Fourier Transform and Windowing

This lecture covers the concept of spectral leakage due to mismatched signal window periods, the use of window functions to enforce signal continuity, and examples of window functions like the Hann window. It also delves into Fourier transforms in N dimensions, DFT in N dimensions, image processing techniques such as noise removal using FFT, and experimental techniques like transmission electron microscopy and scanning tunneling microscopy. The lecture further explores graphene and other 2D materials, including the growth of large-area graphene samples and observations of polycrystalline graphene using TEM. Practical exercises involving TEM images of graphene and STM images of grain boundary defects are also discussed.