Signal and System Analysis: Impulse Response and Convolution

This lecture focuses on the analysis of linear time-invariant (LTI) systems through impulse response and convolution. The instructor begins by reviewing the previous concepts of system modeling using impulse response, emphasizing its importance in both continuous and discrete time systems. The lecture progresses to the composition of systems, discussing parallel and series configurations, and how these affect the overall impulse response. The instructor illustrates the convolution operation, explaining how it combines the input signal with the system's impulse response to determine the output. The concepts of stability and causality are introduced, highlighting their significance in system design. The instructor also addresses the properties of impulse responses, such as memory and invertibility, and their implications for system behavior. Throughout the lecture, practical examples and graphical representations are used to enhance understanding. The session concludes with a discussion on differential equations and their relationship to impulse responses, setting the stage for future topics in frequency response analysis.