John Curl's Blowtorch preamplifier part IV

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#2,122
Yes; the Fourier transform, defined for all linear and continuous functionals on a Schwartz space S(G) where G is an abelian compact group, is a bijection. In particular, for the Schwartz space of the functionals f(t), the F:{f(t):R->R}->{F(jw)} Fourier transformation is also bijective, so the time and frequency domains representations are unique and equivalent. Note the generalization, Fourier doesn't apply to signals only, but to all functions as above, in particular to any transfer function of a circuit, in the time vs. freqency domain representations. Also note that the functional needs to linear and continuous, not a particular function as an argument of the functional.

N.B. a functional is a function taking a function as argument. Functional analysis is the calculus theory of calculus theory 😀.
 
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#2,128
syn08 said:
Yes; the Fourier transform, defined for all linear and continuous functionals on a Schwartz space S(G) where G is an abelian compact group, is a bijection. In particular, for the Schwartz space of the functionals f(t), the F:{f(t):R->R}->{F(jw)} Fourier transformation is also bijective, so the time and frequency domains representations are unique and equivalent. Note the generalization, Fourier doesn't apply to signals only, but to all functions as above, in particular to any transfer function of a circuit, in the time vs. freqency domain representations. Also note that the functional needs to linear and continuous, not a particular function as an argument of the functional.

N.B. a functional is a function taking a function as argument. Functional analysis is the calculus theory of calculus theory 😀.
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Do you use this stuff regularly? I lost almost all of the math I learned in school not even 10 years out.
 
#2,129
Markw4 said:
... What do other members think about that type of behavior, are we all going to start doing too so we can fight back?
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The forum is by audio fanatics for fanatics, expect all kinds of fanatic people. There are civilized, gentleman, educated, cultured, engineer, scientist, layman, expert, along with savage, barbaric, pervert, neurotic, masochist, some others and combinations thereof. The content and wording of your posts define who you are. However, forum rule does not restrict the use of #$%^@! in response to any 野蛮小人 lowlife post in asterisks. 😀
 
#2,130
chris719 said:
Do you use this stuff regularly? I lost almost all of the math I learned in school not even 10 years out.
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No, it's my memory in action. Memories of stuff I studied in the university and/or during my PhD 30-45 years ago and that, for whatever reason, never got scrapped. I guess I enjoyed this stuff, as a mental form of gymnastics. Occasionally pulling from that memory pool is fun.

BTW, what I mentioned above is the fancy way of expressing the very known fact that a circuit differential equation maps through the Fourier transform to an algebraic expression in the frequency domain. Classical example, u=Ldi/dt maps in the frequency domain in U=I*jwL because the d/dt functional (differential operator) transforms to jw.
 
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#2,131
I was looking to divest a few possessions and realized I have several DIY LP's that were issued at the minimum 1000 copies at least one is going for $1000 on ebay. I bought it from Jonathan Anastas - Wikipedia he told me to buy something or get the **** out of the store. I see he has taken a different path. Those last shows of SSD, DYS, Minor Threat, and the Angry Samoans in Boston were memorable.
 
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#2,132
Nelson Pass said:
He designed one back in the good old days - Symmetry Crossover.

I have worked with this as well, and sometimes it gives results, but
routinely the phase response of the drivers themselves joined with
low slopes is a problem.
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YES! Which is clearly my point in bringing cross-overs into the subject of square wave repro from speaker systems.

Seems only a few get it. Think its a dodge. Why is this so hard to understand from EE's and the like? Is there some knowledge that is missing in studies?

If you do not deal with the cross-over and phases of it AND the drivers, combined, you cant get there (Sq wave repro).


THx-RNMarsh
 
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#2,134
john curl said:
Hi Richard, it seems that many people here have not exposed themselves to serious speaker design, because the questions seem so elementary, even naive. This is not a slight, but it shows that many of you should read up on or experience what you are suspicious about. )
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Yep. You got it. No experience to even ask or know the right questions.

I fall into that category in other areas. But, this is really very very basic even. :sigh:


THx-Richard
 
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#2,135
OTOH, half decent square wave capability is conventionally considered unimportant, or at best marginally important. S. Linkwitz for example believed through testing that the timing errors of summed 4th order L-R filters was inaudible even in headphones. Maybe not the last word on the subject, but respectable.


All good fortune,
Chris
 
#2,136
stinius said:
Hi Ovidiu
In my opinion you are very smart and have very deep knowledge.
My question is: Why on earth do you waste your time on this thread?
In my opinion there's a lot of interesting topics to discuss and solve instead of arguing with ****** like Esperado, RNM and the like-minded.

Stein
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gpapag said:
:cop:
Another clean-up of posts containing personal attacks and divisive attempts plus collateral.
Argue over the technical subject, do not turn personal (expressed or implied). Again, mind Forum Rules 1, 2, 3
diyAudio Rules

This is the last of innocuous cleaning ups. Next round will have penalties.

You have been warned.

George
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Two weights, two measures ?
 
#2,138
Chris Hornbeck said:
OTOH, half decent square wave capability is conventionally considered unimportant, or at best marginally important. S. Linkwitz for example believed through testing that the timing errors of summed 4th order L-R filters was inaudible even in headphones. Maybe not the last word on the subject, but respectable.


All good fortune,
Chris
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That is a some what different answer to a different question.... is it audible and to what degree.

IMO it is more accurate reproducer if it can do a square wave well.

Not much different than if an amplifier could or could not repro a sq wave well and looked like some of the speakers..



THx-RNMarsh
 
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#2,139
john curl said:
Hans, making a 'transient perfect' (can pass square waves when summed) filter, appears to always require an overlap, or a filler. Please read carefully the provided data, or try a computer simulation for yourself. There is 'no free lunch!'
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+1
One of the problems is that, if at low frequencies the acoustic sum of two speakers at their crossing frequency is 6dB, the same at high frequencies is only 3dB.
Not to forget that, if our ears are sensible to a "transient perfect" of the initial wave that comes from the front of the speakers to them, our overall "feeling" of the response curve when listening depend a lot of the total acoustic energy. (direct+reverberated signals). Hence the importance of the relative directivity of two speakers at their crossing frequency. And to minimize overlap as much as possible.

"The first - and possibly the most important - thing that must be understood is that electrical and acoustical summing are not the same thing. Just because a crossover network sums flat electrically, this does not imply that it must also sum flat acoustically. With subtractive crossovers, the very worst scenario is presented to the drivers, where there is considerable frequency overlap between the adjacent loudspeaker drivers, and unless they have identical polar response over the entire overlap region (and at least an octave either side), the combined acoustic output will be anything but flat. This seems to have been missed by many of the proponents of these filters." ©Subtractive Crossover Networks

Lot of informations and measurements for the ones interested in this web site (In French).
Une longue mise au point d'une enceinte
 
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#2,140
Gee guys! I thought you knew. It is MIKE who made the Music Rails, but Jack got the patent because it was his turn, apparently. Previously, I think that MIKE got his name on the patent that they mutually applied for. MIKE is an engineer's engineer. I mentioned him previously, and he sometimes works with Jack. Much more than I ever have, that's for sure. Jack and MIKE live relatively close to each other and they share their common experience with the Bybee devices between both of their audio playback systems. MIKE like me, doesn't really understand the Bybee devices, but he certainly hears what they do for his hi fi system. My contribution to them is CTC Blowtorch electronics for both of them, that they have purchased either from me or my deceased business partner, Bob, over the decades. MIKE used to work out of HP, for a number of years. He is now retired.
 
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