Re: [AUDITORY] seeking old Kaiser paper ("Richard F. Lyon" )


Subject: Re: [AUDITORY] seeking old Kaiser paper
From:    "Richard F. Lyon"  <dicklyon@xxxxxxxx>
Date:    Mon, 19 Feb 2018 21:55:33 -0800
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

--f403045c216881cb3a05659e7522 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable Rob, I'm glad we found people who knew Gabel & Roberts. I also picked up a copy of Roberts & Mullis 1987, and noticed that it is missing the correction to impulse invariance that Gabel & Roberts had since 1973. So this correction that Jackson re-discovered in 2000 appears in almost no DSP book. I did find it in one in 2011: https://books.google.com/books?id=3DQtd-e1NtZVkC&pg=3D PA342&dq=3D%22Corrected+Impulse+Invariant+Method%22+jackson&hl=3Den&sa=3DX&= ved=3D 0ahUKEwjo7P7a37DZAhVB9mMKHVD5Bc8Q6AEIKTAA#v=3Donepage&q=3D% 22Corrected%20Impulse%20Invariant%20Method%22%20jackson&f=3Dfalse Getting back to Jim Kaiser, Leland Jackson says "It was Jim who tipped me off that Wolfgang had also written a paper on that, so that we were able to acknowledge each other=E2=80=99s independent work." I'm sure some of you know Jim Kaiser. He has been such a friend to the DSP field, and made lots of contributions to speech and hearing as well. For example, in my book I reference a binaural separation system he made in 1960! He and Leland Jackson and Hank McDonald proposed the hardware DSP architecture that was my intro to DSP systems in my 1973 summer job at Bell Labs, and was the basis for my early work in bit-serial VLSI DSP chips. So it's great to be able to reconnect with Jim and Leland about some of these things. It is an odd side-effect of this little investigation that led me to find that Gabel & Roberts had a table of discrete-time complex gammatone filters up to order 5 in 1973, long before that filter was named or known in the hearing field. Dick On Mon, Feb 19, 2018 at 9:13 AM, Maher, Rob <rmaher@xxxxxxxx> wrote: > Robert Gabel and Richard Roberts were at the University of Colorado. Dick > Roberts was at the Boulder campus, Robert Gabel originally in Denver. > Gabel went on to MIT Lincoln Labs at some point. I believe Dr. Gabel sti= ll > lives in Massachusetts. > > > > I also have a DSP book authored by Dick Roberts and C.T. (Tom) Mullis (ca= . > 1987). Prof. Mullis (Univ. of Colorado-Boulder) is now retired, but I kn= ew > him during the period that I taught part time at Colorado around 2000. M= y > recollection is that Dick Roberts had passed away by then. > > I have a copy of Gabel and Roberts, 2nd edition (1980). It has a > University of Illinois price sticker ($39.95), and I probably bought it i= n > about 1985. > > FWIW, > > Rob Maher > > > > *From:* AUDITORY - Research in Auditory Perception [mailto: > AUDITORY@xxxxxxxx *On Behalf Of *Richard F. Lyon > *Sent:* Tuesday, February 13, 2018 10:25 PM > *To:* AUDITORY@xxxxxxxx > *Subject:* Re: seeking old Kaiser paper > > > > More on gammatones in the Gabel & Roberts "Signals and Linear Systems" > book: > > I got the 1980 second edition and 1973 first edition. Like the 1987 > third, they have a table of z transforms of sampled impulse responses of > gammatone-like filters (complex gammatones); the second and third go to > order 4, but the first goes all the way to order 5! The fifth order has > numerator [1, 11, 11, 1], which I haven't checked, but seems plausible; > that makes zeros at z =3D -9.8990, -1.0000, -0.1010. > > In terms of the funny correction to impulse invariance for impulses with = a > step at t =3D 0 that Leland Jackson and Wolfgang Mecklenbra=C3=BCker sepa= rately > published in 2000, yes, it's in all three editions of Gabel & Roberts, > going back to 1973; and not quite in any of Jim Kaiser's papers. > > Speaking of Jim Kaiser, I sent him a copy of my book, which was delivered > yesterday; his son says "He couldn't remember receiving the book > yesterday. Our healthcare worker found the book this morning on his nigh= t > stand. He had already started reading it but