Difference between revisions of "What Show Jump Response, Group Delay And Phase Response?"
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Die Sprungantwort ist kein typischer Parameter speziell für einen Lautsprecher. Sie ist ein Signal aus der Regelungstechnik und dient bei beliebigen technischen Systemen zur Beschreibung des Verhaltens zwischen Ein- und Ausgang. <br />
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The step response of a loudspeaker is generally associated with the aspect of time correctness. Although it is possible to mathematically extract the aspect ''time'' from the step response, as from any other signal, reducing the significance of the step response to this aspect misses the reality entirely. The step measurement is not a measurement of the time response. It is a measurement of the signal behavior. The graph of the step response relates the voltage values obtained from the sound pressure by the conversion by microphone to their temporal sequence in the same way as when using other signal forms or musical passages. Furthermore, the step response includes the frequency response of the transmission system, as well as all other extractable parameters. Not all parameters are optically differentiable, but they are still included. If you want to evaluate the behaviour of a loudspeaker at high volumes or under different dispersion angles, you can also do this with the help of the step response measurement.<br />
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Es ist innerhalb der Fachwelt Konsens, dass die Sprungantwort das Übertragungsverhalten eines Lautsprechers repräsentiert. Ob auf Achse, unter Winkel, von hinten oder von vorne oder invertiert gemessen, beschreibt sie das Übertragungsverhalten von Lautsprechern so vollständig wie kein anderes Testsignal. Sie sagt damit direkt aus, wie er klingt. Jede kleinste Abweichung vom Idealverlauf ist ein Fehler, eine Nichtlinearität. Für die anderen Parameter gilt hingegen:
+
The step response is therefore something like the genetic code of the loudspeaker. It shows how each cell ticks. The expert gets a clear indication of how this loudspeaker distorts all possible signals and sounds, because there is a clear correlation between the distortion of the step measurement and the distortion of all other signals/sounds.
  
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*Der Frequenzgang auf Achse allein sagt uns nicht, wie ein Lautsprecher wandelt.
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The loudspeaker is an electroacoustic transducer. The elementary task of an electroacoustic transducer is to convert a signal structure fed to it ''into an equivalent'' sound structure. This includes frequency response linearity, low distortion, dynamics, phase response, impulse response, transient response,
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*Der Frequenzgang unter Winkel allein sagt uns nicht, wie ein Lautsprecher wandelt.
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dispersion, etc. The step response of a loudspeaker describes its transmission behaviour and thus whether it performs this conversion correctly in principle. The basic requirement for the development of an electroacoustic transducer is thus defined. In addition, the electroacoustic transducer should generate the sound pressure required for its area of application and do so with as little distortion as possible. Furthermore, there is the requirement of a radiation pattern that is as uniform as possible. Not only quantitative aspects have to be considered. The quality of the sound radiated at different angles is also important. The quality (intelligibility) of the reflections depends on this. Therefore, the step response must also be measured in consideration of the radiation pattern.<br />
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*Die Gruppenlaufzeit allein sagt uns nicht, wie ein Lautsprecher wandelt.
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The step response is not a typical parameter especially for a loudspeaker. It is a signal from control engineering and is used in any technical system to describe the behaviour between input and output. <br />
−
*Die linearen und nichtlinearen Verzerrungen allein sagen uns nicht, wie ein Lautsprecher wandelt.
+
It is a consensus among experts that the step response represents the transmission behaviour of a loudspeaker. Whether measured on axis, at an angle, from the rear or front, or inverted, it describes the transmission behaviour of loudspeakers more completely than any other test signal. It thus directly tells us how it sounds. Every slightest deviation from the ideal curve is an error, a non-linearity. One should take it seriously and know how to interpret it. Nevertheless, only a fraction of loudspeakers are capable of converting input signals into equivalent output signals (sound waves). <br />
 +
For other parameters, however, the following applies:
  
