Signals & Systems I: Fourier Transformation and Distributions

This lecture covers the classical framework for the Fourier transformation, Parseval relation, and weak convergence. It delves into the Fourier transformation in the sense of distributions, Schwartz class functions, and the properties of the generalized Fourier transformation. The instructor explains the fundamental properties, linearity, translation, and the invertibility of the Fourier transformation. Technical conditions, weak sense equality tests, and the concept of temperate distributions are also discussed.