forgot that he had! He > appreciated your inscription. He was able to recall your interactions at > Bell in the early 70's. Long term memory still seems relatively good." > Jim is 89, living in Chapel Hill NC. > > One other reader of this list tells me he's a big fan of Gabel & Roberts, > recently read it cover to cover, and is planning to use it for a course. > It's still in print at a low price in Asian markets. > > I repeat my question: does anybody know these guys (Robert A. Gabel and/o= r > Richard A. Roberts)? > > > > Dick > > > > > > > > On Thu, Feb 1, 2018 at 7:19 PM, Richard F. Lyon <dicklyon@xxxxxxxx> wrote: > > I got a copy that Jim Beauchamp found in a library near him. Thanks, Jim= . > > If anyone wants a copy, let me know. Or of the 1964 Golden & Kaiser BSTJ > paper. > > The "correction" term in the 1966 version is not there in 1963, nor in > 1964. > > The correction term would not be needed, and the problem would never have > existed, if the discrete impulse response at h[0] had been defined in ter= ms > of the continuous impulse response h(t) as (h(0-) + h(0+)/2; that is, as > the average across the step discontinuity at 0 if there is one, as two > different papers in 2000 pointed out. The examples in the older papers a= nd > the correction term in the 1966 paper make it clear that such a reasonabl= e > choice was not made at that time. > > > > This issue (but not its history) is covered in great detail in the 1987 > book Signals and Linear Systems, third edition, by Gabel and Roberts (doe= s > anyone know these guys?). I haven't looked at earlier editions. They no= t > only discuss the discontinuity in depth, but also address repeated poles, > which are ignored in most treatments, and provide a table up to order 4 > repeated poles, which agrees precisely with Volker Hohmann's derivation o= f > zeros in the numerator of the impulse-invariance design of discrete-time > complex gammatone filters: a numerator [1, 4, 1] independent of pole > frequencies and dampings, yielding zeros at z =3D -3.7321 and z =3D -0.26= 79, > which do just a little smoothing on top of the repeated-poles filter. > > > > Dick > > > > On Mon, Jan 29, 2018 at 8:15 PM, Richard F. Lyon <dicklyon@xxxxxxxx> wrote= : > > Does anyone have the 1963 Proceedings of the First Allerton Conference on > Circuit and System Theory? Or just "Design methods for sampled-data > filters" by J. F. Kaiser? > > I'm trying to resolve a disconnect in derivations of the > impulse-invariance method, which was "corrected" in several places over t= he > years, though Kaiser had the key to the correction in his chapter "Digita= l > Filters" in the 1966 "System Analysis by Digital Computer" book, in which > he says his stuff on IIR design closely follows that missing paper as wel= l > as a BSTJ paper that does not have the key piece. > > The key observation is that using the naive impulse invariance method add= s > a constant (frequency independent) term to the frequency response of the > digital filter proportional to the impulse response on the right side of > time zero: T/2 * h(0+). He didn't go as far as the "corrections" which > said to take the impulse response h[k] at k =3D 0 to be (h(0-) + h(0+))/2= , > though it's pretty obvious from there. It's funny that at some point he > got as far as including that unwanted term yet didn't comment on the easy > way to remove it. Maybe in the missing paper... > > Dick > > > > > > > --f403045c216881cb3a05659e7522 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable <div dir=3D"ltr"><div><div><div><div><div>Rob, I&#39;m glad we found people= who knew Gabel &amp; Roberts.<br><br></div>I also picked up a copy of Robe= rts &amp; Mullis 1987, and noticed that it is missing the correction to imp= ulse invariance that Gabel &amp; Roberts had since 1973.=C2=A0 So this corr= ection that Jackson re-discovered in 2000 appears in almost no DSP book.