Subject: Re: Human hearing beats the Fourier uncertainty principle: Research From: Pierre Divenyi <pdivenyi@xxxxxxxx> Date: Sat, 23 Feb 2013 10:35:42 -0800 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>--Apple-Mail-F52FBB5F-7EFE-4C92-A9D7-884A01E7433E Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable Judy brings up the point that theories indicating the listeners beating the u= ncertainty principle are likely to have used inappropriate definitions of ba= ndwidth and/or duration. Attempting to find a right WT combination is,in fac= t, the topic of the 1971 Ronken article I pointed out earlier. The bottom li= ne of this issue is that the auditory signal consists of a certain number of= information bits that no system, physical or biological, can increase or ov= erride. Pardon the typos, it's Apple's fault. On Feb 22, 2013, at 11:18, Judi Lapsley Miller <judi@xxxxxxxx> wrot= e: > A million years ago (it seems), I investigated the acoustical uncertainty p= rinciple for my PhD thesis. I found that humans did a pretty good job at opt= imally resolving narrow-band short-duration noise stimuli, and did best for s= timuli with a bandwidth-duration product of around 2. By optimally, I mean c= ompared to an ideal observer theory. There was no indication my observers we= re able to beat the uncertainty principle, but they came close to operating a= s well as an ideal observer for some bandwidth-duration conditions. > =20 > Any study showing observers =E2=80=9Cbeating=E2=80=9D the uncertainty prin= ciple has subjects who are solving the task differently to what the experime= nter expected, or there are issues with defining bandwidth and duration. IMH= O. > =20 > http://psychophysics.org/judi_thesis.htm > =20 > Judi > =20 > From: AUDITORY - Research in Auditory Perception [mailto:AUDITORY@xxxxxxxx= GILL.CA] On Behalf Of corey > Sent: Friday, 22 February 2013 05:33 > To: AUDITORY@xxxxxxxx > Subject: Re: Human hearing beats the Fourier uncertainty principle: Resear= ch > =20 > I do think this article is misleading. In my opinion the uncertainty prin= ciple is not something to be "overcome". It simply relates the bandwidth of= a waveform to its duration (which is an unassailable fact). In Fourier the= ory frequency is defined for periodic signals (which are of infinite duratio= n). Any finite duration signal can be viewed equally as an infinite duratio= n periodic signal that has been multiplied by a finite duration window. It i= s this windowing process that introduces a spread of frequencies (after all t= he window is a waveform too). It is thus not physically possible to create s= timuli that "beat" the uncertainty principle, which seems to negate the conc= lusions in the remainder of the article. > =20 > On 2013-02-20, at 10:27 AM, James Johnston wrote: >=20 >=20 > Well, yes. Of course, and the FFT is not a minimum-phase filter, while the= ear is very close to such. Well, there goes a large speed factor already, e= h? >=20 > On Wed, Feb 20, 2013 at 8:48 AM, Bastian Epp <bepp@xxxxxxxx> wrote: > Hi list! >=20 > without having read the paper in detail, I just think the discussion shoul= d be done with fair weapons: >=20 > The description of the ear via a FFT is a rather poor model, but a FFT (or= rather the math behind that) can be interpretet as a bank of overlapping ba= ndpass filters (see the Oppenheim Schaefer DSP book)....so this point raised= is not valid.=20 >=20 > I would be surprised if this result would not have been reported before in= the solid psychoacoustics literature before. >=20 > Bests >=20 > BAstian >=20 >=20 > On 02/18/2013 05:00 PM, James Johnston wrote: > I must admit some frustration with this particular paper. First, the > Gabor limit does not apply to the task, and never did. The only limit > here is SNR_based, since there is already expectation of a given set > of frequencies, this is not a task requiring arbitrary detection. > =20 > Then, the fact that the ear is a leading edge detector has been > understood for roughly 100 years now, making "1/100 th of a > wavelength" perhaps not such a big deal. > =20 > It is nice that this performance ability by the human has been clearly > demonstrated, but the headline is inexcusably misleading, and is > already providing fodder for the audiophile "I told you so" bunch who > simply doesn't understand what it means. > =20 > And, in any case, who would use an FFT to detect such a thing? Rather > use a set of bandpass filters, eh? > =20 > On Sun, Feb 17, 2013 at 12:02 PM, Peter Meijer > <feedback@xxxxxxxx> wrote: > =20 > Indeed this relates to a discussion that we had 9 years ago, > =20 > http://www.auditory.org/mhonarc/2004/msg00145.html > =20 > and that formed the basis of my old web page on beating the > frequency-time uncertainty principle, > =20 > http://www.seeingwithsound.com/freqtime.htm > =20 > Best regards, > =20 > Peter Meijer > =20 > =20 > Seeing with Sound - The vOICe > http://www.seeingwithsound.com > =20 > =20 > =20 > Date: Sun, 17 Feb 2013 07:43:35 +0000 > From: "Beerends, J.G. (John)" <john.beerends@xxxxxxxx> > To: AUDITORY@xxxxxxxx > Subject: Re: Human hearing beats the Fourier uncertainty principle: > Research > =20 > For discrimination the uncertainty limit does not exist, one can build > discriminator devices that go below the uncertainty limit in both the time= > and frequency domain, the uncertainty limit is only a measure for the spre= ad > (Delta) in both domains (DfDt>1), it is not a limit to what extent they ca= n > be discriminated. One can also build a device that measures the frequency o= f > a sine wave with an accuracy below the uncertainty limit by exploiting > a-priori knowledge, i.e. if I know that the signal I am measuring is a > short cut out of an infinite duration sine wave of a certain amplitude I c= an > measure the frequency as accurate as I want. > =20 > John Beerends > =20 > =20 > -----Original Message----- > From: AUDITORY - Research in Auditory Perception > [mailto:AUDITORY@xxxxxxxx On Behalf Of Kevin Austin > Sent: Saturday, February 16, 2013 5:07 PM > To: AUDITORY@xxxxxxxx > Subject: Human hearing beats the Fourier uncertainty principle: Research > =20 > Comments? > =20 > =20 > =20 > http://phys.org/news/2013-02-human-fourier-uncertainty-principle.html > =20 > =20 > (Phys.org)-For the first time, physicists have found that humans can > discriminate a sound's frequency (related to a note's pitch) and timing > (whether a note comes before or after another note) more than 10 times > better than the limit imposed by the Fourier uncertainty principle. Not > surprisingly, some of the subjects with the best listening precision were > musicians, but even non-musicians could exceed the uncertainty limit. The > results rule out the majority of auditory processing brain algorithms that= > have been proposed, since only a few models can match this impressive huma= n > performance. > =20 > =20 > Read more at: > http://phys.org/news/2013-02-human-fourier-uncertainty-principle.html#jCp > =20 > Thanks > =20 > Kevin > This e-mail and its contents are subject to the DISCLAIMER at > http://www.tno.nl/emaildisclaimer > =20 > =20 > =20 >=20 > -- > =20 > Bastian Epp > Assistant Professor > ELEK VIP > DTU Electrical Engineering > =20 > Technical University of Denmark > <DTU_email_logo_01.gif> > Department of Electrical Engineering > =C3=98rsteds Plads > Building 352 > 2800 Kgs. Lyngby > Direct +45 45253953 > bepp@xxxxxxxx > www.elektro.dtu.dk/ > =20 > =20 >=20 >=20 >=20 > -- > James D. (jj) Johnston > Independent Audio and Electroacoustics Consultant > =20 --Apple-Mail-F52FBB5F-7EFE-4C92-A9D7-884A01E7433E Content-Type: text/html; charset=utf-8 Content-Transfer-Encoding: quoted-printable <html><head><meta http-equiv=3D"content-type" content=3D"text/html; charset=3D= utf-8"></head><body dir=3D"auto"><div>Judy brings up the point that theories= indicating the listeners beating the uncertainty principle are likely to ha= ve used inappropriate definitions of bandwidth and/or duration. Attempting t= o find a right WT combination is,in fact, the topic of the 1971 Ronken artic= le I pointed out earlier. The bottom line of this issue is that the auditory= signal consists of a certain number of information bits that no system, phy= sical or biological, can increase or override.<br><br>Pardon the typos, it's= Apple's fault.</div><div><br>On Feb 22, 2013, at 11:18, Judi Lapsley Miller= <<a href=3D"mailto:judi@xxxxxxxx">judi@xxxxxxxx</a>>= ; wrote:<br><br></div><blockquote type=3D"cite"><div><meta http-equiv=3D"Con= tent-Type" content=3D"text/html; charset=3Diso-8859-1"><meta name=3D"Generat= or" content=3D"Microsoft Word 14 (filtered medium)"><style><!-- /* Font Definitions */ @xxxxxxxx {font-family:"Cambria Math"; panose-1:2 4 5 3 5 4 6 3 2 4;} @xxxxxxxx {font-family:Calibri; panose-1:2 15 5 2 2 2 4 3 2 4;} @xxxxxxxx {font-family:Tahoma; panose-1:2 11 6 4 3 5 4 4 2 4;} @xxxxxxxx {font-family:Consolas; panose-1:2 11 6 9 2 2 4 3 2 4;} /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {margin:0cm; margin-bottom:.0001pt; font-size:12.0pt; font-family:"Times New Roman","serif";} a:link, span.MsoHyperlink {mso-style-priority:99; color:blue; text-decoration:underline;} a:visited, span.MsoHyperlinkFollowed {mso-style-priority:99; color:purple; text-decoration:underline;} p {mso-style-priority:99; mso-margin-top-alt:auto; margin-right:0cm; mso-margin-bottom-alt:auto; margin-left:0cm; font-size:12.0pt; font-family:"Times New Roman","serif";} pre {mso-style-priority:99; mso-style-link:"HTML Preformatted Char"; margin:0cm; margin-bottom:.0001pt; font-size:10.0pt; font-family:"Courier New";} p.MsoAcetate, li.MsoAcetate, div.MsoAcetate {mso-style-priority:99; mso-style-link:"Balloon Text Char"; margin:0cm; margin-bottom:.0001pt; font-size:8.0pt; font-family:"Tahoma","sans-serif";} span.HTMLPreformattedChar {mso-style-name:"HTML Preformatted Char"; mso-style-priority:99; mso-style-link:"HTML Preformatted"; font-family:Consolas;} span.BalloonTextChar {mso-style-name:"Balloon Text Char"; mso-style-priority:99; mso-style-link:"Balloon Text"; font-family:"Tahoma","sans-serif";} span.EmailStyle22 {mso-style-type:personal-reply; font-family:"Calibri","sans-serif"; color:#1F497D;} .MsoChpDefault {mso-style-type:export-only; font-size:10.0pt;} @xxxxxxxx WordSection1 {size:612.0pt 792.0pt; margin:72.0pt 72.0pt 72.0pt 72.0pt;} div.WordSection1 {page:WordSection1;} --></style><!