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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]=(2n-3)^nu[n-5]</math>
+
<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]=(2n-3)^n\delta{[n-5]}</math>
+
<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 08:51, 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} $

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Questions/answers with a recent ECE grad

Ryne Rayburn