared to direct methods.