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Chapter 6 The Impulse Response and ConvolutionR1 Ω+ L 1 H−ui L () t0 () tWhen the input is the unit step u 0 () t ,it() vin = u 0 () t=∫∞–∞u 0 ( t – τ)h( τ) dτ1ht ()1u ( 0 – τ ) 1e – tu 0 ( t–τ)10t0τ0τht ( – τ)0tτit() vin = u 0 () t∫t= ( 1) ⋅ e – τ dτ= – e τ = e τ =01– t0u 0 ()*h t () t– 0t( 1–e – t )u 0 () tt6.L+ 1 H +v in () tR v out () t−1 Ω−We will first compute the impulse response, that is, the output when the input is the delta function,i.e., v in () t = δt (). Then, by KVLand withi L=xL di L------- + Ridt L = δ()t1⋅ x· + 1 ⋅ x = δ()t6−28Signals and Systems with MATLAB ® Computing and Simulink ® Modeling, Fourth EditionCopyright © Orchard Publications