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Author Topic: A Challenge to Fourier Or Not?...You Decide.  (Read 25998 times)

Johnny B

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A Challenge to Fourier Or Not?...You Decide.
« on: May 20, 2005, 02:40:37 PM »

This author seems to challenge some of the beliefs currently held, I'll leave it to the readers to decide whether he is on to something or not.

http://members.tripod.com/~gabevee/harmonics.html
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"As far as the laws of mathematics refer to reality,
they are not certain; as far as they are certain,
they do not refer to reality."
---Albert Einstein---

I'm also uncertain about everything.

Johnny B

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #1 on: May 21, 2005, 12:52:19 PM »


No one wants to do any math homework and check the stated results?

It must be almost time for the summer break, but school is not out yet, is it? Smile


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"As far as the laws of mathematics refer to reality,
they are not certain; as far as they are certain,
they do not refer to reality."
---Albert Einstein---

I'm also uncertain about everything.

danlavry

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #2 on: May 21, 2005, 01:50:02 PM »

Johnny B wrote on Sat, 21 May 2005 17:52


No one wants to do any math homework and check the stated results?

It must be almost time for the summer break, but school is not out yet, is it? Smile




Johnny,

I did not "check the math" and it is available at a lot of books. It is the math for Fourier SERIES, which is an analysis method suitable for STEADY STATE SIGNALS - that is a signal that is made of never ending repetition of IDENTICAL CYCLES.

Fourier series math is correct, and it was not intended for audio only. It is a very useful tool for many applications.

But the Fourier SERIES is only STEP 1. There is also the Fourier integral, a much further evolved method of enjoying ANY continues wave, over a given time period. The Fourier integral is not restricted to a "forever repetitive" wave, thus it is much better for analysing audio signals.

The math for Fourier integral is more demanding, but the flexibility in terms of ability to deal with all sorts of signals is so much greater.

The Fourier integral (which does not require steady state) is a very powerful math and engineering method to analyse almost any realistic signal, that can be expressed mathematically (be it a sine wave, a step, an FM radio signal, an impulse...

As I already answered you in another thread, the FFT is a computational analysis tool (based on collecting a "chunk of signal data), and FFT (Fast Fourier Transform) is a "subset" of Fourier analysis. It is useful when you are measuring a signal that you do not know (thus can not express mathematically).

I am repeating what I already said in this forum...

Fourier analysis is one of many tools that can be used for designing or understanding audio. I would only consider looking at audio through the eyes of the very limited Fourier series,  when music becomes an infinite repetitive identical cycles....

Regards
Dan Lavry
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Johnny B

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #3 on: May 21, 2005, 02:13:58 PM »

Dan,

Perhaps you missed my lame attempt at humor, that's ok, my wife often misses it and takes me far too seriously when I'm just kidding.

However, I'd be interested in your impressions of what the author of that linked article is really "trying" to say.

I sort of admire one who has a seeking spirit and who is asking or re-asking questions which I feel is in keeping with scientific progress and helps keep the technology forever moving forward.  

I'd also be interested in hearing what others impressions of the linked article are as well.





 
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"As far as the laws of mathematics refer to reality,
they are not certain; as far as they are certain,
they do not refer to reality."
---Albert Einstein---

I'm also uncertain about everything.

danlavry

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #4 on: May 21, 2005, 02:59:10 PM »

Johnny B wrote on Sat, 21 May 2005 19:13

Dan,

Perhaps you missed my attempt at humor, that's ok, my wife often misses it and takes me far too seriously when I'm just kidding.

However, I'd be interested in your take of what the author of that linked article is really trying say.  


First he is talking about Fourier series. Than he states that a non linear transfer curve would yield harmonic distortion. Nothing new.

After that, I disagree with most of what he says and with his most of his conclusions. I do not want to waste my time explaining, but will be glad to respond to a single point or two if you wish to bring any up.

Regards
Dan Lavry
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Johnny B

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #5 on: May 21, 2005, 03:24:30 PM »


I kind of understood him to be trying to get at the linear vs. non-linear phenom that I would guess that most already know about, but I wonder if that might be an area that is worth re-visiting. Of course we know that many people are doing algo's to try to emulate the non-lineraities found in analogue to varying degress of success and failure, but IIRC, he also touches on the harmonic overtone series which is something that has always facinated me.

In addition, if I'm understanding him correctly (I very well may be misunderstanding him completely) I think he is calling into question the ability to accurately represent certain waveforms with existing technology. Again, maybe I misuderstood him.

In any event, however ill- or well-founded a question may be, I always think it's good that people keep asking questions.  

 
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"As far as the laws of mathematics refer to reality,
they are not certain; as far as they are certain,
they do not refer to reality."
---Albert Einstein---

I'm also uncertain about everything.

danlavry

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #6 on: May 21, 2005, 04:45:31 PM »

Johnny B wrote on Sat, 21 May 2005 20:24



...In any event, however ill- or well-founded a question may be, I always think it's good that people keep asking questions.  

 


This is how he ended his writeup:

"We have now two factors in favor of the triode regarding harmonic distortions. 1) The Fourier derived harmonic pattern of the triode is similar to natural sources of music and adds to the harmonics of the music in proportion, making for a perceptibly louder output. 2) And the input of the tube does not load down the previous stage such that it alters the harmonic amplitude proportions. Which one you subscribe to is your choice.

But as for the device of choice? The tube wins this contest."


It does not sound like a question. More like a statement, much of it based on previous statements I disagree with completely...

