On Nov 27, 4:13�pm, robert bristow-johnson <r...@audioimagination.com> wrote:> On 11/27/12 3:45 PM, dszabo wrote: > > > > > > > > > > > Okay, here goes. > > > First, the approximation of the transfer function would be > > > � � �H(j(-w0)) = |H(jw0)| e^j(-phi(w0) + phi'(w0)(w+w0)) > > > This is from the assumptions I made in my previous post. > > > Y(jw) has two non-zero regions, near +w0 and -w0. > > > Near +w0: > > � � �A(j(w+w0)) = 0 > > > Near -w0: > > � � �A(j(w-w0)) = 0 > > > So: > > > �Y(jw) = |H(jw0)|*(1/2)*( (e^j(phi(w0) + phi'(w0)(w-w0))) * A(j(w-w0)) ) > > � � � � � � � � � � � �*( (e^j(-phi(w0)+ phi'(w0)(w+w0))) * A(j(w+w0)) ) > > > The phi'() terms cause an equal phase shift in the A() about +w0 and -w0, > > respectively. �This is equivalent to shifting the original spectrum of A > > before modulation by -phi'(w0). > > > Lets call this new group delay signal b(t) > > > � � �b(t) �= A(t-tao_g) > > � � �B(jw) = A(jw)e^j(-(-phi'(w0))*w) > > > Plugging back into Y(jw): > > > � � �Y(jw) = |H(jw0)|*(1/2)*( ( (e^j(phi(w0))) �* B(j(w-w0)) ) > > � � � � � � � � � � � � � � + ( (e^j(-phi(w0))) * B(j(w+w0)) ) ) > > > �From the relationship used eariler: > > > � � �y(t) = |H(jw0)|*b(t)*(1/2)*( (e^j(phi(w0))) �* (e^j*w0*t) > > � � � � � � � � � � � � � � � � + (e^j(-phi(w0))) * (e^-j*w0*t) ) > > > � � �y(t) = |H(jw0)|*b(t)*(1/2)*( e^ j(w0*t+phi(w0))) > > � � � � � � � � � � � � � � � � + e^-j(w0*t+phi(w0))) ) > > > Or, > > > � � �y(t) = |H(jw0)|*b(t)*cos(w0*t + phi(w0)) > > > Finally, plug in a() and rearrange to introduce the phase delay term: > > > � � �y(t) = |H(jw0)| * a(t-tao_g) * cos(w0(t-tao_phi)) > > > Where, > > � � �tao_g � = -d/dw phi(w0) > > � � �tao_phi = -phi(w0)/w0 > > > Thanks for all the help Robert! > > you're welcome. > > guess what you could do to spread the joy: �you could fix up that page > at Wikipedia (anyone can edit, even anonymously) and add the rest of the > derivation. �i don't have the time to do it now and also i have been > officially banned from editing wikipedia (hasn't stopped me from editing > anonymously). > > anyway, just a thought. > > -- > > r b-j � � � � � � � � �r...@audioimagination.com > > "Imagination is more important than knowledge."Robert, Do you mind if I ask how you got banned from editting wikipedia? Just curious. Cheers, Dave
Definition of Group (Envelope) Delay
Started by ●November 26, 2012
Reply by ●November 28, 20122012-11-28
Reply by ●November 28, 20122012-11-28
On 11/28/12 8:23 AM, Dave wrote:>...> > Robert, > Do you mind if I ask how you got banned from editting wikipedia? >since around, oh, 2005, i had locked horns with editors (who had friends who were admins) around the Intelligent Design article and some LGBT editors around the articles Homophobia and Marriage. these were generally around the opening sentence or lede paragraph where the topic gets defined. the latter two are still quite biased and inaccurate in the lede. the I.D. article has since gotten better. telling people that their edits blatantly portray bias doesn't make them happy. then, in 2007, one really bad editor (Orangemarlin) claimed that i attacked him anonymously (before getting banned, i had never edited Wikipedia anonymously at all). one admin (and a member of arbcom) ran checkuser on it and said that the result was "inconclusive" (which meant that they had no idea if the IP of the attacker was related to me or not, the IPs were totally different, but some people know how to do proxy IP, i don't). there is a whole story: http://en.wikipedia.org/w/index.php?title=Wikipedia:Arbitration/Requests&diff=prev&oldid=138464426#Indefinite_block_of_User:Rbj the RFA makes a reference to an AN/I where this "community ban" is discussed without my knowledge or participation: http://en.wikipedia.org/wiki/Wikipedia:Administrators%27_noticeboard/Archive89#Rbj_blocked http://en.wikipedia.org/w/index.php?title=User_talk%3AOrangemarlin&diff=132192152&oldid=132164456 http://en.wikipedia.org/w/index.php?title=User_talk%3AOrangemarlin&diff=131920866&oldid=131914744 http://en.wikipedia.org/w/index.php?title=User_talk%3AOrangemarlin&diff=132034193&oldid=131954206 i was "community banned" (which means mob rule), but the community ban was declined for appeal by the arbcom. at one time Jimbo said he would look into it, hadn't gotten back and now doesn't return email. so *now* i fly below the radar and edit anonymously. as a result the topics where i am expert at (articles like the Nyquist/Shannon sampling theorem, etc.) go a bit neglected and have really declined in quality. one editor, Dick Lyons (no relation to our Rick) says that i'm a crank or crackpot, another BobK is a retired EE who craps up these articles wholesale. i used to be a check on him (to keep the crap from getting outa hand) but am not anymore. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
