Subject: Re: [AUDITORY] seeking old Kaiser paper From: "Richard F. Lyon" <dicklyon@xxxxxxxx> Date: Wed, 14 Feb 2018 22:22:51 -0800 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>--f403043e6e78ecbff905653a4114 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable And back to the original question: the paper by Jim Kaiser from the 1963 First Allerton Conference. It's actually the second paper in the 1972 IEEE reprint collection entitled "Digital Signal Processing", edited by Rabiner and Rader. I had it in my library all along, but it was hard to figure out. That reprint volume is still great, worth owning. Lots available: https://www.abebooks.com/servlet/SearchResults?sts=3Dt&an=3Drabiner&tn=3Ddi= gital+signal+processing&kn=3D1972+ieee Dick On Tue, Feb 13, 2018 at 9:25 PM, Richard F. Lyon <dicklyon@xxxxxxxx> wrote: > 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, Ji= m. >> >> If anyone wants a copy, let me know. Or of the 1964 Golden & Kaiser BST= J >> 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 hav= e >> existed, if the discrete impulse response at h[0] had been defined in te= rms >> 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 = and >> the correction term in the 1966 paper make it clear that such a reasonab= le >> 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 (do= es >> anyone know these guys?). I haven't looked at earlier editions. They n= ot >> 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 = of >> 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 -0.2= 679, >> 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= the >>> years, though Kaiser had the key to the correction in his chapter "Digi= tal >>> Filters" in the 1966 "System Analysis by Digital Computer" book, in whi= ch >>> he says his stuff on IIR design closely follows that missing paper as w= ell >>> as a BSTJ paper that does not have the key piece. >>> >>> The key observation is that using the naive impulse invariance method >>> adds a constant (frequency independent) term to the frequency response = of >>> the digital filter proportional to the impulse response on the right si= de >>> of time zero: T/2 * h(0+). He didn't go as far as the "corrections" wh= ich >>> 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 h= e >>> got as far as including that unwanted term yet didn't comment on the ea= sy >>> way to remove it. Maybe in the missing paper... >>> >>> Dick >>> >>> >>> >> > --f403043e6e78ecbff905653a4114 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable <div dir=3D"ltr"><div><div><div>And back to the original question:=C2=A0 th= e paper by Jim Kaiser from the 1963 First Allerton Conference.<br></div>It&= #39;s actually the second paper in the 1972 IEEE reprint collection entitle= d "Digital Signal Processing",<br></div>edited by Rabiner and Rad= er.=C2=A0 I had it in my library all along, but it was hard to figure out.<= br><br></div><div>That reprint volume is still great, worth owning.=C2=A0 L= ots available:<br><a href=3D"https://www.abebooks.com/servlet/SearchResults= ?sts=3Dt&an=3Drabiner&tn=3Ddigital+signal+processing&kn=3D1972+= ieee">https://www.abebooks.com/servlet/SearchResults?sts=3Dt&an=3Drabin= er&tn=3Ddigital+signal+processing&kn=3D1972+ieee</a><br><br></div>D= ick<br><br></div><div class=3D"gmail_extra"><br><div class=3D"gmail_quote">= On Tue, Feb 13, 2018 at 9:25 PM, Richard F. Lyon <span dir=3D"ltr"><<a h= ref=3D"mailto:dicklyon@xxxxxxxx" target=3D"_blank">dicklyon@xxxxxxxx</a>><= /span> wrote:<br><blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8= ex;border-left:1px #ccc solid;padding-left:1ex"><div dir=3D"ltr"><span clas= s=3D""><div><div><div><div>More on gammatones in the Gabel & Roberts &q= uot;Signals and Linear Systems" book:<br><br></div>I got the 1980 seco= nd edition and 1973 first edition.=C2=A0 Like the 1987 third, they have a t= able of z transforms of sampled impulse responses of gammatone-like filters= (complex gammatones); the second and third go to order 4, but the first go= es all the way to order 5!=C2=A0 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.<br><br></div>In terms of the funny correcti= on to impulse invariance for impulses with a step at t =3D 0 that Leland Ja= ckson and Wolfgang Mecklenbra=C3=BCker separately published in 2000, yes, i= t's in all three editions of Gabel & Roberts, going back to 1973; a= nd not quite in any of Jim Kaiser's papers.<br><br>Speaking of Jim Kais= er, I sent him a copy of my book, which was delivered yesterday; his son sa= ys "He couldn't remember receiving the book yesterday.