II-B. CT LTI System Analysis: Impulse Response & Convolution

τ :−∞ x(τ)h(t− τ)dτ = x(t) = y(t) Note that i. Linearity justifies superposition principle; ii. Time-Invariance justifies the system’s response to δ(t − n∆τ) is h(t− n∆τ). iii. For time-varying systems, the system response to δ(t − n∆τ) becomes h(t, n∆τ), and y(t) = ∫ ∞ τ :−∞ x(τ)h(t, τ)dτ , where h(t, τ) is the system response at instant t to a unit impulse input located at τ . 3. [Convolution Integral Thm] The output of any LTI system is the convolution of the input x(t) with the system’s impulse response h(t):