2. Time-Domain Representations of LTI Systems
2. Time-Domain Representations of LTI Systems
2. Time-Domain Representations of LTI Systems
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<strong>2.</strong>9 Differential and DifferenceEquation <strong>Representations</strong> <strong>of</strong> <strong>LTI</strong> <strong>Systems</strong>1 d2d dC dt2dt dt y t R y t L y t x tN = 2Ex. Accelerator modeled in Section 1.10 :22 d dny t y t y t x t2Q dt dtn where y(t) = the position <strong>of</strong> the pro<strong>of</strong> mass, x(t) = externalacceleration.<strong>Time</strong>-<strong>Domain</strong> <strong>Representations</strong> <strong>of</strong><strong>LTI</strong> <strong>Systems</strong>N = 2Ex. Second-order difference equation :1y[n]y[ n 1] y[n 2]x[ n]2x[n 1]4(<strong>2.</strong>37) N = 2Difference equations are easily rearranged to obtain recursiveformulas for computing the current output <strong>of</strong> the system from theinput signal and the past outputs.53
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