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[[Category:ECE301Spring2013JVK]] [[Category:ECE]] [[Category:ECE301]] [[Category:probability]] [[Category:problem solving]]
 
[[Category:ECE301Spring2013JVK]] [[Category:ECE]] [[Category:ECE301]] [[Category:probability]] [[Category:problem solving]]
 
EXTRA CREDIT
 
EXTRA CREDIT
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1. [[Category:LTI systems]]
 
1. [[Category:LTI systems]]
 
Linear and Non Linear
 
Linear and Non Linear
  
 
Linear example    <math>y[n] = 54x[n]</math>, <math>h[n] = 62x[n]</math>, <math>y[n] + h[n] = 54x[n] + 62x[n]</math>
 
Linear example    <math>y[n] = 54x[n]</math>, <math>h[n] = 62x[n]</math>, <math>y[n] + h[n] = 54x[n] + 62x[n]</math>
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Non Linear example    <math>y(t) =x^3(t)</math>, <math>h(t) = x^3(t)</math>, <math>y(t) + h(t) = (x(t)+x(t))^2</math> =\= <math>x^2(t) +x^2(t)</math>  
 
Non Linear example    <math>y(t) =x^3(t)</math>, <math>h(t) = x^3(t)</math>, <math>y(t) + h(t) = (x(t)+x(t))^2</math> =\= <math>x^2(t) +x^2(t)</math>  
  
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Invertible example  <math>y(t)=5x(t)</math>
 
Invertible example  <math>y(t)=5x(t)</math>
 
Nonivertible example  <math>y(t)=x^4(t)</math>
 
Nonivertible example  <math>y(t)=x^4(t)</math>
 
  
 
Stable and Nonstable
 
Stable and Nonstable
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Time variant and Time invariant
 
Time variant and Time invariant
 
  
 
Time variant example  <math>y(t)=3tx(t)</math>  
 
Time variant example  <math>y(t)=3tx(t)</math>  
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Part 1:[[Image:Convol_1.jpg]]
 
Part 1:[[Image:Convol_1.jpg]]
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Part 2:[[Image:Convol_2.jpg]]
 
Part 2:[[Image:Convol_2.jpg]]
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Part 3:[[Image:Convol_3.jpg]]
 
Part 3:[[Image:Convol_3.jpg]]
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Part 4:[[Image:Convol_4.jpg]]
 
Part 4:[[Image:Convol_4.jpg]]
  
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I apologize for my terrible quality pictures.
  
 
3.  [[Category:period]]
 
3.  [[Category:period]]
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What is the fundamental period of the following equation.
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<math>y(t)=4sin(3t+pi/6)</math>
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Its fundamental period is <math>= 2pi/3</math>
  
  
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Comments and Questions...
  
 
[[Bonus_point_1_ECE301_Spring2013|Back to first bonus point opportunity, ECE301 Spring 2013]]
 
[[Bonus_point_1_ECE301_Spring2013|Back to first bonus point opportunity, ECE301 Spring 2013]]

Latest revision as of 15:48, 10 February 2013

EXTRA CREDIT

1. Linear and Non Linear

Linear example $ y[n] = 54x[n] $, $ h[n] = 62x[n] $, $ y[n] + h[n] = 54x[n] + 62x[n] $

Non Linear example $ y(t) =x^3(t) $, $ h(t) = x^3(t) $, $ y(t) + h(t) = (x(t)+x(t))^2 $ =\= $ x^2(t) +x^2(t) $

Causal and Non Causal

Causal example $ y[n]=70x[n-1] $ Non Causal example $ y[n]=76x[n+1] $

Memory and Memoryless

Memory example $ y[n]=x[n]+x[n-1] $ Memoryless example $ y[n]=36x[n] $

Invertible and noninvertible

Invertible example $ y(t)=5x(t) $ Nonivertible example $ y(t)=x^4(t) $

Stable and Nonstable

Stable example $ y(t)=sin(3t) $ Nonstable example $ y(t)=4e^3x(t) $

Time variant and Time invariant

Time variant example $ y(t)=3tx(t) $ Time Invariant example $ y(t)=3x(t) $

2.

Part 1:Convol 1.jpg

Part 2:Convol 2.jpg

Part 3:Convol 3.jpg

Part 4:Convol 4.jpg


I apologize for my terrible quality pictures.

3.

What is the fundamental period of the following equation.

$ y(t)=4sin(3t+pi/6) $

Its fundamental period is $ = 2pi/3 $


Comments and Questions...

Back to first bonus point opportunity, ECE301 Spring 2013

Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett