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Subject: Re: How does a mixer work?
References: <firstname.lastname@example.org> <3DB31CC1.2CE2DF@webaccess.net> <email@example.com>
Organization: The Armory
X-Newsreader: trn 4.0-test69 (20 September 1998)
From: firstname.lastname@example.org (Richard Steven Walz)
Date: 22 Oct 2002 05:20:45 GMT
In article ,
Kevin Aylward wrote:
>"Richard Steven Walz" wrote in message
>> In article <3DB31CC1.2CE2DF@webaccess.net>,
>> Chuck Simmons wrote:
>> >Kevin Aylward wrote:
>> >> "John Woodgate" wrote in message
>> >> news:72P7LQAY5ks9EwID@jmwa.demon.co.uk...
>> >> > I read in sci.electronics.design that Kevin Aylward
>> >> > wrote (in
>> >> > >> > er.ntli.net>) about 'How does a mixer work?', on Sat, 19 Oct
>> >> >
>> >> > >But the real question is, are the frequencies really there, are
>> >> > >simple created by the measurement process.
>> >> >
>> >> > Yes, they are *really* there. You can capture each one
>> >> 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
>> >> indeed just an artefact of the measuring system. It is a bit more
>> >> 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
>> >> convenience. There is nothing to stop me expanding in Bessel
>> >> Legende functions or any of suitable set of functions, and
>> >> a "spectrum" analyser that picks out Jo, J1, J2 etc, or the roots
>> >> expansion on Jo(a_nWt). In fact, Fourier himself introduced the
>> >> to solve problems in heat conduction where, there was nothing
>> >> in the problem.
>> >The selection of orthoganol functions is based on the particular
>> >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
>> >In your above case, Bessel functions don't work for perfectly
>> >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
>> >not Fourier analysis. It is just elementary trigonometry. Identities
>> >called identities because both sides of the equation are pointwise
>> >identical. That is, the two sides are equally valid representations.
>> >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
>> >details this). Fourier did not understand them very well either and
>> >numerous errors. In particular, he thought that the series generated
>> >any continuous periodic function converged pointwise to the function.
>> >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
>> >> then any other. People have essentially, been indoctrinated into
>> >> believing that Fourier is special, it isn't. Its just more
>> >No! It took centuries from the first introduction of trigonometric
>> >series for the representation to be realized to be the natural one
>> >periodic functions. It did not help that certain seeming periodic
>> >phenomena cannot be represented by Fourier series. For example, Fouri
>> >methods fail on all traditional musical instruments. Going strictly
>> >the ear, Fourier methods would seem useless right out of the box.
>> 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.
Ah the problem of the implied negative.
Strictly linguistic, let it go.
-Steve Walz email@example.com ftp://ftp.armory.com/pub/user/rstevew
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