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Fourier Transform: LTI Systems
This lecture covers the application of Fourier transform to Linear Time-Invariant (LTI) systems, focusing on the frequency response, convolution property, differentiation property, and solving differential equations. The frequency response of an LTI system is the Fourier transform of the impulse response, which characterizes stable systems. Convolution in the time domain becomes multiplication in the frequency domain for LTI systems. Differentiation in the time domain is represented as multiplication by jw in the frequency domain. An example is provided to illustrate finding the impulse response of a stable LTI system described by a differential equation.