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Old 16th August 2011, 02:11 AM   #15011
FrankWW is offline FrankWW  Canada
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Quote:
Originally Posted by VladimirK View Post
The term of bandwidth limited function, does not imply that this function is slew-rate limited.
Ageev's theorem, proven in 1957, states:
arbitrary changing bandwidth limited function, has time periods of a limited duration, at which the function wil exceed any high slew-rate limit.
I already mentioned this theorem at various forums and threads. First reaction always was that it is impossible. But later on, many people accepted, that the slew-rate is simply a matter of probability, infinite number of harmonics, being sumed, can eventually lead to very high slew rates. I could imagine this, that there is crest-factor for amplitudes, and there is similar factor for slew-rates.
The square-wave test signal, has a high, but quite a limited slew rate, and I am aware of not so many amps, that could nicely do 200 kHz square wave. What is important, the amp should make minimum influence on the low-level signals, passing through the system at the moment of sharp transients.
Vladimir, there's not a lot with direct google search. Is this it? O.N. Ageev?

"ageev's theorem" - Google Search
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Old 16th August 2011, 02:48 AM   #15012
jcx is online now jcx  United States
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I believe it is a red herring - "pure math" results do not have to reflect real world hardware, signal limits - no digital music recording will come close to the conditions, and you may note his formulation doesn't include amplitude limitation of the sum of infinite arbitrary bandwidth limited sines

a known issue that can produce "higher than expected" peaks in a amplitude, bandwidth limited digital waveform is illustrated by the "over 0 dB fs problem"

illustration from: Over The Top?
shows what you can get by deliberate construction, applying the realistic limit that real DAC hardware will amplitude limit so the "run up" to the "over" has to be both amplitude and bandwidth limited

by "eyeball" that isn't an "infinite" slew rate - 2x maybe?

I believe I heard Bob Stuart claim better oversampling audio DACs do use saturation arithmetic in the digital filters and include 3 dB over range for the more common hard clipping of simpler music signals

and some DAW sw is "aware" of the problem and provide tools to view reconstructed signal to avoid the problem in the mastering

Mastering audio: the art and the science - Google Books
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Last edited by jcx; 16th August 2011 at 03:15 AM.
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Old 16th August 2011, 03:08 AM   #15013
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Originally Posted by FrankWW View Post
Vladimir, there's not a lot with direct google search. Is this it? O.N. Ageev?

"ageev's theorem" - Google Search
As statisticly improbable as it is a +crest factor event followed by a -one would be the maximum sample to sample delta one could observe.
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Old 16th August 2011, 04:37 AM   #15014
hhoyt is offline hhoyt  United States
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Default Slew Rate

Quote:
Originally Posted by scott wurcer View Post
As statisticly improbable as it is a +crest factor event followed by a -one would be the maximum sample to sample delta one could observe.
Scott, you are stating the limitations of digital audio sources... ...let's talk about a stylus hitting a rock in an LP groove, as opposed to merely playing the bandwidth-limited music that was recorded on it. Now THAT is some slew rate! And damn it; I want that KAPOW!!! played back with perfect fidelity!!!

Seriously, the actual peak dynamic range and bandwidth of a good LP and playback system far exceeds that of a 16-bit CD. The LP system is much less accurate, and has higher broad-band noise, but has higher resolution and dynamic range. The three versions of Telarc's 1812 Overture demonstrate this beautifully. The cannon shots on the original LP version can send just about any stylus out of the groove onto the label. The compressed LP re-release has 20dB less peak level on the cannons in response to customer complaints. The CD is even more compressed to fit the limited dynamic range of that medium.

You could make a compelling argument that this is an absurd example, yet the limitations of the media stand apart from the argument.

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p.s. on my Tannoy dual-concentric monitors listening extreme near-field I cannot hear that sound on the Jethro Tull song. With the Stax headphones it is low-level, but clear: a "ploik!" sound.
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Old 16th August 2011, 04:40 AM   #15015
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"Ploik!" is an excellent description!
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Old 16th August 2011, 06:08 AM   #15016
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Quote:
Originally Posted by FrankWW View Post
Vladimir, there's not a lot with direct google search. Is this it? O.N. Ageev?

"ageev's theorem" - Google Search
This one is close to the subject, although the site content is very badly translated into english, probably by a software translator
Dmitry Vassilyevich Ageev

A subtraction from this site:

The theorem is proved that the arbitrary function of time with a restricted spectrum can have sites (segments) of restricted duration, on which one it can vary as much as fast. This on the first view the theorem, contradicting to common sense, was met " in bayonets ", when was reported by the professor Ageev on All-Union session by him. Now it is used at construction of digital sound systems.