--[if gte mso 9]><xml> <o:shapedefaults v:ext=3D"edit" spidmax=3D"1026" /> </xml><![endif]--><!--[if gte mso 9]><xml> <o:shapelayout v:ext=3D"edit"> <o:idmap v:ext=3D"edit" data=3D"1" /> </o:shapelayout></xml><![endif]--><div class=3D"WordSection1"><p class=3D"Ms= oNormal"><span style=3D"font-size:11.0pt;font-family:"Calibri",&qu= ot;sans-serif";color:#1F497D">A million years ago (it seems), I investi= gated the acoustical uncertainty principle for my PhD thesis. I found that h= umans did a pretty good job at optimally resolving narrow-band short-duratio= n noise stimuli, and did best for stimuli with a bandwidth-duration product o= f around 2. By optimally, I mean compared to an ideal observer theory. There= was no indication my observers were able to beat the uncertainty principle,= but they came close to operating as well as an ideal observer for some band= width-duration conditions. <o:p></o:p></span></p><p class=3D"MsoNormal"><spa= n style=3D"font-size:11.0pt;font-family:"Calibri","sans-serif= ";color:#1F497D"><o:p> </o:p></span></p><p class=3D"MsoNormal"><sp= an style=3D"font-size:11.0pt;font-family:"Calibri","sans-seri= f";color:#1F497D">Any study showing observers =E2=80=9Cbeating=E2=80=9D= the uncertainty principle has subjects who are solving the task differently= to what the experimenter expected, or there are issues with defining bandwi= dth and duration. IMHO.<o:p></o:p></span></p><p class=3D"MsoNormal"><span st= yle=3D"font-size:11.0pt;font-family:"Calibri","sans-serif&quo= t;;color:#1F497D"><o:p> </o:p></span></p><p class=3D"MsoNormal"><span s= tyle=3D"font-size:11.0pt;font-family:"Calibri","sans-serif&qu= ot;;color:#1F497D"><a href=3D"http://psychophysics.org/judi_thesis.htm">http= ://psychophysics.org/judi_thesis.htm</a><o:p></o:p></span></p><p class=3D"Ms= oNormal"><span style=3D"font-size:11.0pt;font-family:"Calibri",&qu= ot;sans-serif";color:#1F497D"><o:p> </o:p></span></p><p class=3D"M= soNormal"><span style=3D"font-size:11.0pt;font-family:"Calibri",&q= uot;sans-serif";color:#1F497D">Judi<o:p></o:p></span></p><p class=3D"Ms= oNormal"><a name=3D"_MailEndCompose"><span style=3D"font-size:11.0pt;font-fa= mily:"Calibri","sans-serif";color:#1F497D"><o:p> </= o:p></span></a></p><div><div style=3D"border:none;border-top:solid #B5C4DF 1= .0pt;padding:3.0pt 0cm 0cm 0cm"><p class=3D"MsoNormal"><b><span lang=3D"EN-U= S" style=3D"font-size:10.0pt;font-family:"Tahoma","sans-serif= "">From:</span></b><span lang=3D"EN-US" style=3D"font-size:10.0pt;font-= family:"Tahoma","sans-serif""> AUDITORY - Research in Au= ditory Perception [<a href=3D"mailto:AUDITORY@xxxxxxxx">mailto:AUDITO= RY@xxxxxxxx</a>] <b>On Behalf Of </b>corey<br><b>Sent:</b> Friday, 22= February 2013 05:33<br><b>To:</b> <a href=3D"mailto:AUDITORY@xxxxxxxx= A">AUDITORY@xxxxxxxx</a><br><b>Subject:</b> Re: Human hearing beats t= he Fourier uncertainty principle: Research<o:p></o:p></span></p></div></div>= <p class=3D"MsoNormal"><o:p> </o:p></p><p class=3D"MsoNormal">I do thin= k this article is misleading. In my opinion the