Regrads
Dan Lavry
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Johnny B

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #7 on: May 22, 2005, 01:21:21 AM »

Dan,

I understood him to be possibly getting at the early distortion characteristics of tubes vs. transistors or ICs as discussed by Russell O. Hamm in his famous AES white paper. I may be reading something into the linked article that is not there, or just as bad, assuming something that is not appropriate because the author may not have said it.

For all I know, the author might be a guitar player as well, and you know how they love those tube amps. I'd rather try to take a bone away from a big dog than try to take a tube amp away from a guitar player. In any event, clearly he likes tubes or valves best.














 
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"As far as the laws of mathematics refer to reality,
they are not certain; as far as they are certain,
they do not refer to reality."
---Albert Einstein---

I'm also uncertain about everything.

danlavry

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #8 on: May 24, 2005, 02:12:49 PM »

Johnny B wrote on Sun, 22 May 2005 06:21

Dan,

I understood him to be possibly getting at the early distortion characteristics of tubes vs. transistors or ICs as discussed by Russell O. Hamm in his famous AES white paper. I may be reading something into the linked article that is not there, or just as bad, assuming something that is not appropriate because the author may not have said it.

For all I know, the author might be a guitar player as well, and you know how they love those tube amps. I'd rather try to take a bone away from a big dog than try to take a tube amp away from a guitar player. In any event, clearly he likes tubes or valves best.
 



You are talking about a paper that was written in 1972, about technology of the 60's. The paper is based on characteristics of tubes and transistors, used by as poor circuit design that one can imagine. It certainly does not have much to do with electronics today.

I am less than impressed when someone attacks a transistor based on some elementary circuit that no one ever uses, getting everything out of context.

Regards
Dan Lavry
www.lavryengineering.com
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Johnny B

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #9 on: May 24, 2005, 04:16:44 PM »

I think it would interesting for someone such as yourself (i.e. someone with a nice AP Test Box) to go back and try to recreate and perhaps update Russell O. Hamm's White Paper.

Certainly, the re-created and updated test suite could take into account the technological changes or advancements that have occurred since 1973. Perhaps the tests could be conducted at a facility like Sear Sound in NYC.  I could easily see the results being published as a new AES White Paper or possibly leading to a 'zine article.  







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"As far as the laws of mathematics refer to reality,
they are not certain; as far as they are certain,
they do not refer to reality."
---Albert Einstein---

I'm also uncertain about everything.

danlavry

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #10 on: May 24, 2005, 04:45:01 PM »

Johnny B wrote on Tue, 24 May 2005 21:16

I think it would interesting for someone such as yourself (i.e. someone with a nice AP Test Box) to go back and try to recreate and perhaps update Russell O. Hamm's White Paper.

Certainly, the re-created and updated test suite could take into account the technological changes or advancements that have occurred since 1973. Perhaps the tests could be conducted at a facility like Sear Sound in NYC.  I could easily see the results being published as a new AES White Paper or possibly leading to a 'zine article.  




Johnny,

Not my kind of a project. I come from times when transistors were replacing tubes. I do not long for selenium rectifiers, or the days when a 10000 tube computer could not finish a calculation because a tube would fail every few minutes. I do not long for the days when the alternative to computing was a combination of analog discrete amps, integrators, differentiators, potentiometers and a box of wires with banana plugs... Smile

Regards
Dan Lavry
www.lavryengineering.com

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Johnny B

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #11 on: May 24, 2005, 05:27:34 PM »

Ah yes, the days of the Eniac are long gone...but from what I can tell...the days of discrete transistors and all-valve audio components are far from over.

Now if I had a real working brain and a good AP Test Box, I might undertake such a project myself, but alas, I am sadly lacking in both categories. Smile

I do hope that someone far smarter than I will take up the challenge.





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"As far as the laws of mathematics refer to reality,
they are not certain; as far as they are certain,
they do not refer to reality."
---Albert Einstein---

I'm also uncertain about everything.

George_

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #12 on: May 25, 2005, 12:45:00 AM »

Quote:

Dan,

Perhaps you missed my attempt at humor, that's ok, my wife often misses it and takes me far too seriously when I'm just kidding.


Dan,

try not to A/D (Eye/Brain) everything with 32bit/7MHz and think too much over it..Wink

Johnny.. maybe I'm wrong and Dan Lavry is bored all the time.. but I think, he has some work to do with his converters..

Dan, if you are really bored.. I wait for the first 12 channel A/D.. there are lots and lots of 8 and 16 channels.. but I need 10 (12 on the safe side).. It's more cost effective..

Drum recording usually takes more than 8 and less than 16 channels(ok.. no dreamtheater please)Smile

I'm waiting for my christmas present;)

HAVE a nice day!!
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"BORN A ROCKER, DIE A ROCKER"

George Necola

trevord

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #13 on: May 27, 2005, 01:41:19 PM »

danlavry wrote on Tue, 24 May 2005 21:45

I do not long for the days when the alternative to computing was a combination of analog discrete amps, integrators, differentiators, potentiometers and a box of wires with banana plugs... Smile

Regards
Dan Lavry
www.lavryengineering.com



hey ..
what's wrong with analog computing. i was in college in the very last days of analog computing and it was capable of some neat stuff. I even had to take a stab a hydraulic (or fluid) logic, now there's some interesting stuff. Smile

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pipelineaudio

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Re: A Challenge to Fourier Or Not?...You Decide.
« Reply #14 on: May 27, 2005, 08:30:01 PM »

the automatic transmissions from the musclecar era, and in a some what slightly modified form today, are analog hydraulic computers
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