How does a speaker make many freqs at once?
John Bercik
mechanical energy. I am unclear though on how a single cone can
produce multiple frequencies on one moment. Since the cone can only
move forward or backwards, it would seem that at any given moment it
could only produce one frequency. How does this magic really happen?
Thanks,
John Bercik
Dan Popp
Remember that "frequency" involves something in the Time domain. In other
words, "multiple frequencies in one moment" is not a description of what a
speaker does, and indeed (pardon me for saying so) makes no sense. The
combined sound output of many different instruments still only yields one
waveform, which you can see on a computer screen or oscilliscope. At any
given moment, only one digital number (word) describes the voltage that
that sound created. And at any given moment, that digital word or that
analog voltage can describe where that speaker cone should be in its
travel..
Think of your eardrum. It's not moving at EACH of those frequencies
represented in the music (for that you would need 20,000 eardrums, I
guess). It's moving to the *combined* signal presented to it. And at
any given moment, it is just in one position. One moment, one point in
space.
Hope that helps.
Yours,
Dan Popp
Colors Audio
USA
William Sommerwerck
complex has a single electrical value at any instant. The speaker cone attempts
(not very well, usually) to match its displacement to that value.
It's just that simple. You're looking at it from an unduly complex point of
view. The driver does not produce sound on its own -- it REproduces the signal
driving it.
John Bercik
On Sat, 01 Apr 2000 21:35:11 GMT, Dan Popp <color...@neo.rr.com>
wrote:
Les Cargill
John Bercik wrote:
>
> I understand the basics of how a speaker converts electrical energy to
> mechanical energy. I am unclear though on how a single cone can
> produce multiple frequencies on one moment. Since the cone can only
> move forward or backwards, it would seem that at any given moment it
> could only produce one frequency. How does this magic really happen?
> Thanks,
> John Bercik
You can "add up" all the frequencies such that the result is a single
( albeit complex ) signal. This is what the speaker tracks.
--
Les Cargill
http://home.worldnet.att.net/~lcargill
Scott Dorsey
>I understand the basics of how a speaker converts electrical energy to
>mechanical energy. I am unclear though on how a single cone can
>produce multiple frequencies on one moment. Since the cone can only
>move forward or backwards, it would seem that at any given moment it
>could only produce one frequency. How does this magic really happen?
You're thinking about it wrong.
Because the cone can move to any position and in either direction, it can
reproduce any arbitrary waveform (within the mechanical constraints of
the device). Stop thinking about frequencies, and think about amplitudes.
Any waveform, any signal that varies in amplitude with respect to time,
can be represented.
It can reproduce a sine wave, but it can also represent other waveforms.
And, any arbitrary waveform can be represented as the sum of sine waves,
and vice versa (viz Fourier).
--scott
--
"C'est un Nagra. C'est suisse, et tres, tres precis."
Harvey Gerst
>I understand the basics of how a speaker converts electrical energy to
>mechanical energy. I am unclear though on how a single cone can
>produce multiple frequencies on one moment. Since the cone can only
>move forward or backwards, it would seem that at any given moment it
>could only produce one frequency. How does this magic really happen?
>Thanks,
>John Bercik
It's VERY VERY fast!!
Harvey Gerst
Indian Trail Recording Studio
http://www.ITRstudio.com/
Bob Cain
device is that if presented signal that is the sum of a number of
frequencies it will reproduce that signal so that all those frequencies
are present in the motion and no others. A real life signal or sound
pressure field is a complex sum of frequencies at different amplitudes.
Another way to look at it is just the opposite. Speakers do not
typically present frequencies, they present signals that change with
time in much more complex ways than a simple sinusoidal oscilation. It
just happens that signals can be mathematically decomposed into a
changing sum of frequencies. That's not real though, only the signal is
and the rest is just math. Even DSP gurus tend to forget that.
Bob
John Bercik wrote:
>
> I understand the basics of how a speaker converts electrical energy to
> mechanical energy. I am unclear though on how a single cone can
> produce multiple frequencies on one moment. Since the cone can only
> move forward or backwards, it would seem that at any given moment it
> could only produce one frequency. How does this magic really happen?
> Thanks,
> John Bercik
--
"Things should be described as simply as possible, but no simpler."
A. Einstein
hank alrich
> John Bercik <ber...@musc.edu> wrote:
>
> >I understand the basics of how a speaker converts electrical energy to
> >mechanical energy. I am unclear though on how a single cone can
> >produce multiple frequencies on one moment. Since the cone can only
> >move forward or backwards, it would seem that at any given moment it
> >could only produce one frequency. How does this magic really happen?
> >Thanks,
> >John Bercik
>
> It's VERY VERY fast!!
Bzzzzzzzzt! We have an Impopester! Be very aware.
--
hank sez "You got to get it while you can!"
To order the seven-CD set of "Bohemian R.A.P CD"
see http://www.hoohahrecords.com/rap
A Public Service Announcement from secret mountain
Adam Cargill
"In any situation where effect is directly proportional to cause, it is
permissible to consider several causes individually and then combine the resulting
individual effects to find the total effect."
The superposition theorem may be stated as follows:
If cause and effect are linearly related, the total effect of several causes
acting simultaneously is equal to the sum of the effects of the individual causes
acting one at a time.
In electrical circuits, the causes are excitation voltages and currents and the
effects are response voltages and currents.
The algebraic sum of all the amplitudes of all the signals (of different
frequencies) pushing through the amp, at an instant in time, is one single
amplitude. It is this amplitude to which the speaker is responding, at an instant
in time.
Ken Kantor
Have you ever looked at a sound waveform on an oscilloscope, or seen a picture
of one? At any given instant, the vertical position of the waveform is at only
one place, but it is the shape that the movement charts that defines the sound.
Same with a speaker cone. It is simply following the shape of the electrical
waveform as best it can, and in the process of its complex vibrations, many
frequencies are produced simultaneously.
--
Ken Kantor
Vergence Technology, Inc.
www.vergenceaudio.com
www.anxioushippy.com
John Bercik <ber...@musc.edu> wrote in message
news:tgnces01i6leo6da1...@4ax.com...
nuke
>just happens that signals can be mathematically decomposed into a
>changing sum of frequencies. That's not real though, only the signal is
>and the rest is just math. Even DSP gurus tend to forget that.
What kind of nonsense is that?
It absolutely is real, else a hell of a lot of stuff just wouldn't work at all.
There's nothing at all special about audio signals, they are just that,
signals. Frequency domain representations of signals are just as valid as time
domain representations.
A loudspeaker works because it imparts *amplitude* variations into the air. The
cone moves out, the pressure immediately surrounding in the air increases, the
cone moves in, the pressure immediately surrounding decreases.
A single tone results in single, periodic movement of cone, such that it
imparts a sinusoidal pattern of pressure gradiation with respect to time.
Complicated signals which are the sum of many signals will at any instant in
time, have only one amplitude. Therefore the cone only need impart the
amplitude into the surrounding.
Of course the loudspeaker is not an absolute pressure device. Inducing a sound
wave into the air is a matter of differential movement of the cone.
--
Dr. Nuketopia
Spam filtering is off. AO-Hell catches most of it now.
Harvey Gerst
>Harvey Gerst <har...@ITRstudio.com> wrote:
>
>> John Bercik <ber...@musc.edu> wrote:
>>
>> >I understand the basics of how a speaker converts electrical energy to
>> >mechanical energy. I am unclear though on how a single cone can
>> >produce multiple frequencies on one moment. Since the cone can only
>> >move forward or backwards, it would seem that at any given moment it
>> >could only produce one frequency. How does this magic really happen?
>> >Thanks,
>> >John Bercik
>>
>> It's VERY VERY fast!!
>
>Bzzzzzzzzt! We have an Impopester! Be very aware.
Nope, it's really me!! I knew there would be a million correct explanations,
so I didn't bother with the obvious. Couldn't resist the cheap joke. The big
unanswered question is: how does an amplifier pass all those frequencies at
once, thru just two terminals, without getting confused?
Dave Martin
will be 100 square feet in area. However, if you make it one foot thinner
and one foot longer, or 9' x11', it has an area of 99 square feet. What
happened to the other square foot?
--
Dave Martin
DMA, Inc.
Nashville, TN
Harvey Gerst
>At the risk of getting a little arcain....
>
>I would argue that the "reality" of the time domain signal is simply an
>artifact of our conceptual and perceptual biases.
In other words, we "hear" what we "wanna hear".
>We cognitively organize along the time axis.
Mainly because that's the neighborhood I live in.
>If you consider a signal in the frequency domain, it is surely no more or less real.
No more or less real than what? Than the original source? That assumes the
signal is identical in frequency and propagation characteristics. Kinda big
assumption.
>This is a true duality as, say, the particle/wave duality.
Actually it's more like the "breath mint/candy mint" duality.
>The only thing that changes is, essentially, the independent variable that the
>coefficients describing the signal are mapped along.
As S.I Hiyakawa often said, "The map is not the same as the thing being
mapped".
>Isn't this the very essence of Hilbert?
More the very essence of Dilbert, but your description of the process sure
sounded cool. We expect a lot out of a few pieces of paper and wire coils,
dumped inside a wooden box.
It's like a dog walking on it's hind legs - it's not that it's done well, it's
just amazing that it's done at all.
Bob Cain
Ken Kantor wrote:
>
> At the risk of getting a little arcain....
Heh, heh. :-)
>
> I would argue that the "reality" of the time domain signal is simply an
> artifact of our conceptual and perceptual biases. We cognitively organize
> along the time axis. If you consider a signal in the frequency domain, it is
> surely no more or less real. This is a true duality as, say, the particle/wave
> duality. The only thing that changes is, essentially, the independent
> variable that the coefficients describing the signal are mapped along. Isn't
> this the very essence of Hilbert?
I understand your point but I tend to think that in nature you don't
find anything that corresponds to the frequency domain directly.
Despite Fourier, Hilbert and Daubechie's abstractions time just seems
fundamental and frequency an invention. A wavelet decomposition is
similar. Are wavelets real? Being compact they sure seem a firmer
basis for finite duration signals than infinite sinusoids. The most
fundamental thing in nature that corresponds to frequency is the circle
or ellipse. Sure the ear performs a transform but the fact that a
mechanism must be employed to do it just points out the more fundamental
nature of time. This is just an ontological distinction but many
physicists today are reconsidering the nature and even the very
existence of time and I've never heard it cast in the form of a debate
on the nature and existence of frequency. Hmmm, maybe they should.
;-)
Consider that it was an abstract frequency domain consideration that led
to the reality of the spacetime domain quantum wave equation. (Whatever
that is worth it was fun to say.)
How the hell is that for off topic? But hey, the time just changed the
frequency didn't. :-)
Bob
Ken Kantor
I would argue that the "reality" of the time domain signal is simply an
artifact of our conceptual and perceptual biases. We cognitively organize
along the time axis. If you consider a signal in the frequency domain, it is
surely no more or less real. This is a true duality as, say, the particle/wave
duality. The only thing that changes is, essentially, the independent
variable that the coefficients describing the signal are mapped along. Isn't
this the very essence of Hilbert?
--
Ken Kantor
Vergence Technology, Inc.
www.vergenceaudio.com
www.anxioushippy.com
Bob Cain <arc...@znet.com> wrote in message news:38E73033...@znet.com...
> A good speaker is an example of a linear device. A property of a linear
> device is that if presented signal that is the sum of a number of
> frequencies it will reproduce that signal so that all those frequencies
> are present in the motion and no others. A real life signal or sound
> pressure field is a complex sum of frequencies at different amplitudes.
>
> Another way to look at it is just the opposite. Speakers do not
> typically present frequencies, they present signals that change with
> time in much more complex ways than a simple sinusoidal oscilation. It
> just happens that signals can be mathematically decomposed into a
> changing sum of frequencies. That's not real though, only the signal is
> and the rest is just math. Even DSP gurus tend to forget that.