uncertainty principle i= s not something to be "overcome". It simply relates the bandwidth of a= waveform to its duration (which is an unassailable fact). In Fourier t= heory frequency is defined for periodic signals (which are of infinite durat= ion). Any finite duration signal can be viewed equally as an infinite d= uration periodic signal that has been multiplied by a finite duration window= . It is this windowing process that introduces a spread of frequencies= (after all the window is a waveform too). It is thus not physically p= ossible to create stimuli that "beat" the uncertainty principle, which seems= to negate the conclusions in the remainder of the article.<o:p></o:p></p><d= iv><p class=3D"MsoNormal"><o:p> </o:p></p><div><div><p class=3D"MsoNorm= al">On 2013-02-20, at 10:27 AM, James Johnston wrote:<o:p></o:p></p></div><p= class=3D"MsoNormal"><br><br><o:p></o:p></p><p class=3D"MsoNormal" style=3D"= margin-bottom:12.0pt">Well, yes. Of course, and the FFT is not a minimum-pha= se filter, while the ear is very close to such. Well, there goes a large spe= ed factor already, eh? <o:p></o:p></p><div><p class=3D"MsoNormal">On Wed, Fe= b 20, 2013 at 8:48 AM, Bastian Epp <<a href=3D"mailto:bepp@xxxxxxxx= " target=3D"_blank">bepp@xxxxxxxx</a>> wrote:<o:p></o:p></p><div><p= class=3D"MsoNormal">Hi list!<br><br>without having read the paper in detail= , I just think the discussion should be done with fair weapons:<br><br>The d= escription of the ear via a FFT is a rather poor model, but a FFT (or rather= the math behind that) can be interpretet as a bank of overlapping bandpass f= ilters (see the Oppenheim Schaefer DSP book)....so this point raised is not v= alid. <br><br>I would be surprised if this result would not have been report= ed before in the solid psychoacoustics literature before.<br><br>Bests<br><b= r>BAstian<br><br><br>On 02/18/2013 05:00 PM, James Johnston wrote: <o:p></o:= p></p><pre>I must admit some frustration with this particular paper. First, t= he<o:p></o:p></pre><pre>Gabor limit does not apply to the task, and never di= d. The only limit<o:p></o:p></pre><pre>here is SNR_based, since there is alr= eady expectation of a given set<o:p></o:p></pre><pre>of frequencies, this is= not a task requiring arbitrary detection.<o:p></o:p></pre><pre><o:p> <= /o:p></pre><pre>Then, the fact that the ear is a leading edge detector has b= een<o:p></o:p></pre><pre>understood for roughly 100 years now, making "1/100= th of a<o:p></o:p></pre><pre>wavelength" perhaps not such a big deal.<o:p><= /o:p></pre><pre><o:p> </o:p></pre><pre>It is nice that this performance= ability by the human has been clearly<o:p></o:p></pre><pre>demonstrated, bu= t the headline is inexcusably misleading, and is<o:p></o:p></pre><pre>alread= y providing fodder for the audiophile "I told you so" bunch who<o:p></o:p></= pre><pre>simply doesn't understand what it means.<o:p></o:p></pre><pre><o:p>= </o:p></pre><pre>And, in any case, who would use an FFT to detect such= a thing? Rather<o:p></o:p></pre><pre>use a set of bandpass filters, eh?<o:p= ></o:p></pre><pre><o:p> </o:p></pre><pre>On Sun, Feb 17, 2013 at 12:02 P= M, Peter Meijer<o:p></o:p></pre><pre><a href=3D"mailto:feedback@xxxxxxxx= und.com" target=3D"_blank"><feedback@xxxxxxxx></a> wrote:<o= :p></o:p></pre><pre> <o:p></o:p></pre><blockquote style=3D"margin-top:= 5.0pt;margin-bottom:5.0pt"><pre>Indeed this relates to a discussion that we h= ad 9 years ago,<o:p></o:p></pre><pre><o:p> </o:p></pre><pre>  = ; <a href=3D"http://www.auditory.org/mhonarc/2004/msg00145.html" target=3D"_= blank">http://www.auditory.org/mhonarc/2004/msg00145.html</a><o:p></o:p></pr= e><pre><o:p> </o:p></pre><pre>and that formed the basis of my old web p= age on beating the<o:p></o:p></pre><pre>frequency-time uncertainty principle= ,<o:p></o:p></pre><pre><o:p> </o:p></pre><pre> <a href=3D"h= ttp://www.seeingwithsound.com/freqtime.htm" target=3D"_blank">http://www.see= ingwithsound.com/freqtime.htm</a><o:p></o:p></pre><pre><o:p> </o:p></pr= e><pre>Best regards,<o:p></o:p></pre><pre><o:p> </o:p></pre><pre>Peter M= eijer<o:p></o:p></pre><pre><o:p> </o:p></pre><pre><o:p> </o:p></pr= e><pre>Seeing with Sound - The vOICe<o:p></o:p></pre><pre><a href=3D"http://= www.seeingwithsound.com/" target=3D"_blank">http://www.seeingwithsound.com</= a><o:p></o:p></pre><pre><o:p> </o:p></pre><pre><o:p> </o:p></pre><= pre> <o:p></o:p></pre><blockquote style=3D"margin-top:5.0p= t;margin-bottom:5.0pt"><pre>Date: Sun, 17 Feb 2013 07:43:35 +0000<o:p></o:p>= </pre><pre>From: "Beerends, J.G. (John)" <a href=3D"mailto:john.beerends@xxxxxxxx= .NL" target=3D"_blank"><john.beerends@xxxxxxxx></a><o:p></o:p></pre><pre= >To: <a href=3D"mailto:AUDITORY@xxxxxxxx" target=3D"_blank">AUDITORY@xxxxxxxx= LISTS.MCGILL.CA</a><o:p></o:p></pre><pre>Subject: Re: Human hearing beats th= e Fourier uncertainty principle:<o:p></o:p></pre><pre>Research<o:p></o:p></p= re><pre><o:p> </o:p></pre><pre>For discrimination the uncertainty limit= does not exist, one can build<o:p></o:p></pre><pre>discriminator devices th= at go below the uncertainty limit in both the time<o:p></o:p></pre><pre>and f= requency domain, the uncertainty limit is only a measure for the spread<o:p>= </o:p></pre><pre>(Delta) in both domains (DfDt>1), it is not a limit to w= hat extent they can<o:p></o:p></pre><pre>be discriminated. One can also buil= d a device that measures the frequency of<o:p></o:p></pre><pre>a sine wave w= ith an accuracy below the uncertainty limit by exploiting<o:p></o:p></pre><p= re>a-priori knowledge, i.e. if I know that the signal I am measuring i= s a<o:p></o:p></pre><pre>short cut out of an infinite duration sine wave of a= certain amplitude I can<o:p></o:p></pre><pre>measure the frequency as accur= ate as I want.<o:p></o:p></pre><pre><o:p> </o:p></pre><pre>John Beerend= s<o:p></o:p></pre><pre> <o:p></o:p></pre></blo= ckquote><pre> <o:p></o:p></pre><blockquote style=3D"m= argin-top:5.0pt;margin-bottom:5.0pt"><pre>-----Original Message-----<o:p></o= :p></pre><pre>From: AUDITORY - Research in Auditory Perception<o:p></o:p></p= re><pre>[<a href=3D"mailto:AUDITORY@xxxxxxxx" target=3D"_blank">mailt= o:AUDITORY@xxxxxxxx</a>] On Behalf Of Kevin Austin<o:p></o:p></pre><p= re>Sent: Saturday, February 16, 2013 5:07 PM<o:p></o:p></pre><pre>To: <a hre= f=3D"mailto:AUDITORY@xxxxxxxx" target=3D"_blank">AUDITORY@xxxxxxxx= L.CA</a><o:p></o:p></pre><pre>Subject: Human hearing beats the Fourier uncer= tainty principle: Research<o:p></o:p></pre><pre><o:p> </o:p></pre><pre>= Comments?<o:p></o:p></pre><pre><o:p> </o:p></pre><pre><o:p> </o:p>= </pre><pre> <o:p></o:p></pre><blockquote style= =3D"margin-top:5.0pt;margin-bottom:5.0pt"><blockquote style=3D"margin-top:5.= 0pt;margin-bottom:5.0pt"><pre><a href=3D"http://phys.org/news/2013-02-human-= fourier-uncertainty-principle.html" target=3D"_blank">http://phys.org/news/2= 013-02-human-fourier-uncertainty-principle.html</a><o:p></o:p></pre><pre><o:= p> </o:p></pre><pre><o:p> </o:p></pre><pre>(<a href=3D"http://Phys= .org">Phys.org</a>)-For the first time, physicists have found that humans ca= n<o:p></o:p></pre><pre>discriminate a sound's frequency (related to a note's= pitch) and timing<o:p></o:p></pre><pre>(whether a note comes before or afte= r another note) more than 10 times<o:p></o:p></pre><pre>better than the limi= t imposed by the Fourier uncertainty principle. Not<o:p></o:p></pre><pre>sur= prisingly, some of the subjects with the best listening precision were<o:p><= /o:p></pre><pre>musicians, but even non-musicians could exceed the uncertain= ty limit. The<o:p></o:p></pre><pre>results rule out the majority of auditory= processing brain algorithms that<o:p></o:p></pre><pre>have been proposed, s= ince only a few models can match this impressive human<o:p></o:p></pre><pre>= performance.<o:p></o:p></pre><pre> = <o:p></o:p></pre></blockquote></blockquote></blockquote><pre>&n= bsp; <o:p></o:p></pre><blockquote style=3D"margin-top:5.0pt= ;margin-bottom:5.0pt"><blockquote style=3D"margin-top:5.0pt;margin-bottom:5.= 0pt"><blockquote style=3D"margin-top:5.0pt;margin-bottom:5.0pt"><pre>Read mo= re at:<o:p></o:p></pre><pre><a href=3D"http://phys.org/news/2013-02-human-fo= urier-uncertainty-principle.html#jCp" target=3D"_blank">http://phys.org/news= /2013-02-human-fourier-uncertainty-principle.html#jCp</a><o:p></o:p></pre><p= re> <o:p></o:p></pre><= /blockquote></blockquote><pre>Thanks<o:p></o:p></pre><pre><o:p> </o:p><= /pre><pre>Kevin<o:p></o:p></pre><pre>This e-mail and its contents are subjec= t to the DISCLAIMER at<o:p></o:p></pre><pre><a href=3D"http://www.tno.nl/ema= ildisclaimer" target=3D"_blank">http://www.tno.nl/emaildisclaimer</a><o:p></= o:p></pre><pre> <o:p></o:p></pre></blockquote>= </blockquote><pre> <o:p></o:p></pre><p class=3D"MsoNormal" style=3D= "margin-bottom:12.0pt"><o:p> </o:p></p><div><p class=3D"MsoNormal">-- <= o:p></o:p></p><table class=3D"MsoNormalTable" border=3D"0" cellspacing=3D"3"= cellpadding=3D"0"><tbody><tr><td style=3D"padding:.75pt .75pt .75pt .75pt">= <div><table class=3D"MsoNormalTable" border=3D"0" cellspacing=3D"0" cellpadd= ing=3D"0" width=3D"400" style=3D"width:240.0pt;border-collapse:collapse"><tb= ody><tr><td width=3D"400" colspan=3D"2" valign=3D"top" style=3D"width:240.0p= t;padding:0cm 0cm 0cm 0cm"><p class=3D"MsoNormal"><span style=3D"font-size:8= .0pt;font-family:"Arial","sans-serif";color:black"> = ; <o:p></o:p></span></p></td></tr><tr><td width=3D"400" colspan=3D"2" valign= =3D"top" style=3D"width:240.0pt;padding:0cm 0cm 0cm 0cm"><p class=3D"MsoNorm= al"><b><span style=3D"font-size:8.0pt;font-family:"Arial","sa= ns-serif";color:black">Bastian Epp <o:p></o:p></span></b></p></td></tr>= <tr><td width=3D"400" colspan=3D"2" valign=3D"top" style=3D"width:240.0pt;pa= dding:0cm 0cm 0cm 0cm"><p class=3D"MsoNormal"><span style=3D"font-size:8.0pt= ;font-family:"Arial","sans-serif";color:#9B9B9B">Assista= nt Professor <o:p></o:p></span></p></td></tr><tr><td width=3D"400" colspan=3D= "2" valign=3D"top" style=3D"width:240.0pt;padding:0cm 0cm 0cm 0cm;min-height= :0px"><p class=3D"MsoNormal"><span