2. Time-Domain Representations of LTI Systems

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1. Step response:t 1 RCs( t) e u( ) d.RC2.8 Step ResponseFig. 2.25Time-Domain Representations ofLTI Systems51
2.9 Differential and DifferenceEquation Representations of LTI Systems1. Linear constant-coefficient differential equation :Nk 0akddtThe order of the differential or difference equation is (N, M),representing the number of energy storage devices in the system.Ex. RLC circuit depicted in Fig. 2.26.1. Input = voltage source x(t),output = loop current2. KVL Eq. :kky(t)Mk 0bkddtkkx(t)(2.35)d 1 tRy t L y t y d x tdt C Input = x(t), output = y(t)2. Linear constant-coefficient difference equation :Nk 0aky[n k] Mk 0bkx[n k](2.36)Input = x[n], output = y[n]Often, N M, and theorder is describedusing only N.Time-Domain Representations ofLTI Systems52
Page 4 and 5: 2. Impulse Response of LTI System H
Page 7 and 8: 2.3 Convolution Sum Evaluation Proc
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Page 15 and 16: 2.5 Convolution Integral Evaluation
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2. Time-Domain Representations of LTI Systems

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