>
>
> Bob
>
Ambiance Acoustics
news:B464B7FBF0F604C4.EF3F7A99...@lp.airnews.net...
C'mon Harvey. That's why interconnect wires have arrows on them.....sheesh.
;-)
--
Robert J. Salvi, Ambiance Acoustics
http://www.calcube.com
San Diego, CA USA
858-485-7514
Andrew P. Mullhaupt
Harvey Gerst <har...@ITRstudio.com> wrote in message
news:B464B7FBF0F604C4.EF3F7A99...@lp.airnews.net...
> walk...@thegrid.net (hank alrich) wrote:
>
> The big
> unanswered question is: how does an amplifier pass all those frequencies
at
> once, thru just two terminals, without getting confused?
Why is the thermos the greatest invention of all time?
Because it keeps hot stuff hot, and cold stuff cold.
How does it know?
Later,
Andrew Mullhaupt
Arrgh
<dave....@nashville.com> wrote:
>Someone pointed out yesterday that if you design a room that's 10' x10', it
>will be 100 square feet in area. However, if you make it one foot thinner
>and one foot longer, or 9' x11', it has an area of 99 square feet. What
>happened to the other square foot?
Uuhhhhh... is this one of them there 'dither' questions?
--------------------
Tracy Wintermute aka Arrgh
ar...@greenapple.com
Rushcreek Ranch
--------------------
tidewater
They can't, that's why you need at least 2.
I think 5:1 does 5 frequencies.
M
Harvey Gerst
>>Someone pointed out yesterday that if you design a room that's 10' x10', it
>>will be 100 square feet in area. However, if you make it one foot thinner
>>and one foot longer, or 9' x11', it has an area of 99 square feet. What
>>happened to the other square foot?
I usually find it safely tucked in my mouth, its normal resting place.
Ken Kantor
thoughtful reply, I was off increasing my frequency....
I understand this is part physics and part epistemology. Wavelets, sinusoids,
there are an infinite number of orthogonal sets that you can use to describe
signals. The question is if "time" is a special dimension. Sure, it is
subjectively. But it would seem pretty labile mathematically. I need to think
more about your contention that nothing in the natural universe "corresponds to
the frequency domain directly". This might be circular reasoning, to use your
analogy... if we mentated in terms of spectra, not waveforms, wouldn't the
opposite be the case? Wouldn't a given signal just look like a different
representational pattern? Depends on how disconnected our perceptions are
from external reality. I used to think they weren't very. Now I believe they
are. They might be causal and repeatable, but they are still only a mental
model.
Any suggestions for readings on the subject of time? And any suggestions for
what the best microphone to record it would be? TIA.
--
Ken Kantor
Vergence Technology, Inc.
www.vergenceaudio.com
www.anxioushippy.com
Bob Cain <arc...@znet.com> wrote in message news:38E83C4A...@znet.com...
Ken Kantor
> In other words, we "hear" what we "wanna hear".
If that is true, why is my radio always playing such crappy music?
> No more or less real than what? Than the original source? That assumes the
> signal is identical in frequency and propagation characteristics. Kinda big
> assumption.
I was trying to talk about whether "time" or "frequency" was a more "real"
description of a recorded signal. I totally agree that you can't talk about
how real the signal itself is compared to the source. They are different
animals.
> Actually it's more like the "breath mint/candy mint" duality.
Hey! You got peanut butter on my chocolate!! No, you got chocolate on my
peanut butter!!!
Ohhh... this is all starting to hurt my brain.
Ken Kantor
--
Ken Kantor
Vergence Technology, Inc.
www.vergenceaudio.com
www.anxioushippy.com
tidewater <strang...@mindspring.com> wrote in message
news:8c9efb$9vb$1...@slb3.atl.mindspring.net...
Wolfgang Böhler
review calculus...
Regards
Wolfgang
Dave Martin wrote:
> Someone pointed out yesterday that if you design a room that's 10' x10', it
> will be 100 square feet in area. However, if you make it one foot thinner
> and one foot longer, or 9' x11', it has an area of 99 square feet. What
> happened to the other square foot?
>
Bob Cain
Ken Kantor wrote:
>
> Hey, speak for yourself. While you were taking the time to compose a
> thoughtful reply, I was off increasing my frequency....
Wish I could. :-)
>
> I understand this is part physics and part epistemology. Wavelets, sinusoids,
> there are an infinite number of orthogonal sets that you can use to describe
> signals. The question is if "time" is a special dimension. Sure, it is
> subjectively. But it would seem pretty labile mathematically.
Yes. Wonderfully labile.
> I need to think
> more about your contention that nothing in the natural universe "corresponds to
> the frequency domain directly". This might be circular reasoning, to use your
> analogy...
Ouch!
> if we mentated in terms of spectra, not waveforms, wouldn't the
> opposite be the case?
That's where it breaks down for me. Events are the stuff of reality.
You can't describe an event with a finite Fourier transform. As to the
stuff of the brain, we do an amazing job of all kinds of transforms. I
think that is what mentation is all about. We transform our sensory
data in many ways to arrive at an abstract model of what is really out
there. At least some part of it. There is only the model (or map) as
far as we are concerned which provides a pretty darned good basis for
the "all is illusion" non-foundation of some eastern thinking.
> Wouldn't a given signal just look like a different
> representational pattern?
It already does. You can hear it, you can feel it and under the right
drugs you can taste it, see it or smell it. :-)
> Depends on how disconnected our perceptions are
> from external reality. I used to think they weren't very. Now I believe they
> are. They might be causal and repeatable, but they are still only a mental
> model.
Yeah.
>
> Any suggestions for readings on the subject of time? And any suggestions for
> what the best microphone to record it would be? TIA.
