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'''Introduction'''  
 
'''Introduction'''  
  
Upsampling is the process of increasing sampling rate. <br>  
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Upsampling is the process of increasing sampling rate of discret-time signal. In this slecture, I will discuss about how it works and example of upsampling.<br>  
  
<br>  
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<br> [[Image:Block.jpg]] <br>  
  
[[Image:Block.jpg]]
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'''Theory'''<br> Upsampling in the frequency domain. It can be obtain in two different ways.<br> <br>&nbsp; [[Image:Theroy.jpg]] &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'''or '''&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [[Image:CodeCogsEqn.jpg]]<br>  
 
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<br>
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'''Theory'''<br>
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Upsampling in the frequency domain<br>
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<br>&nbsp; [[Image:Theroy.jpg]] &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'''or '''&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [[Image:CodeCogsEqn.jpg]]  
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<br>  
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<br>
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<br> [[Image:Graph1.jpg]]
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[[Image:Graph2.jpg]]
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[[Image:Graph3.jpg]]
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<br>  
 
<br>  
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Upsampling rate D = 2  
 
Upsampling rate D = 2  
  
<br>
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<br>  
  
Here is the sampled signal.<br>
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Here is the example of sampling signal.<br>  
  
 
[[Image:Graphex.jpg]]  
 
[[Image:Graphex.jpg]]  
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[[Image:Graphex3.jpg]]  
 
[[Image:Graphex3.jpg]]  
  
Final upsampled signal<br>  
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Here is the final upsampling signal.<br>
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[[Image:Graphex5.jpg]]
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'''Conclusion'''
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Upsampling by D inserts D - 1 zeros between every element of the original signal. Upsampling can create imaging artifacts. Lowpass filtering following upsampling can remove these imaging artifacts. In the time domain, lowpass filtering interpolates the zeros inserted by upsampling.
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<br>
  
[[Image:Graphex4.jpg]]  
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==[[Upsampling_Hyungsuk_Kim_slecture_review|Questions and comments]]==
  
'''Conclusion'''
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If you have any questions, comments, etc. please post them on [[Upsampling_Hyungsuk_Kim_slecture_review|this page]].
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----
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[[2014_Fall_ECE_438_Boutin_digital_signal_processing_slectures|Back to ECE438 slectures, Fall 2014]]

Latest revision as of 10:01, 14 March 2015

OUTLINE

1. Introduction

2. Theory

3. Example

4. Conclusion

_________________________________________________________________________________________________________

Introduction

Upsampling is the process of increasing sampling rate of discret-time signal. In this slecture, I will discuss about how it works and example of upsampling.


Block.jpg

Theory
Upsampling in the frequency domain. It can be obtain in two different ways.

  Theroy.jpg       or           CodeCogsEqn.jpg


Example

Upsampling rate D = 2


Here is the example of sampling signal.

Graphex.jpg

Upsampling rate D = 2 is applied.

Graphex2.jpg

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

Graphex3.jpg

Here is the final upsampling signal.

Graphex5.jpg

Conclusion

Upsampling by D inserts D - 1 zeros between every element of the original signal. Upsampling can create imaging artifacts. Lowpass filtering following upsampling can remove these imaging artifacts. In the time domain, lowpass filtering interpolates the zeros inserted by upsampling.


Questions and comments

If you have any questions, comments, etc. please post them on this page.


Back to ECE438 slectures, Fall 2014

Alumni Liaison

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

Dr. Paul Garrett