Differential Equations for CT LTI Systems & Complex Exponentials as Eigenfunctions

Inside this lesson

Recognize the first-order linear constant-coefficient differential equation (LCCDE) as a model for causal CT LTI systems
State the impulse response h(t) = e^(-at)u(t) of the stable first-order CT system dy/dt + a·y(t) = x(t)
Explain why complex exponentials are eigenfunctions of LTI systems
Derive the system function H(s) by substituting x(t) = e^(st) into the convolution integral

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Educational content covering topics typical of a first- and second-year electrical engineering curriculum. Not a substitute for accredited coursework, and not suitable for real antenna, transmission-line, or signal-processing system design without review by a licensed professional engineer.