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== Define a DT LTI System == | == Define a DT LTI System == | ||
Let the DT LTI system be: | Let the DT LTI system be: | ||
| − | <math>y[n]= | + | <math>y[n]=u[n-5]</math> |
==Obtain the Unit Impulse Response h[n] and the System Function F[z] of the system== | ==Obtain the Unit Impulse Response h[n] and the System Function F[z] of the system== | ||
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First to obtain the unit impulse response h[n] we plug in <math>\delta{[n]}</math> into our y[n]. | First to obtain the unit impulse response h[n] we plug in <math>\delta{[n]}</math> into our y[n]. | ||
| − | <math>h[n]= | + | <math>h[n]=\delta{[n-5]}</math> |
| − | Then the system function F[z] is obtained by | + | Then the system function F[z] is obtained by |
<math>F[z]=\sum_{m= - \infty}^{\infty}h[m]z^{-m}</math> | <math>F[z]=\sum_{m= - \infty}^{\infty}h[m]z^{-m}</math> | ||
| + | |||
| + | where z is an input into our system. Let <math>z = e^{jk\omega_o}</math> | ||
| + | |||
| + | So when z^n is input into our system, we should get <math>F[z]z^n</math> back out. | ||
| + | |||
| + | |||
| + | <math>F[z]=\sum_{m= - \infty}^{\infty}\delta{[m-5]}e^{-mjk\omega_o}</math> | ||
Revision as of 09:51, 25 September 2008
Define a DT LTI System
Let the DT LTI system be: $ y[n]=u[n-5] $
Obtain the Unit Impulse Response h[n] and the System Function F[z] of the system
First to obtain the unit impulse response h[n] we plug in $ \delta{[n]} $ into our y[n].
$ h[n]=\delta{[n-5]} $
Then the system function F[z] is obtained by
$ F[z]=\sum_{m= - \infty}^{\infty}h[m]z^{-m} $
where z is an input into our system. Let $ z = e^{jk\omega_o} $
So when z^n is input into our system, we should get $ F[z]z^n $ back out.
$ F[z]=\sum_{m= - \infty}^{\infty}\delta{[m-5]}e^{-mjk\omega_o} $