I recommend "The End of Time" by Julian Barbour, Oxford University
Press. I am slogging through it now and it is mercifully free of formal
mathematics but it is still a conceptual monster. Guys like John Baez
of knot and category theory fame, Roger Penrose who seems to know
everything and Lee Smolin of spin network theory to name a few are
taking his odd view very seriously. Paul Davies has a more conventional
view but there isn't much new in his "All About Time." Lee Smolin
dances around it and many other intruiging new ideas in "The Life of the
Cosmos." But only Barbour attempts to demolish it all together. The
relevance to this group that I find as I read the book is that I keep
wanting to ask him, "yeah, but what about music?" As yet I can't fit it
into his paradigm and he annoyingly avoids it. Music seems to me to
have the most intimate and complex relationship to time (not to mention
the most utterly unique in any philosophical sense) in all of creation
and must be addressed by any theory that attempts to eliminate time as a
fundamental physical entity. He is accessable and I plan on taking the
question up with him when I understand his thinking better.
Ian Marks
frequency for each strand. The more strands the greater the bandwidth, comon
sense really.
ian
Harvey Gerst wrote in message ...
>Nope, it's really me!! I knew there would be a million correct
explanations,
>so I didn't bother with the obvious. Couldn't resist the cheap joke. The
big
>unanswered question is: how does an amplifier pass all those frequencies at
>once, thru just two terminals, without getting confused?
>
ke...@listen2us.com
incidentally?
--
Ken Kantor
Vergence Technology, Inc.
www.vergenceaudio.com
www.anxioushippy.com
"Bob Cain" <arc...@znet.com> wrote in message
news:38E86B8A...@znet.com...
Chris Smalt
>
> At the risk of getting a little arcaine....
She don't lie....
Chris :)
Sent via Deja.com http://www.deja.com/
Before you buy.
nuke
>frequency for each strand. The more strands the greater the bandwidth, comon
>sense really.
>
>ian
Don't forget about the billions of atomic bonds breaking every second!
<g>
Bob Cain
ke...@listen2us.com wrote:
>
> Thanks, much! Are you professionally involved with this stuff,
> incidentally?
>
Wish that I were. I came within a nat's ass of a physics degree 35
years ago but at that time physics looked to be a never ending mass of
boring detail and the awesomely beautiful underlying frameworks were
still well hidden so I veered off into computer science via electrical
engineering. I've stayed in touch with theoretical and engineering
physics (and its practitioners) as a partially educated dilettante
because it is still my first love. My second love was computer theory
and now to bring it somewhat together with my zero'th love, music, it's
all merged into studying sound reproduction and recording technology
with the hope of advancing that part of the art in some signifigant way.
And you?
ke...@listen2us.com
heroine.
--
Ken Kantor
Vergence Technology, Inc.
www.vergenceaudio.com
www.anxioushippy.com
"Chris Smalt" <sm...@nedernet.nl> wrote in message
news:8cb04u$s0j$1...@nnrp1.deja.com...
ke...@listen2us.com
gave it all up for art and music. Now "it's all merged into studying sound
reproduction and recording technology with the hope of selling little wood
boxes with woofers and tweeters inside in some significant way."
--
Ken Kantor
Vergence Technology, Inc.
www.vergenceaudio.com
www.anxioushippy.com
"Bob Cain" <arc...@znet.com> wrote in message
news:38E90A29...@znet.com...
Andrew P. Mullhaupt
>
> That's where it breaks down for me. Events are the stuff of reality.
> You can't describe an event with a finite Fourier transform.
Why not flip over all the cards.
1. If you have smooth band- and time-limited signals, there is no real
distinction between the descriptive power time and frequency. Since this
includes essentially all "real world" audio signals, there is no compelling
reason to spend a lot of effort understanding the distinction.
2. If you want to consider wider classes of signals, (and it is convenient
for theoretical reasons at times to do so), then time and frequency are not
equivalent. If you want to get to the bottom of the question, you have to
address the question of convergence of Fourier series, which was one of the
burning unsolved problems of the nineteenth century. It was only after the
development of the somewhat unintuitive theory of the Lebesgue integral that
a satisfactory explanation of some practical aspects of convergence of
Fourier series was obtained - the Riemann integral (and it's equivalent
formulations) is not adequate for this problem. Even so, the solution of the
problem that everyone wanted - that a Fourier series of a "nice" function
converges at every point where it "ought" to, was not to be. Examples were
found in the late nineteenth century that dashed that hope. Only in 1964 was
a result proved which is in some sense satisfactory - Lennart Carleson's
theorem that the Fourier series of a square (Lebesgue) integrable function
converges pointwise almost everywhere - and the proof of that result is
difficult, and has resisted several serious attempts at simplification in
the intervening decades.
So this is one of those ones where we do know the answer in detail, but in
practice you might want to leave it for later.
If you can't wait, then it's time to bone up on Harmonic Analysis, and
Yitzhak Katznelson's book _An Introduction to Harmonic Analysis_
http://www.amazon.com/exec/obidos/ASIN/0486633314/o/qid=954817543/sr=8-1/ref
=aps_sr_b_1_1/103-4012974-1647812
is a good place to start. At least that's the one that my generation of
mathematicians was hit with. Cruel and unusual doesn't start until you start
getting into E. M. Stein's stuff.
Later,
Andrew Mullhaupt
hank alrich
> If you consider a signal in the frequency domain, it is surely no more or
> less real. This is a true duality as, say, the particle/wave duality.
> The only thing that changes is, essentially, the independent variable that
> the coefficients describing the signal are mapped along. Isn't this the
> very essence of Hilbert?
He loves it when you talk that way to him.
--
hank sez "You got to get it while you can!"
To order the seven-CD set of "Bohemian R.A.P CD"
see http://www.hoohahrecords.com/rap
A Public Service Announcement from secret mountain
hank alrich
jim andrews
>
> My physics is also tangential. EE, acoustics and some biophysics. Then
> gave it all up for art and music. Now "it's all merged into studying sound
> reproduction and recording technology with the hope of selling little wood
> boxes with woofers and tweeters inside in some significant way."