In 1955, Mr.. D. V. Ageev introduced and scientifically substantiated, the basic concepts of spectral analysis. They introduced a new concept - an active band of the frequency spectrum function of time and given way to calculate. D. V. Ageev proceeded from the, . that at any given time span that the main contribution to the formation of functions makes it not the whole spectrum, . but only some "active" part of, . reflected in the well-known in our country monograph "The spectra and analysis of Academician A,
. A. Kharkevich. The new concept was suitable for the analysis of systems that process signals, the instantaneous frequency of which varies slowly enough. Portfolio D. V. Ageyeva in this direction were associated with the work of other scientists: Academician A. A. Kharkevich, as well as American scholars P. Fano and K. Page, who introduced the concept of "instantaneous spectrum", defined as the spectrum of the final segment of the process immediately preceding the given moment.

In 1957. D. V. Ageev proved a remarkable theorem, which can reasonably be attributed words of the famous German writer with. Zweig, "truth is beautiful, seemingly implausible". The theorem reads as follows: Suppose that the interval (t1, t2) given any continuous function U (t) and arbitrary frequency F. Then we can construct a function whose spectrum does not contain frequencies higher than F, arbitrarily close (in the mean-square sense) to U (t) in the interval (t1, t2).

. For example, in the time interval of duration 1 s, you can specify a function that changes its sign a million times, and continue it beyond this period of time so that the spectral width of the extended function does not exceed the value of, say, 0.1 Hz
. On this, at first sight paradoxical theorem in detail wrote in his excellent history book "Signals, noise, errors ... (M.: "Communication", 1978) A prominent national scientists. M. Fink. In particular, he remembers that after the D. V. Ageev in 1957,. the All-Union Scientific Session of the Scientific-Technical Society of. A. S. Popov explained that theorem, most listeners did not believe in its fairness and even try to find errors in the presented proof. Theorem Ageyeva significantly expanded representation of engineers of the laws governing the formation of the spectrum of signals and has found practical application in creating digital sound systems.

In 1939, Mr.. American engineer J. G. Chaffee invented demodulator is a frequency-modulated signals (FM) with feedback on the frequency (demodulator PSD). As is known, the frequency modulation has a threshold. This means, . that for the FM signal demodulator can specify a threshold for the signal: if the received signal has a lower (relative to the threshold) level, . a reception is virtually impossible because of the sharp decline in the quality of reception,
. Experiments showed that the demodulator has a high purity as compared to conventional FM demodulator lower threshold, t. e. it is more resistant to interference. Prior studies undertaken in the STI D. V. Ageev and his pupil I. G. Rodionov (1955), theoretical studies of many complex issues relating to the demodulator PSD, including its sustainability and design, not been conducted. These scientists first developed the theory of tracking receiving FM signals, published in the Proceedings of the STI, but in 1958. - In the monograph "FM radio reception with the servo tuning". Tracking demodulators FM signals are widely used only in the mid 60-ies. in satellite and tropospheric communication systems, for which most pressing problem was to reduce the energy potential of communication lines.

In the results presented in the monograph D. V. Ageyeva and I. G. Rodionova, based later on the witness receive FM signals, the study of large domestic specialists L. YA. Kantor A. S. Winitzki, SW. A. Afanasyev et al

In addition to the significant contribution to the theory of communication, D. V. Ageev with pupils achieved notable results in the field of radio engineering, which is reflected in the book D. V. Ageyeva and C. S. Zelmanova "Fundamentals of the theory of resonance in linear systems". In addition, together with his pupil A. V. Kovich Ageev introduced a new concept of "dynamic resonance - resonance in the oscillator circuit with nonlinear resistance and depends on the amplitude of the fluctuations in its frequency, the phenomenon of resonance in linear systems with variable parameters, . and also developed methods for assessing distortions, . arising during the passage of FM signals through different paths connected,
. Since 1951. D. V. Ageev s. V. Malanova, K. P. Sexually etc.. developed a general theory of GPI amplification of radio signals, which is based on a large number of methods for improving the energy efficiency of amplifying devices. This promoted a way of improving efficiency (for. n. d.) amplifier using pulse-width modulation (PWM), proposed in 1932. major Soviet academician A radio personnel. L. Mintz and Professor C. V. Persson. In accordance with this method to be increased tone in the modulator is converted into a sequence of pulses of constant amplitude with double-sided PWM. The frequency of the pulse sequence substantially higher than the frequency in. A. Nyquist equal 2FB, (FB - the upper frequency spectrum of the amplified signal). Pulses of low power with PWM control switching current flowing through the powerful amplifier tubes. At the load of the amplifier is allocated amplified sound. Since the spectrum of double-sided PWM audio frequency spectral components have significant intensity, then to. n. d. amplifier operating on this principle, is close to 100%. In conventional amplifiers to the same. n. d. is only about 20%.

