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<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>Hello everyone,<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>Craig, thanks for sending the solution for hw #3. <o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>Everyone, please <b><span style='font-weight:bold'>***update/correct***</span></b>
the solution so that the normalization reflects the summation over frequency lines
neighboring the peaks. <o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>By just including the power in the peak line one gets normalization
factors that are too small. (For example, Craig gets ~0.41 = (2/pi)^2 for
sine window instead of 1/2.)<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'> <o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>Enclosed is a small demo program to show this for the case of
sine-windowed DFT. Here is its output:<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'> <o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'> <o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>Normalization Example: (2/N*DFT of sine-windowed unit-amplitude
sinusoid)<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'> <o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'> <o:p></o:p></span></font></p>
<p class=MsoPlainText><st1:place w:st="on"><st1:PlaceName w:st="on"><font
size=2 face="Courier New"><span style='font-size:10.0pt'>Spectral</span></font></st1:PlaceName>
<st1:PlaceType w:st="on">Peak</st1:PlaceType></st1:place>:
0.636619834785 (Approx. 2/pi = 0.636619772368 as noted by
Craig)<o:p></o:p></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'> <o:p></o:p></span></font></p>
<p class=MsoPlainText><st1:place w:st="on"><st1:PlaceName w:st="on"><font
size=2 face="Courier New"><span style='font-size:10.0pt'>Spectral</span></font></st1:PlaceName>
<st1:PlaceType w:st="on">Peak</st1:PlaceType></st1:place> + 1
neighbor(s) on each side: <o:p></o:p></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>[ 0.21220653 0.63661983 0.21220653]<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'> <o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'> <o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>Sum over peak: 0.405284814042 (Approx. (2/pi)^2 =
0.405284734569 as noted by Craig)<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'> <o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>Sum over Broadened peak: 0.495348035409 (Approx.
<w^2> = 1/2 as in book p. 229 for sine window)<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>Marina Bosi<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>Consulting Professor, Department of Music<o:p></o:p></span></font></p>
<p class=MsoPlainText><st1:place w:st="on"><st1:PlaceName w:st="on"><font
size=2 face="Courier New"><span style='font-size:10.0pt'>Stanford</span></font></st1:PlaceName>
<st1:PlaceType w:st="on">University</st1:PlaceType></st1:place><o:p></o:p></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><st1:place w:st="on"><st1:PlaceName w:st="on"><font
size=2 face="Courier New"><span style='font-size:10.0pt'>Computer</span></font></st1:PlaceName>
<st1:PlaceType w:st="on">Center</st1:PlaceType></st1:place> for Research in
Music and Acoustics<o:p></o:p></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>The Knoll, <st1:Street w:st="on"><st1:address w:st="on">660
Lomita Court</st1:address></st1:Street><o:p></o:p></span></font></p>
<p class=MsoPlainText><st1:place w:st="on"><st1:City w:st="on"><font size=2
face="Courier New"><span style='font-size:10.0pt'>Stanford</span></font></st1:City>,
<st1:State w:st="on">California</st1:State> <st1:PostalCode w:st="on">94305-8180</st1:PostalCode>,
<st1:country-region w:st="on">USA</st1:country-region></st1:place><o:p></o:p></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>http://ccrma.stanford.edu<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>mbosi@stanford.edu<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>-----Original Message-----<br>
From: 422-bounces@ccrma.Stanford.EDU [mailto:422-bounces@ccrma.Stanford.EDU] On
Behalf Of Craig Sapp<br>
Sent: Friday, March 05, 2010 8:54 AM<br>
To: 422@ccrma.Stanford.EDU<br>
Subject: [mus422] Hw3 solutions</span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>Hello Music 422 class,<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>Attached are solutions to HW3 giving illustrations of the 1 kHz<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>sinewave peak aligned in SPL between the MDCT and the DFT (plot 4 on<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>page 2 illustrates the 1/2 bin shift between the two transforms),<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>including Kaiser-Bessel Derived windows using alpha of 1 and 4.
Also<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>on page 3 are a pair of functions which can be used to calculate the<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>reference amplitude for a given window/transform/transform size<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>without the need to keep track of normalization factors in order to<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>display the transform with dB_spl.<o:p></o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'><o:p> </o:p></span></font></p>
<p class=MsoPlainText><font size=2 face="Courier New"><span style='font-size:
10.0pt'>-=+Craig<o:p></o:p></span></font></p>
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