Impulse Response and Laplace Transform

This lecture covers the concepts of impulse response and Laplace transform in dynamical systems. It starts with the definition of the unit step function and its utility in signal extraction. The lecture then delves into the properties of impulse signals, including time shifts and formal definitions. It explains the physical interpretation of impulse functions in modeling short-time physical signals. The lecture also discusses the convolution integral, linear time-invariant systems, and the output of such systems. It concludes with examples illustrating the convolution of signals and the application of Laplace transform in finding the output for a given input.