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<br>  
 
<br>  
  
'''Theory'''<br>&nbsp; [[Image:Theroy.jpg]] &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'''or '''&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [[Image:CodeCogsEqn.jpg]]  
+
'''Theory'''<br>
 +
Upsampling in the frequency domain<br>
 +
<br>&nbsp; [[Image:Theroy.jpg]] &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'''or '''&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [[Image:CodeCogsEqn.jpg]]  
  
 
<br>  
 
<br>  
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Upsampling rate D = 2  
 
Upsampling rate D = 2  
 +
 +
<br>
 +
 +
Here is the sampled signal.<br>
  
 
[[Image:Graphex.jpg]]  
 
[[Image:Graphex.jpg]]  
  
<br>
+
Upsampling rate D = 2 is applied.<br>  
  
[[Image:Graphex2.jpg]]
+
[[Image:Graphex2.jpg]]  
  
<br>
+
Low-Pass filter of cutoff π/2, gain 2 is applied.<br>  
  
[[Image:Graphex3.jpg]]
+
[[Image:Graphex3.jpg]]  
  
<br>
+
Final upsampled signal<br>  
  
[[Image:Graphex4.jpg]]
+
[[Image:Graphex4.jpg]]  
  
 
'''Conclusion'''
 
'''Conclusion'''

Revision as of 07:06, 10 October 2014

OUTLINE

1. Introduction

2. Theory

3. Example

4. Conclusion

_________________________________________________________________________________________________________

Introduction

Upsampling is the process of increasing sampling rate.


Block.jpg


Theory
Upsampling in the frequency domain

  Theroy.jpg       or           CodeCogsEqn.jpg




Graph1.jpg

Graph2.jpg

Graph3.jpg


Example

Upsampling rate D = 2


Here is the sampled signal.

Graphex.jpg

Upsampling rate D = 2 is applied.

Graphex2.jpg

Low-Pass filter of cutoff π/2, gain 2 is applied.

Graphex3.jpg

Final upsampled signal

Graphex4.jpg

Conclusion

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To all math majors: "Mathematics is a wonderfully rich subject."

Dr. Paul Garrett