Line 1: Line 1:
 
== Define a DT LTI system ==
 
== Define a DT LTI system ==
 
<math>y[n] = x[n+1] + x[n]\,</math>  
 
<math>y[n] = x[n+1] + x[n]\,</math>  
 +
  
 
== Obtain the Unit Impulse Response h[n] ==
 
== Obtain the Unit Impulse Response h[n] ==
Line 7: Line 8:
  
 
<math>h[n] = \delta[n+1] + \delta[n]\,</math>
 
<math>h[n] = \delta[n+1] + \delta[n]\,</math>
 +
  
 
== Obtain the System Function <math>F(z)\,</math> of the System ==
 
== Obtain the System Function <math>F(z)\,</math> of the System ==
 +
<math>F(z) = \sum^{\infty}_{m=\infty} h[n] * x[n] dn\,</math> where <math>x[n] = e^{jwn} \,</math>

Revision as of 11:21, 25 September 2008

Define a DT LTI system

$ y[n] = x[n+1] + x[n]\, $


Obtain the Unit Impulse Response h[n]

By definition, to obtain the unit impulse response from a system defined by $ y[n] = x[n]\, $, simply replace the $ x[n]\, $ by $ \delta[n]\, $.


$ h[n] = \delta[n+1] + \delta[n]\, $


Obtain the System Function $ F(z)\, $ of the System

$ F(z) = \sum^{\infty}_{m=\infty} h[n] * x[n] dn\, $ where $ x[n] = e^{jwn} \, $

Alumni Liaison

Prof. Math. Ohio State and Associate Dean
Outstanding Alumnus Purdue Math 2008

Jeff McNeal