2. Time-Domain Representations of LTI Systems

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2.9 Differential and DifferenceEquation Representations of LTI Systems◆ Initial conditions : y[1] and y[2].◆ The initial conditions for Nth-order difference equation are the Nvalues , 1 ,..., 1 ,y N y N y◆ The initial conditions for Nth-order differential equation are the Nvalues2 N 1d d dy t y t y t y t , , ..., t0 , 2 N 1dt t0 dt t0 dtt0Time-Domain Representations ofLTI Systems55
2.9 Differential and DifferenceEquation Representations of LTI SystemsExample 2.15: Recursive Evaluation of a Difference EquationFind the first two output values y[0] and y[1] for the system describedby Eq. (2.38), assuming that the input is x[n] = (1/2) n u[n] and the initialconditions are y[1] = 1 and y[2] = 2.1. Substitute the appropriate values into Eq. (2.39) to obtain2. Substitute for y[0] in Eq. (2.40) to findTime-Domain Representations ofLTI Systems56
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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Page 21 and 22: 2.6 Interconnection of LTI Systems2
Page 23 and 24: 2.7 Relations Between LTISystem Pro
Page 31 and 32: 2.8 Step Response◆ Continuous-tim
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Page 41 and 42: 2.10 SolvingDifferential and Differ
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2. Time-Domain Representations of LTI Systems

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