<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE document PUBLIC "-//CNX//DTD CNXML 0.5 plus MathML//EN" "http://cnx.rice.edu/cnxml/0.5/DTD/cnxml_mathml.dtd">
<document xmlns="http://cnx.rice.edu/cnxml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:bib="http://bibtexml.sf.net/" id="conversion">


  <name>Resampling with Rational Factor</name>

  <metadata>
  <md:version>2.11</md:version>
  <md:created>2002/01/11</md:created>
  <md:revised>2005/10/05 15:14:34.417 GMT-5</md:revised>
  <md:authorlist>
      <md:author id="schniter">
      <md:firstname>Phil</md:firstname>
      
      <md:surname>Schniter</md:surname>
      <md:email>schniter@ee.eng.ohio-state.edu</md:email>
    </md:author>
  </md:authorlist>

  <md:maintainerlist>
    <md:maintainer id="jago">
      <md:firstname>Adan</md:firstname>
      
      <md:surname>Galvan</md:surname>
      <md:email>jago@rice.edu</md:email>
    </md:maintainer>
    <md:maintainer id="emaloney">
      <md:firstname>Erin</md:firstname>
      
      <md:surname>Maloney</md:surname>
      <md:email>emaloney@rice.edu</md:email>
    </md:maintainer>
    <md:maintainer id="schniter">
      <md:firstname>Phil</md:firstname>
      
      <md:surname>Schniter</md:surname>
      <md:email>schniter@ee.eng.ohio-state.edu</md:email>
    </md:maintainer>
  </md:maintainerlist>
  
  <md:keywordlist>
    <md:keyword>decimation</md:keyword>
    <md:keyword>interpolation</md:keyword>
    <md:keyword>resampling</md:keyword>
    <md:keyword>sample-rate conversion</md:keyword>
  </md:keywordlist>

  <md:abstract>Describes the process of resampling, or sample-rate conversion.</md:abstract>
</metadata>



  <content>

    <para id="para1">
      Interpolation by <m:math><m:ci>L</m:ci></m:math> and decimation
      by <m:math><m:ci>M</m:ci></m:math> can be combined to change the
      effective sampling rate of a signal by the rational factor
      <m:math><m:apply><m:divide/><m:ci>L</m:ci><m:ci>M</m:ci></m:apply></m:math>
      . This process is called <term>resampling</term> or
      <term>sample-rate conversion</term>. Rather than cascading an
      anti-imaging filter for interpolation with an anti-aliasing
      filter for decimation, we implement one filter with the minimum
      of the two cutoffs
      <m:math><m:interval><m:apply><m:divide/><m:pi/><m:ci>L</m:ci></m:apply>
      <m:apply><m:divide/><m:pi/><m:ci>M</m:ci></m:apply></m:interval></m:math>
      and the multiplication of the two DC gains
      (<m:math><m:ci>L</m:ci></m:math> and
      <m:math><m:cn>1</m:cn></m:math>), as illustrated in <cnxn target="fig1" strength="9"/>.
    </para>

    <figure id="fig1">
      <media type="image/png" src="m10448fig1.png"/>
      <caption/>
    </figure>


  </content>
</document>
