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/iframe></center><br><br> <br><br> </center> </td></tr> </table> <center> <table> <tr> <td width="600"> <center><hr width="400"><font size="2"><b>The <a href="http://www.cyber-spy.com/">Cyber-Spy.Com</a> Usenet Archive Feeds Directly<br>From The Open And Publicly Available Newsgroup<br>Sci.Electronics.Design<br><br>This Group And Thousands Of Others Are Available<br>On Most IS NNTP News Servers On Port 119.<br><br><a href="http://www.cyber-spy.com/">Cyber-Spy.Com</a> Is NOT Responsible For Any Topic,<br>Opinions Or Content Posted To This Or Any Other<br>Newsgroup. This Web Archive Of The Newsgroup And<br>Posts Are For Informational Purposes Only.<br><br></b></font><hr width="400"></center> <center><font size="2"><pre><b> Newsgroups: sci.electronics.design Subject: Re: How does a mixer work? References: <51ca721c.0210161956.73a25483@posting.google.com> <3DB31CC1.2CE2DF@webaccess.net> <3db3ae2d$0$37690$8eec23a@newsreader.tycho.net> <lmOs9.40$JW5.4004@newsfep3-gui.server.ntli.net> Organization: The Armory X-Newsreader: trn 4.0-test69 (20 September 1998) From: rstevew@deeptht.armory.com (Richard Steven Walz) Date: 22 Oct 2002 05:20:45 GMT Message-ID: <3db4e02c$0$79557$8eec23a@newsreader.tycho.net> NNTP-Posting-Host: da8f861a.newsreader.tycho.net In article <lmOs9.40$JW5.4004@newsfep3-gui.server.ntli.net>, Kevin Aylward <kevin@anasoft.co.uk> wrote: >"Richard Steven Walz" <rstevew@deeptht.armory.com> wrote in message >news:3db3ae2d$0$37690$8eec23a@newsreader.tycho.net... >> In article <3DB31CC1.2CE2DF@webaccess.net>, >> Chuck Simmons <chrlsim@webaccess.net> wrote: >> >Kevin Aylward wrote: >> >> >> >> "John Woodgate" <jmw@jmwa.demon.contraspam.yuk> wrote in message >> >> news:72P7LQAY5ks9EwID@jmwa.demon.co.uk... >> >> > I read in sci.electronics.design that Kevin Aylward >> >> > <kevin@anasoft.co.uk> wrote (in >> >> <Jkhs9.1717$An4.132297@newsfep1-win.serv >> >> > er.ntli.net>) about 'How does a mixer work?', on Sat, 19 Oct >2002: >> >> > >> >> > >But the real question is, are the frequencies really there, are >they >> >> > >simple created by the measurement process. >> >> > >> >> > Yes, they are *really* there. You can capture each one >individually >> >> with >> >> > a narrow-band filter. That's why you can see them on a spectrum >> >> > analyser. OTOH, there is no signal component at the original >> >> modulation >> >> > frequency. That's why you have to rectify the signal to get the >> >> > modulation back. >> >> >> >> Ahmmm. This was a leading question John:-) >> >> >> >> In fact one can easily argue that they are *not* really* there and >are >> >> indeed just an artefact of the measuring system. It is a bit more >subtle >> >> then you are considering here. >> >> >> >> The expansion of a function in a sine/cosine series of orthogonal >> >> functions is not unique or special at all. Its simple one of >general >> >> convenience. There is nothing to stop me expanding in Bessel >functions, >> >> Legende functions or any of suitable set of functions, and >constructing >> >> a "spectrum" analyser that picks out Jo, J1, J2 etc, or the roots >of an >> >> expansion on Jo(a_nWt). In fact, Fourier himself introduced the >series >> >> to solve problems in heat conduction where, there was nothing >repetitive >> >> in the problem. >> > >> >The selection of orthoganol functions is based on the particular >basis >> >satisfy initial conditions (for ODEs) or boundary values (for PDEs). >> >Convergence fails if the boundary values are not perfectly satisfied. >> >This means that you cannot helter skelter use anything for any >problem. >> >In your above case, Bessel functions don't work for perfectly >periodic >> >functions. As I recall, they happen to be the right animal for the >> >simple pendulum problem which is a non-linear ODE. In any event, >> >applying simple trigonometric identities to purely sinusoidal signals >is >> >not Fourier analysis. It is just elementary trigonometry. Identities >are >> >called identities because both sides of the equation are pointwise >> >identical. That is, the two sides are equally valid representations. >AM >> >modulation and sidebands result from a simple identity and not from >> >fourier analysis. >> > >> >Fourier did not introduce trigonometric series. That came about a >> >century or more earlier (Boyer, in one of his histories of >mathematics >> >details this). Fourier did not understand them very well either and >made >> >numerous errors. In particular, he thought that the series generated >by >> >any continuous periodic function converged pointwise to the function. >Of >> >course this is ridiculous. However, his application was periodic in >> >fact. He was investigating heat generation in the boring of cannon >> >barrels. The equilibrium is periodic for a barrel of infinite length >> >being bored with a typical boring bit if the coordinate origin moves >> >with the bit. >> > >> >> The fact that, for example, our ears are constructed as a Fourier >> >> analyser, does not make the Fourier expansion of a signal any more >real >> >> then any other. People have essentially, been indoctrinated into >> >> believing that Fourier is special, it isn't. Its just more >familiar. >> > >> >No! It took centuries from the first introduction of trigonometric >> >series for the representation to be realized to be the natural one >for >> >periodic functions. It did not help that certain seeming periodic >> >phenomena cannot be represented by Fourier series. For example, Fouri >er >> >methods fail on all traditional musical instruments. Going strictly >by >> >the ear, Fourier methods would seem useless right out of the box. >> > >> >Chuck >> -------------------------- >> TRUE, our ears do NOT do PHASE AT ALL!! > >That's right, they are Fourier analyses, so why say true, when your very >statement implies that the claim "..Fourier methods would seem useless >right..", is false. > >Kevin Aylward ------------------------ Ah the problem of the implied negative. Strictly linguistic, let it go. -Steve -- -Steve Walz rstevew@armory.com ftp://ftp.armory.com/pub/user/rstevew Electronics Site!! 1000's of Files and Dirs!! With Schematics Galore!! http://www.armory.com/~rstevew or http://www.armory.com/~rstevew/Public </b></pre></font><hr width="650"><a href="http://www.cyber-spy.com/electo-index.html"><font size="3">Go Back To The <a href="http://www.cyber-spy.com/">Cyber-Spy.Com</a><br>Usenet Web Archive Index Of<br>The sci.electronics.design Newsgroup</font></a><br><br></center></td><img src="http://cyber-spy.com/cgi-bin/livecntr.pl?0+1+unetsci" width="1" height="1" alt="The Cyber-Spy Toolkit - powerful internet spy software - live police scanners - usenet fbi secrets archive - newsgroup spy electronics archive - search engine spy tools - download TCST today!"> </tr> </table> </center> <center> <br><center><hr size="3"></center> <table width="100%" cellpadding="0" border="0" cellspacing="0"> <tr> <td align="left" valign="top"><small><b><i><a href="http://www.cyber-spy.com/index.html">Cyber-Spy.Com Live Resources</a></i></b></small></td> <td align="right" valign="top"><small> Copyright Alpha Omega Delta,<br> All rights reserved. </small></td> </tr> </table> <center><hr size="3"></center> <br><br> <br><br></center> </body></html>