Signal Processing: Fourier Transform and Fast Algorithm

This lecture covers the concepts of DTFT, DFT, cyclic convolution, duality, and properties of FFT. It explains the cost of implementing DFT, the rapid Fourier transform, and the fast algorithm (FFT). The instructor discusses the need for a fast algorithm due to the high computational cost of DFT, especially for real data cases. The lecture also delves into temporal decimation, factorization of n for faster calculations, and the cost analysis of FFT operations. Additionally, it explores the division of frequencies in FFT, the concept of butterflies, and the cost comparison between addition and multiplication in FFT operations.