(a) Finding the unit impulse response h[n] and the system function H(z).)
(a) Finding the unit impulse response h[n] and the system function H(z).)
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<math>x[n] \rightarrow system \rightarrow y[n] = 5x[n]</math>
 
<math>x[n] \rightarrow system \rightarrow y[n] = 5x[n]</math>
  
==a) Finding the unit impulse response h[n] and the system function H(z).==
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==a) Finding the unit impulse response h[n] and the system function F(z).==
  
 
<math>x[n] = \delta [n] \rightarrow system \rightarrow y[n]=5\delta [n]</math>
 
<math>x[n] = \delta [n] \rightarrow system \rightarrow y[n]=5\delta [n]</math>
  
 
Therefore the unit impulse response, <big><math>h[n] = 5\delta [n]</math></big>
 
Therefore the unit impulse response, <big><math>h[n] = 5\delta [n]</math></big>
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 +
For a DT LTI system,
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<math>Z^n \rightarrow system \rightarrow F(z)Z^n</math>

Revision as of 14:01, 26 September 2008

Defining the DT LTI system

$ x[n] \rightarrow system \rightarrow y[n] = 5x[n] $

a) Finding the unit impulse response h[n] and the system function F(z).

$ x[n] = \delta [n] \rightarrow system \rightarrow y[n]=5\delta [n] $

Therefore the unit impulse response, $ h[n] = 5\delta [n] $

For a DT LTI system,

$ Z^n \rightarrow system \rightarrow F(z)Z^n $

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Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett