2. Time-Domain Representations of LTI Systems
2. Time-Domain Representations of LTI Systems
2. Time-Domain Representations of LTI Systems
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
<strong>2.</strong>11 Characteristics <strong>of</strong> <strong>Systems</strong> Describedby Differential and Difference Equations<strong>2.</strong> The Forced Response (only valid for t 0 or n 0)The forced response is the system output due to the input signalassuming zero initial conditions.The at-rest conditions for a discrete-time system, y[N] = 0, …,y[1] = 0, must be translated forward to times n = 0, 1, …, N1before solving for the undetermined coefficients, such as whenone is determining the complete solution.Example <strong>2.</strong>26: First-Order Recursive System : Forced ResponseThe system in Example <strong>2.</strong>21 is described by the difference equation1y n yn 1xn4Find the forced response <strong>of</strong> this system if the input isx[n] = (1/2) n u[n].<strong>Time</strong>-<strong>Domain</strong> <strong>Representations</strong> <strong>of</strong><strong>LTI</strong> <strong>Systems</strong>73
Change language