=C2= =A0 I did find it in one in 2011:<br><a href=3D"https://books.google.com/bo= oks?id=3DQtd-e1NtZVkC&amp;pg=3DPA342&amp;dq=3D%22Corrected+Impulse+Invarian= t+Method%22+jackson&amp;hl=3Den&amp;sa=3DX&amp;ved=3D0ahUKEwjo7P7a37DZAhVB9= mMKHVD5Bc8Q6AEIKTAA#v=3Donepage&amp;q=3D%22Corrected%20Impulse%20Invariant%= 20Method%22%20jackson&amp;f=3Dfalse" target=3D"_blank">https://books.google= .com/<wbr>books?id=3DQtd-e1NtZVkC&amp;pg=3D<wbr>PA342&amp;dq=3D%22Corrected= +Impulse+<wbr>Invariant+Method%22+jackson&amp;<wbr>hl=3Den&amp;sa=3DX&amp;v= ed=3D<wbr>0ahUKEwjo7P7a37DZAhVB9mMKHVD5B<wbr>c8Q6AEIKTAA#v=3Donepage&amp;q= =3D%<wbr>22Corrected%20Impulse%<wbr>20Invariant%20Method%22%<wbr>20jackson&= amp;f=3Dfalse</a><br><br></div>Getting back to Jim Kaiser, Leland Jackson s= ays &quot;It was Jim who tipped me off that Wolfgang had also written a pap= er on that, so that we were able to acknowledge each other=E2=80=99s indepe= ndent work.&quot;<br><br></div>I&#39;m sure some of you know Jim Kaiser.=C2= =A0 He has been such a friend to the DSP field, and made lots of contributi= ons to speech and hearing as well.=C2=A0 For example, in my book I referenc= e a binaural separation system he made in 1960!<br><br></div>He and Leland = Jackson and Hank McDonald proposed the hardware DSP architecture that was m= y intro to DSP systems in my 1973 summer job at Bell Labs, and was the basi= s for my early work in bit-serial VLSI DSP chips.=C2=A0 So it&#39;s great t= o be able to reconnect with Jim and Leland about some of these things.<br><= br></div><div>It is an odd side-effect of this little investigation that le= d me to find that Gabel &amp; Roberts had a table of discrete-time complex = gammatone filters up to order 5 in 1973, long before that filter was named = or known in the hearing field.<br><br></div>Dick<br><br><div><div><div><div= ><br><br></div></div></div></div></div><div class=3D"gmail_extra"><br><div = class=3D"gmail_quote">On Mon, Feb 19, 2018 at 9:13 AM, Maher, Rob <span dir= =3D"ltr">&lt;<a href=3D"mailto:rmaher@xxxxxxxx" target=3D"_blank">rmaher= @xxxxxxxx</a>&gt;</span> wrote:<br><blockquote class=3D"gmail_quote" sty= le=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"> <div link=3D"blue" vlink=3D"purple" lang=3D"EN-US"> <div class=3D"m_-1354308993029322785WordSection1"><span class=3D""> <p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca= libri&quot;,sans-serif;color:#1f497d">Robert Gabel and Richard Roberts were= at the University of Colorado. Dick Roberts was at the Boulder campus, Rob= ert Gabel originally in Denver.=C2=A0 Gabel went on to MIT Lincoln Labs at some point.=C2=A0 I believe Dr. Gabel still lives i= n Massachusetts.<u></u><u></u></span></p> <p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca= libri&quot;,sans-serif;color:#1f497d"><u></u>=C2=A0<u></u></span></p> <p class=3D"MsoNormal" style=3D"margin-bottom:12.0pt"><span style=3D"font-s= ize:11.0pt;font-family:&quot;Calibri&quot;,sans-serif;color:#1f497d">I also= have a DSP book authored by Dick Roberts and C.T. (Tom) Mullis (ca. 1987).= =C2=A0 Prof. Mullis (Univ. of Colorado-Boulder) is now retired, but I knew him during the period that I taught part time at Color= ado around 2000.=C2=A0 My recollection is that Dick Roberts had passed away= by then.<u></u><u></u></span></p> <p class=3D"MsoNormal" style=3D"margin-bottom:12.0pt"><span style=3D"font-s= ize:11.0pt;font-family:&quot;Calibri&quot;,sans-serif;color:#1f497d">I have= a copy of Gabel and Roberts, 2<sup>nd</sup> edition (1980). It has a Unive= rsity of Illinois price sticker ($39.95), and I probably bought it in about 1985.