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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]]  
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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> Upsampling represents graphically in matlab. <br> [[Image:Graph1.jpg]]
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Revision as of 07:49, 10 October 2014

OUTLINE

1. Introduction

2. Theory

3. Example

4. Conclusion

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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 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

Here is the final upsampled 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.

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

Dr. Paul Garrett