Signals & Systems I: Distributions and Linear Systems

This lecture covers the abstract definition of distributions in signals and systems, integration by parts, properties of Schwartz test functions, localization of distributions, multiplication of functions, exponential functions, linear systems, impulse response, time invariance, convolution operators, and elementary properties of convolution. It also discusses causal systems, infinite impulse response, finite impulse response, convolution of signals, and the algebra of convolution operators.