=C2=A0 <u></u><u></u></span></p> <p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca= libri&quot;,sans-serif;color:#1f497d">FWIW,<u></u><u></u></span></p> <p class=3D"MsoNormal" style=3D"margin-bottom:12.0pt"><span style=3D"font-s= ize:11.0pt;font-family:&quot;Calibri&quot;,sans-serif;color:#1f497d">Rob Ma= her<u></u><u></u></span></p> <p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca= libri&quot;,sans-serif;color:#1f497d"><u></u>=C2=A0<u></u></span></p> <p class=3D"MsoNormal"><b><span style=3D"font-size:11.0pt;font-family:&quot= ;Calibri&quot;,sans-serif">From:</span></b><span style=3D"font-size:11.0pt;= font-family:&quot;Calibri&quot;,sans-serif"> AUDITORY - Research in Auditor= y Perception [mailto:<a href=3D"mailto:AUDITORY@xxxxxxxx" target=3D"= _blank">AUDITORY@xxxxxxxx<wbr>CA</a>] <b>On Behalf Of </b>Richard F. Lyon<br> <b>Sent:</b> Tuesday, February 13, 2018 10:25 PM<br> <b>To:</b> <a href=3D"mailto:AUDITORY@xxxxxxxx" target=3D"_blank">AU= DITORY@xxxxxxxx</a><br> <b>Subject:</b> Re: seeking old Kaiser paper<u></u><u></u></span></p> <p class=3D"MsoNormal"><u></u>=C2=A0<u></u></p> </span><div> <div> <div> <div> <div> <p class=3D"MsoNormal" style=3D"margin-bottom:12.0pt">More on gammatones in= the Gabel &amp; Roberts &quot;Signals and Linear Systems&quot; book:<u></u= ><u></u></p> </div><span class=3D""> <p class=3D"MsoNormal" style=3D"margin-bottom:12.0pt">I got the 1980 second= edition and 1973 first edition.=C2=A0 Like the 1987 third, they have a tab= le of z transforms of sampled impulse responses of gammatone-like filters (= complex gammatones); the second and third go to order 4, but the first goes all the way to order 5!=C2=A0 The fifth = order has numerator [1, 11, 11, 1], which I haven&#39;t checked, but seems = plausible; that makes zeros at z =3D -9.8990, -1.0000, -0.1010.<u></u><u></= u></p> </span></div><span class=3D""> <p class=3D"MsoNormal" style=3D"margin-bottom:12.0pt">In terms of the funny= correction to impulse invariance for impulses with a step at t =3D 0 that = Leland Jackson and Wolfgang Mecklenbra=C3=BCker separately published in 200= 0, yes, it&#39;s in all three editions of Gabel &amp; Roberts, going back to 1973; and not quite in any of Jim Kaiser&#39;= s papers.<br> <br> Speaking of Jim Kaiser, I sent him a copy of my book, which was delivered y= esterday; his son says &quot;He couldn&#39;t remember receiving the book ye= sterday.=C2=A0 Our healthcare worker found the book this morning on his nig= ht stand.=C2=A0 He had already started reading it but forgot that he had!=C2=A0 He appreciated your inscription.=C2=A0 He was ab= le to recall your interactions at Bell in the early 70&#39;s.=C2=A0 Long te= rm memory still seems relatively good.&quot;=C2=A0 Jim is 89, living in Cha= pel Hill NC.<u></u><u></u></p> </span></div><span class=3D""> <p class=3D"MsoNormal" style=3D"margin-bottom:12.0pt">One other reader of t= his list tells me he&#39;s a big fan of Gabel &amp; Roberts, recently read = it cover to cover, and is planning to use it for a course.=C2=A0 It&#39;s s= till in print at a low price in Asian markets.<u></u><u></u></p> </span></div><span class=3D""> <div> <p class=3D"MsoNormal">I repeat my question: does anybody know these guys (= Robert A. Gabel and/or Richard A. Roberts)?<u></u><u></u></p> </div> <div> <p class=3D"MsoNormal"><u></u>=C2=A0<u></u></p> </div> <p class=3D"MsoNormal" style=3D"margin-bottom:12.0pt">Dick<u></u><u></u></p= > </span><div><div class=3D"h5"><div> <p class=3D"MsoNormal"><u></u>=C2=A0<u></u></p> <div> <p class=3D"MsoNormal" style=3D"margin-bottom:12.0pt"><u></u>=C2=A0<u></u><= /p> </div> <div> <p class=3D"MsoNormal"><u></u>=C2=A0<u></u></p> <div> <p class=3D"MsoNormal">On Thu, Feb 1, 2018 at 7:19 PM, Richard F. Lyon &lt;= <a href=3D"mailto:dicklyon@xxxxxxxx" target=3D"_blank">dicklyon@xxxxxxxx</a>&= gt; wrote:<u></u><u></u></p> <blockquote style=3D"border:none;border-left:solid #cccccc 1.0pt;padding:0i= n 0in 0in 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0in;margin-= bottom:5.0pt"> <div> <div> <div> <div> <div> <p class=3D"MsoNormal" style=3D"margin-bottom:12.0pt">I got a copy that Jim= Beauchamp found in a library near him.=C2=A0 Thanks, Jim.<u></u><u></u></p= > </div> <p class=3D"MsoNormal" style=3D"margin-bottom:12.0pt">If anyone wants a cop= y, let me know.=C2=A0 Or of the 1964 Golden &amp; Kaiser BSTJ paper.<u></u>= <u></u></p> </div> <p class=3D"MsoNormal" style=3D"margin-bottom:12.0pt">The &quot;correction&= quot; term in the 1966 version is not there in 1963, nor in 1964.