Signals & Systems I: Weighting Windows and Gibbs Phenomenon

This lecture covers the concept of weighting windows in signals and systems, focusing on the motivation behind time weighting and frequency limitation. It discusses the Gibbs phenomenon in truncated series, error evaluation, and the choice of the best window function. The instructor explains the reconstruction of signals using Fourier series and the impact of different window functions on the mean square error. The lecture also delves into frequency limitation, filtering, and the relative height of secondary lobes in signals. Examples of rectangular and triangular signals are used to illustrate the scale relation and time-frequency localization.