Signals & Systems I: Distributions and Linear Systems

This lecture introduces the concept of distributions in signals and systems, defining 8(t) as a linear functional associated with each function f(t). It explores the properties of 8(t) as a distribution, its relation with the Dirac delta function, and its integral representation. The lecture also covers the localization and multiplication of distributions, as well as the response of linear systems, including the impulse response and convolution. Various examples of linear systems, such as amplifiers, integrators, and causal systems, are discussed, along with the concept of causality and the convolution of signals. The lecture concludes with the interpretation of convolution as the response of a system and provides a table of convolutions for basic signals.