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Fast Fourier Transform (FFT): Basics and Applications
This lecture covers the Fast Fourier Transform (FFT) algorithm, including the review of the Discrete Fourier transform (DFT), interpolation formula, and FFT implementation. It explains the practical aspects of DFT, the FFT algorithm's efficiency, and its application in computational physics. The lecture also delves into the Fourier transform in N dimensions, image processing, and experimental techniques like TEM and STM. Additionally, it discusses filters, spectral leakage, windowing, and the analysis of microscopy images. The presentation concludes with examples of graphene and other 2D materials observed through TEM and STM.