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Es ist leicht mit jeder beliebigen Signalform / Klangstruktur nachzuweisen, dass ein Lautsprecher mit deformierter Sprungantwort auch andere Signale verzerrt und dass ein Lautsprecher mit einer Sprungantwort ganz nahe dem Idealverlauf auch jedes andere Signal sehr genau wandelt. Unser Trommelfell nimmt durch diese Abweichungen im Druck-Zeit-Verlauf ein dementsprechendes Klangbild wahr.<br />
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*The frequency response on axis alone does not tell us how a speaker converts.
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Beim Lautsprecher handelt es sich um einen elektroakustischen Wandler. Die elementare Aufgabe eines elektroakustischen Wandlers besteht darin, eine ihm zugeführte Signalstruktur ''in eine äquivalente'' Schallstruktur zu wandeln. Das schließt Frequenzganglinearität, Verzerrungsarmut, Dynamik, Phasengang, Impulswiedergabe, Ein- und Ausschwingverhalten,
+
The frequency response under angle alone does not tell us how a loudspeaker converts.
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Abstrahlverhalten usw. mit ein. <br />
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Group delay alone does not tell us how a loudspeaker performs.
 +
The linear and non-linear distortions alone do not tell us how a loudspeaker is transducing.
 +
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[[File:Ess series 450.jpg]]<br />
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''[[ESS Connoisseur Series AMT 450]]'''
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|}
  
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'''Die Sprungantwort hat ihren gleichmäßigen Verlauf NUR dann, wenn:'''
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Interpreting the transducer response of a loudspeaker from frequency and phase response is much less meaningful. This is due to the very assumptions and exclusions that underlie these measurement models. It is easy to prove with any signal shape / sound structure that a loudspeaker with a deformed step response also distorts other signals and that a loudspeaker with a step response very close to the ideal response also transforms any other signal very accurately. Our eardrum perceives a corresponding sound image due to these deviations in the pressure-time curve.
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*der Frequenzgang auf Achse linear ist, dessen Grenzbereiche auch sehr gut zu erkennen sind. Entsprechendes gilt unter Winkel.  
 
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*die Gruppenlaufzeit linear ist, oder auch der Phasengang.
 
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*die linearen und nichtlinearen Verzerrungen minimal sind.
 
  
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| [[Datei:Kleine Elfe.jpg]]<br />
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By far the greatest errors are made by loudspeakers when converting a dynamic signal structure. Errors and non-linearities that we recognize in a frequency response diagram are also reflected in the step response. Errors and nonlinearities that we see when measuring phase response or group delay are also reflected in the step response. And if we put enough energy into the step response, we will also see the compression and distortion of a transducer. By the way, this is also true for amplifiers. Here we can also see very well the intervention and the characteristics of protection circuits. But above all, the step response stands for the connecting, for the overall representation of many other measurements.
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''[[Myro Kleine Elfe]]''
+
A loudspeaker with a deformed step response never has a constant group delay or a uniform phase response. Furthermore, the step response is the only measurement signal that represents the transducer quality of a loudspeaker in a complex way and at the same time it is also relatively widespread.
 +
The step response is therefore ideally suited for the evaluation of the large number of loudspeaker models.
  
 +
{| class="wikitable" border="1"
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[[File:Kleine Elfe.jpg]]<br />
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''[[Myro Little Elf]]'''
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Any professional knows that a speaker that converts properly is necessarily capable of a proper step response, that it can consequently also convert any input signal into the same output signal, whether a sine wave or any other waveform. And if the speaker can do this, and ''only'' then, it can properly convert a music signal. No loudspeaker that delivers a distorted step response is capable of ''input = output'', that is, of reproducing music signals correctly, without distortion.<br />
 +
With a correctly shaped step response in the basic characteristic, one immediately recognizes the direct connection between frequency response linearity and shaping of the step response.<br />
 +
With a step response that is incorrectly shaped in the basic characteristic, the direct relationship between frequency response linearity and the shape of the step response is practically no longer recognizable, although it is presented here as well.<br />
 +
 +
'''The step response has its uniform characteristic ONLY if:'''
 +
*the frequency response is linear on axis, whose border areas can also be seen very well. The same applies under angles.
 +
*the group delay is linear, or also the phase response.
 +
*the linear and non-linear distortions are minimal.
 +
 +
In the above cases, the reverse is not true! A linear frequency response does not indicate a correct step response. Neither does a uniform phase response. Thus "correct conversion" is not guaranteed! BUT: If the phase frequency response is correct (without phase rotations at the takeovers) and this not only in the steady state, but also in the transient state, then the step response is also correct, has the same linearity and thus also the correct basic characteristic (square wave over high and low pass filter).<br />
 +
Phase and amplitude interact, but the amplitude response can be improved even if the phase response deteriorates at the same time. (There are many examples of this in loudspeakers with 2nd or 3rd order filters etc.) This is the case when the measurement signal puts the loudspeaker in a steady state and the evaluations therefore only allow statements about this. For the step response, however, the phase in the transient, in the impulse dynamics, is important!<br />
 +
 +
A short description can be found at the magazine ''Fairaudio'' about the [http://www.fairaudio.de/hifi-lexikon-begriffe/sprungantwort.html step response] and the [http://www.fairaudio.de/hifi-lexikon-begriffe/impulsantwort.html impulse response].
 +
 +
Errors in the development of electroacoustic transducers mostly occur when the complex result of the step response is transferred into the mentioned differentiations and the developer develops further on this differentiated model level and optimizes his development object. <br />
 +
To improve the step response, the phase response '''and''' amplitude response must be improved together. Improving the amplitude response without improving the phase response, or more precisely the time relationships in the transient, does not improve the step response. Disregarding the correct polarity, for whatever reason, definitely leads to a wrong step response, to the wrong reproduction of transient response.
 
