Linear Time Invariant Systems: Impulse Response and Convolution

This lecture focuses on linear time invariant (LTI) systems, emphasizing the concept of impulse response and convolution. The instructor begins by reviewing previous definitions related to systems, including causal, linear, stable, and memory systems. The discussion progresses to the mathematical representation of systems, introducing convolution as a new operation to model a wide range of systems. The instructor explains how the impulse response characterizes the behavior of LTI systems, allowing for the modeling of input-output relationships. Through examples, the instructor demonstrates how to compute the output of a system using the impulse response and convolution. The lecture also covers properties of convolution, such as commutativity and distributivity, and illustrates how these properties apply to LTI systems. The instructor emphasizes the importance of understanding the impulse response for analyzing system stability and behavior. The session concludes with a discussion on the implications of these concepts in engineering applications, reinforcing the foundational role of impulse response in system analysis.