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Signals & Systems I: Characteristic Modes and Green Functions
This lecture covers the concept of characteristic modes, including solutions of differential equations, exponential and oscillating modes, and factorization of differential operators. It also discusses the causal green function, inverse operators, stability criteria, and the effect of characteristic modes on system response. The instructor explains the position of characteristic roots, BIBO stability, and resonance phenomena in systems. Additionally, the lecture explores the response to complex sinusoidal excitations and the frequency response of systems, emphasizing the importance of frequency domain analysis.