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<name xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:bib="http://bibtexml.sf.net/">Pitch Detection</name>
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  <md:version xmlns:bib="http://bibtexml.sf.net/">1.2</md:version>
  <md:created xmlns:bib="http://bibtexml.sf.net/">2005/12/14 04:30:54 US/Central</md:created>
  <md:revised xmlns:bib="http://bibtexml.sf.net/">2005/12/14 21:57:44.059 US/Central</md:revised>
  <md:authorlist xmlns:bib="http://bibtexml.sf.net/">
      <md:author xmlns:bib="http://bibtexml.sf.net/" id="yjw">
      <md:firstname xmlns:bib="http://bibtexml.sf.net/">Yi-Chieh</md:firstname>
      
      <md:surname xmlns:bib="http://bibtexml.sf.net/">Wu</md:surname>
      <md:email xmlns:bib="http://bibtexml.sf.net/">yjw@rice.edu</md:email>
    </md:author>
      <md:author xmlns:bib="http://bibtexml.sf.net/" id="kringg">
      <md:firstname xmlns:bib="http://bibtexml.sf.net/">Kyle</md:firstname>
      
      <md:surname xmlns:bib="http://bibtexml.sf.net/">Ringgenberg</md:surname>
      <md:email xmlns:bib="http://bibtexml.sf.net/">kringg@rice.edu</md:email>
    </md:author>
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    <md:maintainer xmlns:bib="http://bibtexml.sf.net/" id="yjw">
      <md:firstname xmlns:bib="http://bibtexml.sf.net/">Yi-Chieh</md:firstname>
      
      <md:surname xmlns:bib="http://bibtexml.sf.net/">Wu</md:surname>
      <md:email xmlns:bib="http://bibtexml.sf.net/">yjw@rice.edu</md:email>
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    <md:maintainer xmlns:bib="http://bibtexml.sf.net/" id="kringg">
      <md:firstname xmlns:bib="http://bibtexml.sf.net/">Kyle</md:firstname>
      
      <md:surname xmlns:bib="http://bibtexml.sf.net/">Ringgenberg</md:surname>
      <md:email xmlns:bib="http://bibtexml.sf.net/">kringg@rice.edu</md:email>
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  <md:abstract xmlns:bib="http://bibtexml.sf.net/">Finding the pitch of a musical signal.</md:abstract>
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<section xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:bib="http://bibtexml.sf.net/" id="id4378067"><name xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:bib="http://bibtexml.sf.net/">Pitch Detection</name>
<para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:bib="http://bibtexml.sf.net/" id="id6959083">Detecting the pitch of an input signal seems
deceptively simple. Many groups have tackled this challenge by
simply taking the Fourier transform of the signal, and then finding
the frequency with the highest spectral magnitude. As elegant as it may seem, this
approach does not work for many musical instruments. Instead,
we have chosen to approach the problem from a more expandable point
of view.</para>
<para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:bib="http://bibtexml.sf.net/" id="id7436417">One of the problems with finding the
fundamental frequency lies in simple definition. In our case, we
will define this as being the frequency that the human ear
recognizes as being dominate. The human auditory system responds
most sensitively to the equivalent of the lowest common denominator of the produced frequencies. This can be modeled by finding the strongest set of frequencies amplitudes, and taking the lowest frequency value of that group. This process is quite effective, though it does rely on the condition that the fundamental frequency actually exists, and isn't just simulated via a combination of higher harmonics. The
following example illustrates this more concretely.</para>
<figure xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:bib="http://bibtexml.sf.net/" id="id6232187"><media xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:bib="http://bibtexml.sf.net/" type="image/jpg" src="Graphic1"/>
<caption xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:bib="http://bibtexml.sf.net/">Frequence vs. Time for Trumpet playing a concert 'A'=440 Hz</caption></figure>
<para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:bib="http://bibtexml.sf.net/" id="id5676315">In the above waveform, we want to find the
frequency heard by the human ear as being the fundamental pitch. To
do this, we first look at the five highest peaks, which occur at
440, 880, 1320, 1760, and 2640 Hz. From this set of values, we
grab the lowest occurring frequency. Hence, the fundamental
frequency of the above signal would be stated as being 440 Hz, or a
concert 'A'... which is, in fact, the pitch that was played.</para>
</section>
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