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Linear Time Invariant(LTI) Systems

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Def Linear Time Invariant System Linear Time Invariant system is a linear function transformation with invariant time defined by a Fourier pair: impulse response function and a transfer function . In real domain, the output function is given by: Specially, for delta impulse, we have In Fourier domain, the output function is given by:

Prop For any input function and the corresponding output function , we have following properties:

Missing \begin{aligned} or extra \end{aligned}\mathcal{LTI}[y_{\mathrm{in}}(t)+z_{\mathrm{in}}(t)] = y_{\mathrm{out}}(t)+z_{\mathrm{out}}(t) \\ \mathcal{LTI}[y_{\mathrm{in}}(t+\tau)]= y_{\mathrm{out}}(t+\tau) \end{aligned}$$

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