Properties of Fourier and inverse Fourier transforms

This lecture covers the properties of Fourier and inverse Fourier transforms, focusing on the analysis of finite wave trains and Gaussian functions. The instructor explains the spectral properties of non-periodic signals, the Fourier transform of finite wave trains, and the relationship between pulse length and frequency spread. Additionally, the lecture delves into the Fourier transform of a delta function, the use of calculus of residues in Fourier transforms, and the convenience of the Fourier integral form. The concepts are further extended to 3D space, discussing Fourier and Inverse Fourier Transforms in a three-dimensional context.