D. V. Ageev lived long and fruitful life, full of intense creative labor. He and his many disciples were made first-class work in many areas of radio engineering. These results influenced the research carried out later than other domestic scientists, and included in the book, which taught thousands of professionals.

Yet due influence on the development of world science research results D. V. Ageyeva not had since been published on time and in less accessible publications, and thus became known only to a limited circle of specialists. Very rarely they were published in leading professional journals abroad. Unfortunately, he E. V. Ageev paid insufficient attention to the publications of his works.

. Another important reason for the influence of domestic science in the world was not enough, is that for decades it was virtually isolated from the processes of development of world science
. Domestic scholars have generally been denied the opportunity to participate in international scientific conferences, to communicate freely with their foreign colleagues and published in foreign scientific journals. In addition, severely limited the ability of our scientists and strict rules of publication of scientific results in the open press. State policy, leading to a closed society that does not allow the national scientific achievements become part of the global science and, of course, reduces the overall cultural level of the nation. This is the beginning of XX century, wrote convincingly a prominent Russian physicist, H. A. Minds, whose words ring true today: "The political significance of the nation can be strong only under the condition that its cultural level corresponds to its weight lifting. In our time, weapons, courage is not the only factors that ensure success in the struggle of peoples for their development and existence .... If we turn to our country, you realize that we, unfortunately, still largely adopt and borrow and invest very little in the cultural life of mankind. "

Last edited by VladimirK; 16th August 2011 at 06:26 AM.
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Old 16th August 2011, 07:05 AM   #15017
jcx is online now jcx  United States
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Originally Posted by hhoyt View Post
...Seriously, the actual peak dynamic range and bandwidth of a good LP and playback system far exceeds that of a 16-bit CD. The LP system is much less accurate, and has higher broad-band noise, but has higher resolution and dynamic range. The three versions of Telarc's 1812 Overture demonstrate this beautifully. The cannon shots on the original LP version can send just about any stylus out of the groove onto the label. The compressed LP re-release has 20dB less peak level on the cannons in response to customer complaints. The CD is even more compressed to fit the limited dynamic range of that medium.

You could make a compelling argument that this is an absurd example, yet the limitations of the media stand apart from the argument.

Howie
seriously you should look at noise shaped dithered 16/44 CD compared with say 100 cm/s of a really good cart at mid frequency - I think CD still has the LP beat handily - Loudness Wars compression isn't happening due to the "limited dynamic range" of CD as a media

as I read it extended high frequency response beyond 20 KHz (at reduced amplitude, outer grooves only, with high tracking/tracing distortion...) is the only hard spec that vinyl playback can clearly claim superior numbers on

Last edited by jcx; 16th August 2011 at 07:10 AM.
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Old 16th August 2011, 07:18 AM   #15018
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Quote:
Originally Posted by jcx View Post
seriously you should look at noise shaped dithered 16/44 CD compared with say 100 cm/s of a really good cart at mid frequency - I think CD still has the LP beat handily - Loudness Wars compression isn't happening due to the "limited dynamic range" of CD as a media

as I read it extended high frequency response beyond 20 KHz (at reduced amplitude, outer grooves only, with high tracking/tracing distortion...) is the only hard spec that vinyl playback can clearly claim superior numbers on
Hard spec of vinyl is one thing, audible qualities may be totally different.
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Old 16th August 2011, 07:58 AM   #15019
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Active mistracking of a quality stylus can reach 500KHz. Measured it, myself.
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Old 16th August 2011, 10:08 AM   #15020
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Originally Posted by VladimirK View Post

In 1957. D. V. Ageev proved a remarkable theorem, which can reasonably be attributed words of the famous German writer with. Zweig, "truth is beautiful, seemingly implausible". The theorem reads as follows: Suppose that the interval (t1, t2) given any continuous function U (t) and arbitrary frequency F. Then we can construct a function whose spectrum does not contain frequencies higher than F, arbitrarily close (in the mean-square sense) to U (t) in the interval (t1, t2).

. For example, in the time interval of duration 1 s, you can specify a function that changes its sign a million times, and continue it beyond this period of time so that the spectral width of the extended function does not exceed the value of, say, 0.1 Hz
. On this, at first sight paradoxical theorem in detail wrote in his excellent history book "Signals, noise, errors ... (M.: "Communication", 1978) A prominent national scientists. M. Fink. In particular, he remembers that after the D. V. Ageev in 1957,. the All-Union Scientific Session of the Scientific-Technical Society of. A. S. Popov explained that theorem, most listeners did not believe in its fairness and even try to find errors in the presented proof. Theorem Ageyeva significantly expanded representation of engineers of the laws governing the formation of the spectrum of signals and has found practical application in creating digital sound systems.
Very interesting, thanks for posting it.
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