=C2=A0 Our h= ealthcare worker found the book this morning on his night stand.=C2=A0 He h= ad already started reading it but forgot that he had!=C2=A0 He appreciated = your inscription.=C2=A0 He was able to recall your interactions at Bell in = the early 70's.=C2=A0 Long term memory still seems relatively good.&quo= t;=C2=A0 Jim is 89, living in Chapel Hill NC.<br><br></div>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.=C2=A0 It= 9;s still in print at a low price in Asian markets.<br><br></div><div>I rep= eat my question: does anybody know these guys (Robert A. Gabel and/or Richa= rd A. Roberts)?<br></div><div><br></div>Dick<br><br></span><div><div class= =3D"h5"><div><br><div><br><br></div><div class=3D"gmail_extra"><br><div cla= ss=3D"gmail_quote">On Thu, Feb 1, 2018 at 7:19 PM, Richard F. Lyon <span di= r=3D"ltr"><<a href=3D"mailto:dicklyon@xxxxxxxx" target=3D"_blank">dicklyo= n@xxxxxxxx</a>></span> wrote:<br><blockquote class=3D"gmail_quote" style= =3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding= -left:1ex"><div dir=3D"ltr"><span><div><div><div><div>I got a copy that Jim= Beauchamp found in a library near him.=C2=A0 Thanks, Jim.<br><br></div>If = anyone wants a copy, let me know.=C2=A0 Or of the 1964 Golden & Kaiser = BSTJ paper.<br><br></div>The "correction" term in the 1966 versio= n is not there in 1963, nor in 1964.<br><br></div>The correction term would= not be needed, and the problem would never have existed, if the discrete i= mpulse 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 2000 pointe= d out.=C2=A0 The examples in the older papers and the correction term in th= e 1966 paper make it clear that such a reasonable choice was not made at th= at time.</div><div><br></div><div>This issue (but not its history) is cover= ed in great detail in the 1987 book Signals and Linear Systems, third editi= on, by Gabel and Roberts (does anyone know these guys?).=C2=A0 I haven'= 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 treat= ments, and provide a table up to order 4 repeated poles, which agrees preci= sely with Volker Hohmann's derivation of zeros in the numerator of the = impulse-invariance design of discrete-time complex gammatone filters: a num= erator [1, 4, 1] independent of pole frequencies and dampings, yielding zer= os at z =3D -3.7321 and z =3D -0.2679, which do just a little smoothing on = top of the repeated-poles filter.<br></div><div><br></div>Dick<br><br></spa= n><div class=3D"gmail_extra"><br><div class=3D"gmail_quote"><span>On Mon, J= an 29, 2018 at 8:15 PM, Richard F. Lyon <span dir=3D"ltr"><<a href=3D"ma= ilto:dicklyon@xxxxxxxx" target=3D"_blank">dicklyon@xxxxxxxx</a>></span> wr= ote:<br></span><div><div class=3D"m_-3288923307471289349gmail-m_-8688326529= 919252405h5"><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px = 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div class= =3D"m_-3288923307471289349gmail-m_-8688326529919252405m_8989889143801983931= gmail-HOEnZb"><div class=3D"m_-3288923307471289349gmail-m_-8688326529919252= 405m_8989889143801983931gmail-h5"><div dir=3D"ltr"><div><div><div>Does anyo= ne have the 1963 Proceedings of the First Allerton Conference on Circuit an= d System Theory?=C2=A0 Or just "Design methods for sampled-data filter= s" by J. F. Kaiser?=C2=A0 <br><br></div>I'm trying to resolve a di= sconnect in derivations of the impulse-invariance method, which was "c= orrected" in several places over the years, though Kaiser had the key = to the correction in his chapter "Digital Filters" in the 1966 &q= uot;System Analysis by Digital Computer" book, in which he says his st= uff on IIR design closely follows that missing paper as well as a BSTJ pape= r that does not have the key piece.=C2=A0 <br><br></div>The key observation= is that using the naive impulse invariance method adds a constant (frequen= cy independent) term to the frequency response of the digital filter propor= tional to the impulse response on the right side of time zero: T/2 * h(0+).= =C2=A0 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.=C2=A0 It's funny that at some point= he got as far as including that unwanted term yet didn't comment on th= e easy way to remove it.=C2=A0 Maybe in the missing paper...<br><br></div>D= ick<br><br><div><div><br></div></div></div> </div></div></blockquote></div></div></div><br></div></div> </blockquote></div><br></div></div></div></div></div> </blockquote></div><br></div> --f403043e6e78ecbff905653a4114--