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>11 Characteristics <strong>of</strong> <strong>Systems</strong> Describedby Differential and Difference EquationsComplete solution: y = y (n) + y (f)y (n) = natural response, y (f) = forced response1. The Natural Response (Zero(Input)Example <strong>2.</strong>24: RC Circuit (continued): Natural ResponseThe system In Example <strong>2.</strong>17 is described by the differential equationdy t RC y t x tdtFind the natural response <strong>of</strong> the this system, assuming thaty(0) = 2 V, R = 1 and C = 1 F. 1. Homogeneous sol. :<strong>2.</strong> I.C.: y(0) = 2 V3. Natural Response :<strong>Time</strong>-<strong>Domain</strong> <strong>Representations</strong> <strong>of</strong><strong>LTI</strong> <strong>Systems</strong>71
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