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== Introduction ==
 
== Introduction ==
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With microprocessors becoming ever increasingly faster, smaller, and cheaper, it is preferable to use digital signal processing as a way to compensate for distortions caused by analog circuitry.  One area that this can be applied is in signal reconstruction, where a low pass analog filter is used on the output of a digital-to-analog converter to attenuate unwanted frequency components above the Nyquist frequency.
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The problem with analog low pass filters is that higher the order, the more resistors, capacitors, and op-amps are required in its construction.  More circuit components means more circuit board space, which is a precious commodity with today's hand-held devices.
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Here, it will be explained how up-sampling can be used to relax requirements on analog low pass filter design while decreasing signal distortion.
  
 
== A Representative DT Signal ==
 
== A Representative DT Signal ==
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[[Image:Xd_w_plot.png‎]]
 
[[Image:Xd_w_plot.png‎]]
  
== Without Upsampling ==
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== Without Up-sampling ==
  
 
[[Image:Dac_diag.png‎]]
 
[[Image:Dac_diag.png‎]]
 
[[Image:W1_f_plot.png]]
 
[[Image:W1_f_plot.png]]
  
== With Upsampling ==
+
== With Up-sampling ==
  
 
[[Image:Upsampling_diag.png]]
 
[[Image:Upsampling_diag.png]]

Revision as of 17:39, 22 September 2009

Introduction

With microprocessors becoming ever increasingly faster, smaller, and cheaper, it is preferable to use digital signal processing as a way to compensate for distortions caused by analog circuitry. One area that this can be applied is in signal reconstruction, where a low pass analog filter is used on the output of a digital-to-analog converter to attenuate unwanted frequency components above the Nyquist frequency.

The problem with analog low pass filters is that higher the order, the more resistors, capacitors, and op-amps are required in its construction. More circuit components means more circuit board space, which is a precious commodity with today's hand-held devices.

Here, it will be explained how up-sampling can be used to relax requirements on analog low pass filter design while decreasing signal distortion.

A Representative DT Signal

X f plot.png Xd w plot.png

Without Up-sampling

Dac diag.png W1 f plot.png

With Up-sampling

Upsampling diag.png U w plot.png V w plot.png W2 f plot.png

How Analog Filter Design is Affected

Alumni Liaison

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

Dr. Paul Garrett