Well, if it matters, the set of NHTPro A-20s we installed
in the studio last month have significantly improved our
mixes!
jim andrews
basset sound
austin, tejas
Bob Cain
"Andrew P. Mullhaupt" wrote:
>
> Bob Cain <arc...@znet.com> wrote in message
> news:38E86B8A...@znet.com...
> >
> > That's where it breaks down for me. Events are the stuff of reality.
> > You can't describe an event with a finite Fourier transform.
>
> Why not flip over all the cards.
You mean draw your sword! :-)
>
> 1. If you have smooth band- and time-limited signals, there is no real
> distinction between the descriptive power time and frequency. Since this
> includes essentially all "real world" audio signals, there is no compelling
> reason to spend a lot of effort understanding the distinction.
But I believe there is. It is more than just a transform of domain and
more than a question of descriptive power. The Fourier transform is a
functional decomposition using a sinusoidal basis which is just one of
an infinite set of possible bases. Your knowledge is obviously much
deeper than mine so I need to ask whether functional decompositions are
in some way symmetric or maybe the word I want is relative? Can reality
be expressed using one basis just as fundamentally as any other? Can a
function of time as we normally think of it be considered just a
functional decomposition of something more fundamentally expressed using
some other basis or doesn't it matter a whit? I hope I am asking a
meaningful question. I am operating under the belief that the answer is
no and that the oldest and most obvious view (call it a field in
spacetime) is the fundamental one while the other newer ones are
invention. Cool invention, but still invention.
>
> 2. If you want to consider wider classes of signals, (and it is convenient
> for theoretical reasons at times to do so), then time and frequency are not
> equivalent. If you want to get to the bottom of the question, you have to
> address the question of convergence of Fourier series, which was one of the
> burning unsolved problems of the nineteenth century. It was only after the
> development of the somewhat unintuitive theory of the Lebesgue integral that
> a satisfactory explanation of some practical aspects of convergence of
> Fourier series was obtained - the Riemann integral (and it's equivalent
> formulations) is not adequate for this problem. Even so, the solution of the
> problem that everyone wanted - that a Fourier series of a "nice" function
> converges at every point where it "ought" to, was not to be. Examples were
> found in the late nineteenth century that dashed that hope. Only in 1964 was
> a result proved which is in some sense satisfactory - Lennart Carleson's
> theorem that the Fourier series of a square (Lebesgue) integrable function
> converges pointwise almost everywhere - and the proof of that result is
> difficult, and has resisted several serious attempts at simplification in
> the intervening decades.
I didn't know that. The sources I have studied, mainly wavelet theory
presentations, simply presume that the considered transforms of square
integrable functions converge. At any rate, is this really germane to
the ontological question of what is reality and what is invention?
>
> So this is one of those ones where we do know the answer in detail, but in
> practice you might want to leave it for later.
Or consider it answered so we can move on and use it.
>
> If you can't wait, then it's time to bone up on Harmonic Analysis, and
> Yitzhak Katznelson's book _An Introduction to Harmonic Analysis_
>
> http://www.amazon.com/exec/obidos/ASIN/0486633314/o/qid=954817543/sr=8-1/ref
> =aps_sr_b_1_1/103-4012974-1647812
I'm afraid I am too old for those kind of calisthenics. It seeps in too
slowly any more.
>
> is a good place to start. At least that's the one that my generation of
> mathematicians was hit with. Cruel and unusual doesn't start until you start
> getting into E. M. Stein's stuff.
Are these considerations left to the mathematicians of your generation
or are they the stuff of an engineering education now? I hope the
latter.
Peace,
Bob
P.S. I haven't dropped my end of our offline spark/smooth debate but I
need to let your last note cook a bit.
Ted Spencer
it to waves on the sea. A speaker cone moves back and forth a relatively large
distance at relatively low speed (low frequencies) while it simultaneously
moves smaller distances at higher speeds (high frequencies). The slow moving
cone is vibrating at higher frequencies as it moves. On to the ocean thing: the
low frequencies are like large ocean swells. The mid frequecies are the smaller
waves that ride along on top of the swells. The high frequencies are the even
smaller wavelets that are on the surface of the waves. The highest frequencies
are the ripples on the surfaces of the wavelets. Yet at any given moment (in a
fixed location in the case of the water) the water (cone position) is at a
specific height. So the surface of a speaker oscillates at multiple,
superimposed frequecies just like the surface of the ocean consists of many
simultaneous wave sizes. Got it? Ok now it's time for milk and cookies and a
nap.
Ted Spencer, NYC
"I'm a lot more like I used to be than I am" - James Taylor
David Light
>One way to describe how a speaker reproduces multiple frequencies is to compare
>it to waves on the sea. A speaker cone moves back and forth a relatively large
>distance at relatively low speed (low frequencies) while it simultaneously
So if you put your ear up really close to a loudspeaker can you hear
the ocean?
Kalman Rubinson
Only with the new B+Ws.
Kal
--
Ken Kantor
I am getting in way over my head, so please take this as a question, not a
point of debate:
In the context of the original question about physical signals, don't you think
it is a mistake to equate a signal's spectrum with its Fourier Transform? For
example, the instantaneous frequency of a signal might not conform to it's FT.
Second question:
I agree with you about the equivalent descriptive power of time and frequency
on real-world signals. But even though the Heisenberg Box may approach a
straight line on special classes of signal, aren't there just as many that are
better localized in frequency as there are that are better localized in time?
To be reductionistic: the delta function vs. the pure sinusoid.
--
Ken Kantor
Vergence Technology, Inc.
www.vergenceaudio.com
www.anxioushippy.com
Andrew P. Mullhaupt <amul...@zen-pharaohs.com> wrote in message
news:8cbmnr$m9k$1...@slb2.atl.mindspring.net...
>
> Why not flip over all the cards.
>
> 1. If you have smooth band- and time-limited signals, there is no real
> distinction between the descriptive power time and frequency. Since this
> includes essentially all "real world" audio signals, there is no compelling
> reason to spend a lot of effort understanding the distinction.