<u></u><u>= </u></p> </div> <p class=3D"MsoNormal">The correction term would not be needed, and the pro= blem would never have existed, if the discrete impulse response at h[0] had= been defined in terms of the continuous impulse response h(t) as (h(0-) + = h(0+)/2; that is, as the average across the step discontinuity at 0 if there is one, as two different papers in 20= 00 pointed out.=C2=A0 The examples in the older papers and the correction t= erm in the 1966 paper make it clear that such a reasonable choice was not m= ade at that time.<u></u><u></u></p> </div> <div> <p class=3D"MsoNormal"><u></u>=C2=A0<u></u></p> </div> <div> <p class=3D"MsoNormal">This issue (but not its history) is covered in great= detail in the 1987 book Signals and Linear Systems, third edition, by Gabe= l and Roberts (does anyone know these guys?).=C2=A0 I haven&#39;t looked at= earlier editions.=C2=A0 They not only discuss the discontinuity in depth, but also address repeated poles, which are ignored= in most treatments, and provide a table up to order 4 repeated poles, whic= h agrees precisely with Volker Hohmann&#39;s derivation of zeros in the num= erator of the impulse-invariance design of discrete-time complex gammatone filters: a numerator [1, 4, 1] independ= ent of pole frequencies and dampings, yielding zeros at z =3D -3.7321 and z= =3D -0.2679, which do just a little smoothing on top of the repeated-poles= filter.<u></u><u></u></p> </div> <div> <p class=3D"MsoNormal"><u></u>=C2=A0<u></u></p> </div> <p class=3D"MsoNormal" style=3D"margin-bottom:12.0pt">Dick<u></u><u></u></p= > <div> <p class=3D"MsoNormal"><u></u>=C2=A0<u></u></p> <div> <p class=3D"MsoNormal">On Mon, Jan 29, 2018 at 8:15 PM, Richard F. Lyon &lt= ;<a href=3D"mailto:dicklyon@xxxxxxxx" target=3D"_blank">dicklyon@xxxxxxxx</a>= &gt; wrote:<u></u><u></u></p> <div> <div> <blockquote style=3D"border:none;border-left:solid #cccccc 1.0pt;padding:0i= n 0in 0in 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0in;margin-= bottom:5.0pt"> <div> <div> <div> <div> <div> <div> <p class=3D"MsoNormal" style=3D"margin-bottom:12.0pt">Does anyone have the = 1963 Proceedings of the First Allerton Conference on Circuit and System The= ory?=C2=A0 Or just &quot;Design methods for sampled-data filters&quot; by J= . F. Kaiser?=C2=A0 <u></u><u></u></p> </div> <p class=3D"MsoNormal" style=3D"margin-bottom:12.0pt">I&#39;m trying to res= olve a disconnect in derivations of the impulse-invariance method, which wa= s &quot;corrected&quot; in several places over the years, though Kaiser had= the key to the correction in his chapter &quot;Digital Filters&quot; in the 1966 &quot;System Analysis by Digital Computer&quot; = book, in which he says his stuff on IIR design closely follows that missing= paper as well as a BSTJ paper that does not have the key piece.=C2=A0 <u></u><u></u></p> </div> <p class=3D"MsoNormal" style=3D"margin-bottom:12.0pt">The key observation i= s that using the naive impulse invariance method adds a constant (frequency= independent) term to the frequency response of the digital filter proporti= onal to the impulse response on the right side of time zero: T/2 * h(0+).=C2=A0 He didn&#39;t go as far as the= &quot;corrections&quot; which said to take the impulse response h[k] at k = =3D 0 to be (h(0-) + h(0+))/2, though it&#39;s pretty obvious from there.= =C2=A0 It&#39;s funny that at some point he got as far as including that unwanted term yet didn&#39;t comment on the easy way to remove it.=C2= =A0 Maybe in the missing paper...<u></u><u></u></p> </div> <p class=3D"MsoNormal" style=3D"margin-bottom:12.0pt">Dick<u></u><u></u></p= > <div> <div> <p class=3D"MsoNormal"><u></u>=C2=A0<u></u></p> </div> </div> </div> </div> </div> </blockquote> </div> </div> </div> <p class=3D"MsoNormal"><u></u>=C2=A0<u></u></p> </div> </div> </blockquote> </div> <p class=3D"MsoNormal"><u></u>=C2=A0<u></u></p> </div> </div> </div></div></div> </div> </div> </blockquote></div><br></div> --f403045c216881cb3a05659e7522--


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