Re: Human hearing beats the Fourier uncertainty principle: Research (Leon van Noorden )

Subject: Re: Human hearing beats the Fourier uncertainty principle: Research From: Leon van Noorden <leonvannoorden@xxxxxxxx> Date: Sun, 24 Feb 2013 15:05:45 +0100 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY> --Apple-Mail=_DBBA966D-C5CC-4DF3-B7B1-37EAD8EE828F Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset=windows-1252 I like the experiment but not the conclusion. This kind of uncertainty principles applies to situations in which the = delta t and delta f have to be determined simultaneously. In the case of these short stimuli, the observer is able to use his = short term auditory memory, also called echoic memory, to listen first = to the delta f and then again to the delta t, or the other way around. = As I have shown in my PhD dissertation long time ago temporal acuity = drops quite a lot between tones of different frequency in the case of = long or continuous sequences, which overload the echoic memory. Leon van Noorden "Temporal Coherence in the Perception of Tone Sequences (L.P.A.S. van = Noorden, 1975):=20 http://alexandria.tue.nl/extra1/PRF2A/7707058.pdf On 23 Feb 2013, at 19:35, Pierre Divenyi <pdivenyi@xxxxxxxx> = wrote: > Judy brings up the point that theories indicating the listeners = beating the uncertainty principle are likely to have used inappropriate = definitions of bandwidth and/or duration. Attempting to find a right WT = combination is,in fact, the topic of the 1971 Ronken article 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, = physical or biological, can increase or override. >=20 > Pardon the typos, it's Apple's fault. >=20 > On Feb 22, 2013, at 11:18, Judi Lapsley Miller = <judi@xxxxxxxx> wrote: >=20 >> A million years ago (it seems), I investigated the acoustical = uncertainty principle for my PhD thesis. I found that humans did a = pretty good job at optimally resolving narrow-band short-duration noise = stimuli, and did best for stimuli with a bandwidth-duration product of = 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 bandwidth-duration conditions. >> =20 >> Any study showing observers =93beating=94 the uncertainty principle = has subjects who are solving the task differently to what the = experimenter expected, or there are issues with defining bandwidth and = duration. IMHO. >> =20 >> http://psychophysics.org/judi_thesis.htm >> =20 >> Judi >> =20 >> From: AUDITORY - Research in Auditory Perception = [mailto:AUDITORY@xxxxxxxx On Behalf Of corey >> Sent: Friday, 22 February 2013 05:33 >> To: AUDITORY@xxxxxxxx >> Subject: Re: Human hearing beats the Fourier uncertainty principle: = Research >> =20 >> I do think this article is misleading. In my opinion the uncertainty = principle is not something to be "overcome". It simply relates the = bandwidth of a waveform to its duration (which is an unassailable fact). = In Fourier theory frequency is defined for periodic signals (which are = of infinite duration). Any finite duration signal can be viewed equally = as an infinite duration 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 possible to create stimuli that "beat" the = uncertainty principle, which seems to negate the conclusions 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, eh? >>=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 = should 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 bandpass 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 = spread >> (Delta) in both domains (DfDt>1), it is not a limit to what extent = they can >> be discriminated. One can also build a device that measures the = frequency of >> 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 can >> 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 = human >> 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 >> =D8rsteds 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=_DBBA966D-C5CC-4DF3-B7B1-37EAD8EE828F Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset=windows-1252 <html><head><meta http-equiv=3D"Content-Type" content=3D"text/html = charset=3Dwindows-1252"><meta http-equiv=3D"Content-Type" = content=3D"text/html charset=3Dwindows-1252"></head><body = style=3D"word-wrap: break-word; -webkit-nbsp-mode: space; = -webkit-line-break: after-white-space; "><div>I like the experiment but = not the conclusion.</div><div><br></div><div>This kind of uncertainty = principles applies to situations in which the delta t and delta f have = to be determined simultaneously.</div><div>In the case of these short = stimuli, the observer is able to use his short term auditory memory, = also called echoic memory, to listen first to the delta f and then again = to the delta t, or the other way around. As I have shown in my PhD = dissertation long time ago temporal acuity drops quite a lot =  between tones of different frequency in the case of long or = continuous sequences, which overload the echoic = memory.</div><div><br></div><div>Leon van = Noorden</div><div><br></div><div>"Temporal Coherence in the Perception = of Tone Sequences (L.P.A.S. van Noorden, 1975): </div><div><a = href=3D"http://alexandria.tue.nl/extra1/PRF2A/7707058.pdf">http://alexandr= ia.tue.nl/extra1/PRF2A/7707058.pdf</a></div><div><br></div><br><div><div>O= n 23 Feb 2013, at 19:35, Pierre Divenyi <<a = href=3D"mailto:pdivenyi@xxxxxxxx">pdivenyi@xxxxxxxx</a= >> wrote:</div><br class=3D"Apple-interchange-newline"><blockquote = type=3D"cite"><meta http-equiv=3D"content-type" content=3D"text/html; = charset=3Dutf-8"><div dir=3D"auto"><div>Judy brings up the point that = theories indicating the listeners beating the uncertainty principle are = likely to have used inappropriate definitions of bandwidth and/or = duration. Attempting to find a right WT combination is,in fact, the = topic of the 1971 Ronken article 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, physical 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"><meta = http-equiv=3D"Content-Type" content=3D"text/html; = charset=3Diso-8859-1"><meta name=3D"Generator" content=3D"Microsoft Word = 14 (filtered medium)"><style></style><div class=3D"WordSection1"><p = class=3D"MsoNormal"><span = style=3D"font-size:11.0pt;font-family:"Calibri","sans-serif= ";color:#1F497D">A million years ago (it seems), I investigated the = acoustical uncertainty principle for my PhD thesis. I found that humans = did a pretty good job at optimally resolving narrow-band short-duration = noise stimuli, and did best for stimuli with a bandwidth-duration = product of 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 bandwidth-duration conditions. = <o:p></o:p></span></p><p class=3D"MsoNormal"><span = style=3D"font-size:11.0pt;font-family:"Calibri","sans-serif= ";color:#1F497D"> </span></p><p class=3D"MsoNormal"><span = style=3D"font-size:11.0pt;font-family:"Calibri","sans-serif= ";color:#1F497D">Any study showing observers =93beating=94 the = uncertainty principle has subjects who are solving the task differently = to what the experimenter expected, or there are issues with defining = bandwidth and duration. IMHO.<o:p></o:p></span></p><p = class=3D"MsoNormal"><span = style=3D"font-size:11.0pt;font-family:"Calibri","sans-serif= ";color:#1F497D"> </span></p><p class=3D"MsoNormal"><span = style=3D"font-size:11.0pt;font-family:"Calibri","sans-serif= ";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"MsoNormal"><span = style=3D"font-size:11.0pt;font-family:"Calibri","sans-serif= ";color:#1F497D"> </span></p><p class=3D"MsoNormal"><span = style=3D"font-size:11.0pt;font-family:"Calibri","sans-serif= ";color:#1F497D">Judi<o:p></o:p></span></p><p class=3D"MsoNormal"><a = name=3D"_MailEndCompose"><span = style=3D"font-size:11.0pt;font-family:"Calibri","sans-serif= ";color:#1F497D"> </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-US" = style=3D"font-size:10.0pt;font-family:"Tahoma","sans-serif&= quot;">From:</span></b><span lang=3D"EN-US" = style=3D"font-size:10.0pt;font-family:"Tahoma","sans-serif&= quot;"> AUDITORY - Research in Auditory Perception [<a = href=3D"mailto:AUDITORY@xxxxxxxx">mailto:AUDITORY@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">AUDITORY@xxxxxxxx</a><br><= b>Subject:</b> Re: Human hearing beats the 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 = think this article is misleading.  In my opinion the uncertainty = principle is not something to be "overcome".  It simply relates the = bandwidth of a waveform to its duration (which is an unassailable fact). =  In Fourier theory frequency is defined for periodic signals (which = are of infinite duration).  Any finite duration signal can be = viewed equally as an infinite duration 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 possible 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><div><p = class=3D"MsoNormal"><o:p> </o:p></p><div><div><p = class=3D"MsoNormal">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-phase filter, while the ear is very close to such. Well, there = goes a large speed factor already, eh? <o:p></o:p></p><div><p = class=3D"MsoNormal">On Wed, Feb 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 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 bandpass filters (see the Oppenheim = Schaefer DSP book)....so this point raised is not valid. <br><br>I would = be surprised if this result would not have been reported before in the = solid psychoacoustics literature = before.<br><br>Bests<br><br>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, the<o:p></o:p></pre><pre>Gabor limit = does not apply to the task, and never did. The only = limit<o:p></o:p></pre><pre>here is SNR_based, since there is already = 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 = been<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, but the headline is = inexcusably misleading, and is<o:p></o:p></pre><pre>already 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 PM, Peter Meijer<o:p></o:p></pre><pre><a = href=3D"mailto:feedback@xxxxxxxx" = 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 had 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></pre><pre><o:p> </o:p></pre><pre>and that formed the = basis of my old web page 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"http://www.seeingwithsound.com/freqtime.htm" = target=3D"_blank">http://www.seeingwithsound.com/freqtime.htm</a><o:p></o:= p></pre><pre><o:p> </o:p></pre><pre>Best = regards,<o:p></o:p></pre><pre><o:p> </o:p></pre><pre>Peter = Meijer<o:p></o:p></pre><pre><o:p> </o:p></pre><pre><o:p> </o:p><= /pre><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:5.0pt;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" = 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</a><o:p></o:p></pre><pre>Subjec= t: Re: Human hearing beats the Fourier uncertainty = principle:<o:p></o:p></pre><pre>Research<o:p></o:p></pre><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 that go below = the uncertainty limit in both the time<o:p></o:p></pre><pre>and = frequency 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 what extent they can<o:p></o:p></pre><pre>be = discriminated. One can also build a device that measures the frequency = of<o:p></o:p></pre><pre>a sine wave with an accuracy below the = uncertainty limit by exploiting<o:p></o:p></pre><pre>a-priori knowledge, = i.e. if I know  that the signal I am measuring is = 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 accurate as I = want.<o:p></o:p></pre><pre><o:p> </o:p></pre><pre>John = Beerends<o:p></o:p></pre><pre>      = <o:p></o:p></pre></blockquote><pre>    <o:p></o:p></pr= e><blockquote = style=3D"margin-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></pre><pre>[<a = href=3D"mailto:AUDITORY@xxxxxxxx" = target=3D"_blank">mailto:AUDITORY@xxxxxxxx</a>] On Behalf Of = Kevin Austin<o:p></o:p></pre><pre>Sent: Saturday, February 16, 2013 5:07 = PM<o:p></o:p></pre><pre>To: <a href=3D"mailto:AUDITORY@xxxxxxxx" = target=3D"_blank">AUDITORY@xxxxxxxx</a><o:p></o:p></pre><pre>Subjec= t: Human hearing beats the Fourier uncertainty 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>&nb= sp;     <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.h= tml" = target=3D"_blank">http://phys.org/news/2013-02-human-fourier-uncertainty-p= rinciple.html</a><o:p></o:p></pre><pre><o:p> </o:p></pre><pre><o:p>&n= bsp;</o:p></pre><pre>(<a href=3D"http://phys.org/">Phys.org</a>)-For the = first time, physicists have found that humans = can<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 after another note) more than 10 = times<o:p></o:p></pre><pre>better than the limit imposed by the Fourier = uncertainty principle. Not<o:p></o:p></pre><pre>surprisingly, some of = the subjects with the best listening precision = were<o:p></o:p></pre><pre>musicians, but even non-musicians could exceed = the uncertainty 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, since only a few models = can match this impressive = human<o:p></o:p></pre><pre>performance.<o:p></o:p></pre><pre>  &= nbsp;       = <o:p></o:p></pre></blockquote></blockquote></blockquote><pre>  &= nbsp; <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 more = at:<o:p></o:p></pre><pre><a = href=3D"http://phys.org/news/2013-02-human-fourier-uncertainty-principle.h= tml#jCp" = target=3D"_blank">http://phys.org/news/2013-02-human-fourier-uncertainty-p= rinciple.html#jCp</a><o:p></o:p></pre><pre>     &= nbsp;    = <o:p></o:p></pre></blockquote></blockquote><pre>Thanks<o:p></o:p></pre><pr= e><o:p> </o:p></pre><pre>Kevin<o:p></o:p></pre><pre>This e-mail and = its contents are subject to the DISCLAIMER at<o:p></o:p></pre><pre><a = href=3D"http://www.tno.nl/emaildisclaimer" = target=3D"_blank">http://www.tno.nl/emaildisclaimer</a><o:p></o:p></pre><p= re>      = <o:p></o:p></pre></blockquote></blockquote><pre>  <o:p></o:p></p= re><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"><table class=3D"MsoNormalTable" = border=3D"0" cellspacing=3D"0" cellpadding=3D"0" width=3D"400" = style=3D"width:240.0pt;border-collapse:collapse"><tbody><tr><td = width=3D"400" colspan=3D"2" valign=3D"top" = style=3D"width:240.0pt;padding:0cm 0cm 0cm 0cm"><p = class=3D"MsoNormal"><span style=3D"font-size: 8pt; font-family: Arial, = sans-serif; ">  <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"MsoNormal"><b><span style=3D"font-size: 8pt; = font-family: Arial, sans-serif; ">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;padding:0cm 0cm 0cm 0cm"><p = class=3D"MsoNormal"><span = style=3D"font-size:8.0pt;font-family:"Arial","sans-serif&qu= ot;;color:#9B9B9B">Assistant 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: = 8pt; font-family: Arial, sans-serif; ">ELEK VIP = <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"MsoNormal"><span style=3D"font-size: 8pt; font-family: Arial, = sans-serif; ">DTU Electrical Engineering = <o:p></o:p></span></p></td></tr><tr><td width=3D"400" colspan=3D"2" = valign=3D"top" style=3D"width:240.0pt;border:none;border-bottom:solid = #AEAEAE 1.0pt;padding:0cm 0cm 0cm 0cm"><p class=3D"MsoNormal" = style=3D"mso-line-height-alt:0pt"><span style=3D"font-size: 8pt; = font-family: Arial, sans-serif; ">  = <o:p></o:p></span></p></td></tr><tr><td width=3D"350" valign=3D"top" = style=3D"width:210.0pt;padding:6.0pt 0cm 0cm 0cm"><div style=3D"margin: = 0cm 0cm 0.0001pt; "><b><span style=3D"font-size: 8pt; font-family: = Arial, sans-serif; ">Technical University of = Denmark<o:p></o:p></span></b></div></td><td width=3D"50" rowspan=3D"8" = valign=3D"top" style=3D"width:30.0pt;padding:6.0pt 0cm 0cm 0cm"><p = class=3D"MsoNormal" align=3D"right" style=3D"text-align:right"><span = style=3D"font-size: 8pt; font-family: Arial, sans-serif; = "><DTU_email_logo_01.gif> <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: 8pt; font-family: Arial, sans-serif; ">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: 8pt; font-family: Arial, sans-serif; ">=D8rsteds = Plads <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: 8pt; = font-family: Arial, sans-serif; ">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: 8pt; font-family: = Arial, sans-serif; ">2800 Kgs. Lyngby = <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: 8pt; font-family: = Arial, sans-serif; ">Direct +45 45253953 = <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: 8pt; font-family: = Arial, sans-serif; "><a href=3D"mailto:bepp@xxxxxxxx" = 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: 8pt; font-family: = Arial, sans-serif; "><a href=3D"http://www.elektro.dtu.dk/" = target=3D"_blank">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"MsoNormal"> <o:p></o:p></p></div></td></tr></tbody></table><= /div></div></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></div></blockquote></div></= blockquote></div><br></body></html>= --Apple-Mail=_DBBA966D-C5CC-4DF3-B7B1-37EAD8EE828F--

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