>
> 2. If you want to consider wider classes of signals, (and it is convenient
> for theoretical reasons at times to do so), then time and frequency are not
> equivalent. If you want to get to the bottom of the question, you have to
> address the question of convergence of Fourier series, which was one of the
> burning unsolved problems of the nineteenth century. It was only after the
> development of the somewhat unintuitive theory of the Lebesgue integral that
> a satisfactory explanation of some practical aspects of convergence of
> Fourier series was obtained - the Riemann integral (and it's equivalent
> formulations) is not adequate for this problem. Even so, the solution of the
> problem that everyone wanted - that a Fourier series of a "nice" function
> converges at every point where it "ought" to, was not to be. Examples were
> found in the late nineteenth century that dashed that hope. Only in 1964 was
> a result proved which is in some sense satisfactory - Lennart Carleson's
> theorem that the Fourier series of a square (Lebesgue) integrable function
> converges pointwise almost everywhere - and the proof of that result is
> difficult, and has resisted several serious attempts at simplification in
> the intervening decades.
>
> So this is one of those ones where we do know the answer in detail, but in
> practice you might want to leave it for later.
>
> If you can't wait, then it's time to bone up on Harmonic Analysis, and
> Yitzhak Katznelson's book _An Introduction to Harmonic Analysis_
>
> http://www.amazon.com/exec/obidos/ASIN/0486633314/o/qid=954817543/sr=8-1/ref
> =aps_sr_b_1_1/103-4012974-1647812
>
> is a good place to start. At least that's the one that my generation of
> mathematicians was hit with. Cruel and unusual doesn't start until you start
> getting into E. M. Stein's stuff.
>
> Later,
> Andrew Mullhaupt
>
>
tidewater
ke...@listen2us.com wrote in message ...
>My physics is also tangential. EE, acoustics and some biophysics.
>
>Ken Kantor
Awesome! I need a spaceship!
When can you start?
I also would like something that you can drink, but retains all the
nutritional value of a Big Mac, and it's hot and tasty, right from the can.
Lemme know!
tidewater
David Light wrote in message <38e98554...@news.visi.net>...
> So if you put your ear up really close to a loudspeaker can you hear
>the ocean?
Not next time.
M
Ken Kantor
--
Ken Kantor
Vergence Technology, Inc.
www.vergenceaudio.com
www.anxioushippy.com
tidewater <strang...@mindspring.com> wrote in message
news:8cbrff$p8l$1...@slb6.atl.mindspring.net...
Harvey Gerst
>On 04 Apr 2000 02:21:50 GMT, pres...@aol.com (Ted Spencer) wrote:
>
>>One way to describe how a speaker reproduces multiple frequencies is to compare
>>it to waves on the sea. A speaker cone moves back and forth a relatively large
>>distance at relatively low speed (low frequencies) while it simultaneously
>
> So if you put your ear up really close to a loudspeaker can you hear
>the ocean?
Now THAT'S funny!!!
Noel Bachelor
<har...@ITRstudio.com> allegedly wrote something like:
> The big
> unanswered question is: how does an amplifier pass all those frequencies at
> once, thru just two terminals, without getting confused?
The same way that digital recorders handle them all with 1s and 0s.
Noel Bachelor nbachATozemailDOTcomDOTau
Language Recordings Inc (Darwin Australia)
remove 'oel' from userid in reply field
Andrew P. Mullhaupt
Ken Kantor <ke...@listen2us.com> wrote in message
news:WgeG4.9685$k5.1...@news1.frmt1.sfba.home.com...
> Andrew,
>
> I am getting in way over my head, so please take this as a question, not a
> point of debate:
>
> In the context of the original question about physical signals, don't you
think
> it is a mistake to equate a signal's spectrum with its Fourier Transform?
No, not for band and time limited signals.
> For example, the instantaneous frequency
"Instantaneous" frequency is something that can have a lot of meaings. There
isn't a single well defined choice. Here's a simple example why:
Suppose you have the sinusoidally frequency modulated sine wave, that is
f ( t ) = cos ( a sin t )
where a is the amplitude of the modulation. Using the fact that
cos ( a sin t ) = sum J[n](a) cos ( n t )
where the sum is over all integers n and J[n](a) is the n_th Bessel function
evaluated at a, we see that this signal which could be thought of as having
instantaneous frequency
(a sin t ) / 2 pi t
can also be thought of as a constant superposition of components with
frequencies
n / 2 pi
(leaving aside the interpretation of the positive and negative frequencies).
So what's the frequency, Kenneth?
[ Sorry, but I couldn't resist. ]
Moral of the story: _instantaneous_ frequency is a slippery concept.
> of a signal might not conform to it's FT.
If it's time and band limited, then you don't really need to play with the
bad stuff. Band limiting makes the signal smooth, and so you can dispense
with the convergence problems. This is why in real world signal processing,
band and time limited functions are such a popular sandbox to play in.
So no, don't worry about that problem either.
> Second question:
> But even though the Heisenberg Box may approach a
> straight line on special classes of signal, aren't there just as many that
are
> better localized in frequency as there are that are better localized in
time?
> To be reductionistic: the delta function vs. the pure sinusoid.
The delta "function" is not band limited.
The sinusoid is not time limited.
This is why these seemingly innocuous functions can make you scratch your
head.
You cannot find _either_ one in the real world. But they can be helpful
idealizations which the real world may (or may not) approximate.
It turns out it doesn't matter if a signal is narrow band or of short
duration, as long as it's _both_ time and band limited, you can shake and
bake on either side of the picture with impunity.
Later,
Andrew Mullhaupt
Andrew P. Mullhaupt
>
>
> "Andrew P. Mullhaupt" wrote:
> >
> > Bob Cain <arc...@znet.com> wrote in message
> > news:38E86B8A...@znet.com...
> > >
> > > That's where it breaks down for me. Events are the stuff of reality.
> > > You can't describe an event with a finite Fourier transform.