style=3D"font-size:8.0pt;font-family:&quo= t;Arial","sans-serif";color:black">ELEK VIP <o:p></o:p></span= ></p></td></tr><tr><td width=3D"400" colspan=3D"2" valign=3D"top" style=3D"w= idth:240.0pt;padding:0cm 0cm 0cm 0cm"><p class=3D"MsoNormal"><span style=3D"= font-size:8.0pt;font-family:"Arial","sans-serif";color:b= lack">DTU Electrical Engineering <o:p></o:p></span></p></td></tr><tr><td wid= th=3D"400" colspan=3D"2" valign=3D"top" style=3D"width:240.0pt;border:none;b= order-bottom:solid #AEAEAE 1.0pt;padding:0cm 0cm 0cm 0cm"><p class=3D"MsoNor= mal" style=3D"mso-line-height-alt:0pt"><span style=3D"font-size:8.0pt;font-f= amily:"Arial","sans-serif";color:black"> <o:p></o:= p></span></p></td></tr><tr><td width=3D"350" valign=3D"top" style=3D"width:2= 10.0pt;padding:6.0pt 0cm 0cm 0cm"><p style=3D"margin:0cm;margin-bottom:.0001= pt"><b><span style=3D"font-size:8.0pt;font-family:"Arial","sa= ns-serif";color:black">Technical University of Denmark<o:p></o:p></span= ></b></p></td><td width=3D"50" rowspan=3D"8" valign=3D"top" style=3D"width:3= 0.0pt;padding:6.0pt 0cm 0cm 0cm"><p class=3D"MsoNormal" align=3D"right" styl= e=3D"text-align:right"><span style=3D"font-size:8.0pt;font-family:"Aria= l","sans-serif";color:black"><DTU_email_logo_01.gif> <o= :p></o:p></span></p></td></tr><tr><td style=3D"padding:0cm 0cm 0cm 0cm"><p c= lass=3D"MsoNormal"><span style=3D"font-size:8.0pt;font-family:"Arial&qu= ot;,"sans-serif";color:black">Department of Electrical Engineering= <o:p></o:p></span></p></td></tr><tr><td style=3D"padding:0cm 0cm 0cm 0cm"><= p class=3D"MsoNormal"><span style=3D"font-size:8.0pt;font-family:"Arial= ","sans-serif";color:black">=C3=98rsteds Plads <o:p></o:p></s= pan></p></td></tr><tr><td style=3D"padding:0cm 0cm 0cm 0cm"><p class=3D"MsoN= ormal"><span style=3D"font-size:8.0pt;font-family:"Arial","sa= ns-serif";color:black">Building 352 <o:p></o:p></span></p></td></tr><tr= ><td style=3D"padding:0cm 0cm 0cm 0cm"><p class=3D"MsoNormal"><span style=3D= "font-size:8.0pt;font-family:"Arial","sans-serif";color:= black">2800 Kgs. Lyngby <o:p></o:p></span></p></td></tr><tr><td style=3D"pad= ding:0cm 0cm 0cm 0cm"><p class=3D"MsoNormal"><span style=3D"font-size:8.0pt;= font-family:"Arial","sans-serif";color:black">Direct +45= 45253953 <o:p></o:p></span></p></td></tr><tr><td style=3D"padding:0cm 0cm 0= cm 0cm"><p class=3D"MsoNormal"><span style=3D"font-size:8.0pt;font-family:&q= uot;Arial","sans-serif";color:black"><a href=3D"mailto:bepp@xxxxxxxx= lektro.dtu.dk" target=3D"_blank">bepp@xxxxxxxx</a> <o:p></o:p></span><= /p></td></tr><tr><td style=3D"padding:0cm 0cm 0cm 0cm"><p class=3D"MsoNormal= "><span style=3D"font-size:8.0pt;font-family:"Arial","sans-se= rif";color:black"><a href=3D"http://www.elektro.dtu.dk/" target=3D"_bla= nk">www.elektro.dtu.dk/</a> <o:p></o:p></span></p></td></tr></tbody></table>= <div><p class=3D"MsoNormal"><o:p> </o:p></p></div><div><p class=3D"MsoN= ormal"> <o:p></o:p></p></div></div></td></tr></tbody></table></div></di= v></div><p class=3D"MsoNormal"><br><br clear=3D"all"><br>-- <o:p></o:p></p><= div><p class=3D"MsoNormal">James D. (jj) Johnston<o:p></o:p></p></div><div><= p class=3D"MsoNormal">Independent Audio and Electroacoustics Consultant<o:p>= </o:p></p></div></div><p class=3D"MsoNormal"><o:p> </o:p></p></div></di= v></div></blockquote></body></html>= --Apple-Mail-F52FBB5F-7EFE-4C92-A9D7-884A01E7433E--