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  <name xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Multirate Filtering: Introduction (Thai Version)</name>
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    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">multirate sampling</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">multirate system</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">decimation</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">interpolation</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">sample-rate compressor</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">sample-rate expander</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">upsample</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">downsample</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">DSP</md:keyword>
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  <md:abstract xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">A sample-rate compressor removes (D-1) of every D input samples.  A sample-rate expander inserts (U-1) zeros after every input sample.  </md:abstract>
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  <content xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
    <section xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="sec1">
      <name xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Introduction</name>
      <para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="p1">
	ในแบบฝึกหัดนี้ คุณจะได้เรียนรู้เกี่ยวกับผลของการใช้  <term xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">multirate processing</term>
	 โดยจะใช้ระบบใน <cnxn xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" target="fig1"/>.  <term xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">sample-rate
	  compressor</term> 
	(<m:math>
	  <m:apply>
	    <m:mo>↓</m:mo>
	    <m:ci>D</m:ci>
	  </m:apply>
	</m:math>) ใน block-diagram จะทำการกำจัดค่า
	<m:math>
	  <m:apply>
	    <m:minus/>
	    <m:ci>D</m:ci>
	    <m:cn>1</m:cn>
	  </m:apply>
	</m:math> ของทุกๆ
	<m:math>
	  <m:ci>D</m:ci>
	</m:math> input samples, ในขณะที่ <term xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">sample-rate
	  expander</term> 
	(<m:math>
	  <m:apply>
	    <m:mo>↑</m:mo>
	    <m:ci>U</m:ci>
	  </m:apply>
	</m:math>) จะเพิ่มค่า
	<m:math>
	  <m:apply>
	    <m:minus/>
	    <m:ci>U</m:ci>
	    <m:cn>1</m:cn>
	  </m:apply>
	</m:math>ศูนย์หลังจากทุกๆ   input sample.  โดยที่มี
	compression และ expansion factors set เป็นค่าเดียวกัน(
	<m:math>
	  <m:apply>
	    <m:eq/>
	    <m:ci>D</m:ci>
	    <m:ci>U</m:ci>
	  </m:apply>
	</m:math>), filters FIR 1 และ FIR 3 จะทำงานที่  sample rate
	<m:math>
	  <m:ci><m:msub> 
	      <m:mi>F</m:mi> 
	      <m:mi>s</m:mi>
	    </m:msub></m:ci> 
	</m:math>, ขณะที่ filter FIR 2 จะทำงานที่ lower rate ของ
	<m:math>
	  <m:apply>
	    <m:divide/>
	    <m:ci><m:msub>
		<m:mi>F</m:mi>
		<m:mi>s</m:mi>
	      </m:msub></m:ci>
	    <m:ci>D</m:ci>
	  </m:apply>
	</m:math>.
      </para>

      <figure xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="fig1">
	<media xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" type="image/png" src="multirate_sys.png"/>
	<caption xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Net multirate system</caption>
      </figure>

      <para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="p2">
	ในภายหลัง คุณจะได้  implement ระบบและควบคุม compression และ
	 expansion factors ในขณะ runtime ด้วย interface ที่มีให้
	คุณจะสามารถทำการ  disable filter ตัวใดตัวหนึ่งหรือทั้งหมดเพื่อทำการ
	ศึกษผลกระทบของ  multirate.  ให้ระบุว่า FIR 1และ FIR 3 ทำอะไร
	และผลจะเป็นอย่างไรถ้าไม่มี filter ทั้งสอง
      </para>
    </section>

  </content>
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