> >
>
>
> >
> > distinction between the descriptive power time and frequency. Since this
> > includes essentially all "real world" audio signals, there is no
compelling
> > reason to spend a lot of effort understanding the distinction.
>
I'd be surprised.
> Can reality be expressed using one basis just as fundamentally as any
other?
Nobody knows. "Reality" is a big thing.
The answers that are easy to give are:
The signals you will find in audio _can_ be equally well described in either
the time or frequency domain.
The signals you will find on the blackboards of mathematicians and
electrical engineers _may not_ be equally well described in the frequency
domain as in the time domain. You won't find the really wacky ones in your
audio, though.
> Can a function of time as we normally think of it be considered just a
> functional decomposition of something more fundamentally expressed using
> some other basis or doesn't it matter a whit? I hope I am asking a
> meaningful question.
It's a meaningful question. The answer mathematics provides is not helpful,
though. You can express functions in all sorts of wacky ways that can claim,
if you hold them up to the light properly, to be "more fundamental". I won't
bother quoting one of the really sick and wacky ones here, but just mention
that David Hilbert asked a simple question and it turned out to have a very
surprising answer.
> I am operating under the belief that the answer is
> no and that the oldest and most obvious view (call it a field in
> spacetime) is the fundamental one while the other newer ones are
> invention.
The word "fundamental" is devoid of objective meaning in physics. It is used
in grant applications to put forward the research you want to be paid for
more than you want the other guy to get the money.
And the field view may not actually be the oldest. I'm pretty sure that you
can find various ancient texts referring to sound in different ways that may
or may not be useful in the modern world view.
> I didn't know that. The sources I have studied, mainly wavelet theory
> presentations, simply presume that the considered transforms of square
> integrable functions converge.
They rely on the machinery of the Lebesgue integral, and as far as I've seen
usually stick with the square integrable convergence - which is a relatively
easy result.
I don't know the state of the convergence art in the wavelet point of view,
and it will not become interesting to me for the forseeable future. I expect
it is quite similar to the state of the art for Fourier series convergence,
since the same people who beat their heads against the one problem invented
the other. (Michael Frazier is an example).
I should point out that I don't care about wavelet convergence too much
because the work Kurt Riedel and I have done provides a way around the
wavelet explanation and affords much the same signal processing in a
classical filtering setting.
> At any rate, is this really germane to
> the ontological question of what is reality and what is invention?
Sure. Anything you _talk_ about as a description of a signal is invention.
There is no fundamental description of a signal. The signal is what it is.
What you say about it is stuff you do.
> Are these considerations left to the mathematicians of your generation
> or are they the stuff of an engineering education now? I hope the
> latter.
Electrical engineers in some fields are quite well aware of these
considerations. In fact, the guys who did their Ph. D.s at Brooklyn Poly in
the '50s were all over this sort of stuff.
Later,
Andrew Mullhaupt
ke...@listen2us.com
(Sorry about the DN, but the PacBell newsserver at work is really
problematic today.)
In article <38E97678...@activepower.com>,
jim andrews <jand...@activepower.com> wrote:
>
> Well, if it matters, the set of NHTPro A-20s we installed
> in the studio last month have significantly improved our
> mixes!
>
> jim andrews
> basset sound
> austin, tejas
>
ke...@listen2us.com
I was thinking of the well-worn issue of the summation of two sine waves,
and how the instantaneous frequency is generally defined to be the average
freq, which does not appear in the FT. But I admit that this is slippery,
and these are not time-limited signals anyway.
--
Ken Kantor
Vergence Technology, Inc.
www.vergenceaudio.com
www.anxioushippy.com
"Andrew P. Mullhaupt" <amul...@zen-pharaohs.com> wrote in message
news:8cc3ls$8r2$1...@nntp9.atl.mindspring.net...
Andrew P. Mullhaupt
<ke...@listen2us.com> wrote in message
news:glsG4.1$Ec4...@news.pacbell.net...
> OK, thanks. I get this.
>
> I was thinking of the well-worn issue of the summation of two sine waves,
> and how the instantaneous frequency is generally defined to be the average
> freq,
I'm guessing that's the one that comes from the Hilbert transform. It's a
non-insane way to do business.
> which does not appear in the FT.
That's for sure.
> But I admit that this is slippery,
> and these are not time-limited signals anyway.
You can always make a signal time-limited by multiplying it by a signal
which smoothly decays to zero say, six billion years in the past and future
and considering whether in reality you can tell the difference - usually the
answer is no, and the coast is clear.
Later,
Andrew Mullhaupt
Andrew P. Mullhaupt
<ken_k...@my-deja.com> wrote in message
news:8ce6p5$dlj$1...@nnrp1.deja.com...
> In article <8ce2il$h6u$1...@slb7.atl.mindspring.net>,
> "Andrew P. Mullhaupt" <amul...@zen-pharaohs.com> wrote:
>
> > You can always make a signal time-limited by multiplying it by a
> signal
> > which smoothly decays to zero say, six billion years in the past and
> future
> > and considering whether in reality you can tell the difference -
> usually the
> > answer is no, and the coast is clear.
> Bummer... my Audio Precision System Two won't give me more than 16ks of
> windowing.
Hey. This is rec.audio.pro. None of that third world off-brand prosumer
stuff allowed....
> I'll have to email their Tech Support about this 6 billion
> year thing. But at least, for now, I can be sure that the Big Bang and
> the Apocolyse will be highly attentuated.
Well yeah. And you don't get Dorsey trying to autotune those trumpet blasts,
either.
Later,
Andrew Mullhaupt
Bob Cain
"Andrew P. Mullhaupt" wrote:
>
> It's a meaningful question. The answer mathematics provides is not helpful,
> though. You can express functions in all sorts of wacky ways that can claim,
> if you hold them up to the light properly, to be "more fundamental". I won't
> bother quoting one of the really sick and wacky ones here, but just mention
> that David Hilbert asked a simple question and it turned out to have a very
> surprising answer.
He whets the appetite.
