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>10 SolvingDifferential and Difference Equations3. The Complete SolutionComplete solution: y = y (h) + y (p)y (h) = homogeneous solution, y (p) = particular solutionThe procedure for finding complete solution <strong>of</strong> differential ordifference equations is summarized as follows :Procedure <strong>2.</strong>3: Solving a Differential or Difference equation1. Find the form <strong>of</strong> the homogeneous solution y (h) from the roots <strong>of</strong>the characteristic equation.<strong>2.</strong> Find a particular solution y (p) by assuming that it is <strong>of</strong> the sameform as the input, yet is independent <strong>of</strong> all terms in thehomogeneous solution.3. Determine the coefficients in the homogeneous solution so thatthe complete solution y = y (h) + y (p) satisfies the initial conditions.★ Note that the initial translation is needed in some cases.<strong>Time</strong>-<strong>Domain</strong> <strong>Representations</strong> <strong>of</strong><strong>LTI</strong> <strong>Systems</strong>68
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