>
> I should point out that I don't care about wavelet convergence too much
> because the work Kurt Riedel and I have done provides a way around the
> wavelet explanation and affords much the same signal processing in a
> classical filtering setting.
And sets the hook! Is there a reference to your work approachable by a
mathematical dilettante?
>
> Sure. Anything you _talk_ about as a description of a signal is invention.
> There is no fundamental description of a signal. The signal is what it is.
> What you say about it is stuff you do.
I think we finally come around to agreement.
Bob
ken_k...@my-deja.com
year thing. But at least, for now, I can be sure that the Big Bang and
the Apocolyse will be highly attentuated.
In article <8ce2il$h6u$1...@slb7.atl.mindspring.net>,
"Andrew P. Mullhaupt" <amul...@zen-pharaohs.com> wrote:
> You can always make a signal time-limited by multiplying it by a
signal
> which smoothly decays to zero say, six billion years in the past and
future
> and considering whether in reality you can tell the difference -
usually the
> answer is no, and the coast is clear.
>
> Later,
> Andrew Mullhaupt
Andrew P. Mullhaupt
>
>
> "Andrew P. Mullhaupt" wrote:
> >
> > I won't
> > bother quoting one of the really sick and wacky ones here, but just
mention
> > that David Hilbert asked a simple question and it turned out to have a
very
> > surprising answer.
>
> He whets the appetite.
Yeah, but for an entirely different tangent - Sprecher's Theorem, which is
the solution to Hilbert's 13th problem. Here is a description:
"In 1900, Hilbert posed, as his 13th problem, the question of whether
continuous functions of several variables could be represented by finite
combinations of continuous functions of fewer variables. The problem was
investigated in the late 50s by several workers, and Sprecher showed that
the answer was a qualified `yes'."
Sprecher put the finishing touches on work started by Kolmogorov and Arnold,
which I believe Kolmogorov outlined in his 1958 address to the ICM along
with what became the Kolmogorov-Arnold-Moser theory.
You can contrive all sorts of sicko representations of functions from
surprises like Sprecher's theorem. The trick is to make them look likely.
One thing that can provide the appearance of sensibility for Sprecher's
theorem is the connectionist (nouveau-speak for neural net) point of view.
> > I should point out that I don't care about wavelet convergence too much
> > because the work Kurt Riedel and I have done provides a way around the
> > wavelet explanation and affords much the same signal processing in a
> > classical filtering setting.
>
> And sets the hook! Is there a reference to your work approachable by a
> mathematical dilettante?
The stuff on the web site www.zen-pharaohs.com is as kind and gentle as
we've done, although it's a bit old and not completely elementary. The main
thing is that we have figured out numerically and statistically good and
computationally fast ways to work with really high order filters, including
adaptive filters. And it turns out that these filters are realized by
choosing particularly clever coordinates for state space so that the state
variable filters have all sorts of good properties, mostly interpretable in
terms of orthogonal expansions. If you put the poles of these filters in a
geometric progression and have lots and lots of them then you get wavelets.
We just found a fast and accurate way to do stuff including that.
Later,
Andrew Mullhaupt
nuke
> And it turns out that these filters are realized by
>choosing particularly clever coordinates for state space so that the state
>variable filters have all sorts of good properties, mostly interpretable
>in
>terms of orthogonal expansions.
Yes!
In fact, I was posed with a classification problem involving multiple variables
in an image processing system. It was kind of a tough problem, as it was image
data and it was subject to the vagaries of the image capture system.
Anyway, it defied an easy solution until I hit upon the idea of a
transformation of coordinates in n-space. With the right transformation, the
data subject to capture variations was easily factored out and the relevant
components processed by means of a statistical classifier.
I'd love to say more, but it isn't relevant to this newsgroup, and it belongs
to a company I used to work for.
But to the point at hand, there are advantages to looking at the same signal
from a different perspective. That's all a time-domain or frequency-domain
representation is, just a different way of looking at the same thing. The
signal isn't different because of it, but some ways of looking at it present an
advantage for certain problems.
--
Dr. Nuketopia
Spam filtering is off. AO-Hell catches most of it now.
Andrew P. Mullhaupt
nuke <lar...@aol.com> wrote in message
news:20000405052550...@ng-fh1.aol.com...
> Andrew Mullhaupt wrote:
> > And it turns out that these filters are realized by
> >choosing particularly clever coordinates for state space so that the
state
> >variable filters have all sorts of good properties, mostly interpretable
> >in
> >terms of orthogonal expansions.
>
> Yes!
Right. We're not the only ones pursuing this avenue of investigation.
> In fact, I was posed with a classification problem involving multiple
variables
> in an image processing system. It was kind of a tough problem, as it was
image
> data and it was subject to the vagaries of the image capture system.
>
> Anyway, it defied an easy solution until I hit upon the idea of a
> transformation of coordinates in n-space. With the right transformation,
the
> data subject to capture variations was easily factored out and the
relevant
> components processed by means of a statistical classifier.
>
> But to the point at hand, there are advantages to looking at the same
signal
> from a different perspective. That's all a time-domain or frequency-domain
> representation is, just a different way of looking at the same thing. The
> signal isn't different because of it, but some ways of looking at it
present an
> advantage for certain problems.
Exactly. This is why band- and time- limited signals are the sandbox of
choice. Why live with only one toolset when the both of them are
complementary?
Later,
Andrew Mullhaupt
Stefek Zaba
> ................................................. Guys like John Baez
> of knot and category theory fame, Roger Penrose who seems to know
> everything......................
"Seems" is right. Penrose is a fine mathematician in his specialism; outside
it, *he's* pretty convinced he's still operating at a similar level; those
who know something about whatever he's choosing to pontificate merely sigh
and have one more example to add to the sad roll-call of out-of-genre
know-it-alls. (The names "Pons" and "Fleischman" leap irrepressably to mind,
for example...)
Stefek
(ObRAP: "Why does a dog lick its balls? 'Cause it's time, 'cause it's time. :-)
jason
this is the nature of sound
speakers are the same
-jason