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In den genannten Fällen gilt der Umkehrschluss nicht! Ein linearer Frequenzgang weist nicht auf eine richtige Sprungantwort hin. Ein gleichmäßiger Phasengang ebenfalls nicht. Damit ist "richtig wandeln" nicht gewährleistet! Phase und Amplitude stehen in einer Wechselwirkung, jedoch lässt sich der Amplitudengang auch bei gleichzeitiger Verschlechterung des Phasengangs verbessern. (Dafür gibt es viele Beispiele von Lautsprechern mit Filtern 2. oder 3. Ordnung etc.) Und zwar dann, wenn das Messsignal den Lautsprecher in einen eingeschwungenen Zustand versetzt und die Auswertungen deshalb nur Aussagen darüber zulassen. Für die Sprungantwort ist aber die Phase im Einschwingen, in der Impulsdynamik, von Bedeutung!
 
  
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Fehler bei der Entwicklung von elektroakustischen Wandlern treten meistens dann auf, wenn das komplexe Ergebnis der Sprungantwort in die genannten Differenzierungen überführt wird und der Entwickler auf dieser differenzierten Modellebene weiter entwickelt und sein Entwicklungsobjekt optimiert.<br />
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As a designer, you hear the sound responses of the loudspeaker during the measurement process and thus have a direct sound impression of what you can see on the screen. If you don't have this hearing experience, it takes some imagination to be able to imagine a sound formed from these sound waves. The loudspeaker delivers a sound similar in basic pattern every time it is stimulated with a signal. Anyone who was present during the measurement process would be able to hear this. The loudspeaker produces these transient noises in their characteristic typical of the loudspeaker regardless of whether we are listening to classical music, pop, rock or jazz over it or whether we want to listen to the soundtracks of films or understand the dialogues. It is easy to imagine, even for the layman, that the correct reproduction of vibrations results in fewer but distinct vibrations that are correct in their pitches. The sound image sounds clearer, more dynamic, less filled with artificial vibrations and more intelligible with a properly transducing speaker. There is a clear space between the tones and sounds, less filler, less distortion. The untrained listener would think it sounds thinner. But it doesn't in terms of energy content, only in terms of the nothingness between the tones! The comparison of a smeared, dusty disc with a freshly cleaned disc literally suggests itself here.<br />
 +
There are non-linearities in the transmission behaviour of loudspeakers, which basically result from the limited transmission bandwidth. These limits are also clearly visible in loudspeakers with largely correct step response.
  
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Es gibt Nichtlinearitäten im Übertragungsverhalten von Lautsprechern, die grundsätzlich aus der begrenzten Übertragungsbandbreite resultieren. Diese Grenzen sind bei Lautsprechern mit weitgehend korrekter Sprungantwort auch klar zu sehen. <br />
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Grundsätzlich gilt:
+
Basically:
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*Der Hochtöner bestimmt die maximale Anstiegsgeschindigkeit eines Impulses.
+
*The tweeter determines the maximum slew rate of an impulse.
−
*Das synchrone Einschwingen des Hochtöners mit dem Mittel- und Tieftöner bewirkt die volle Impuls-Dynamik. Eine Bassdrum beispielsweise klingt dann schnell und knackig, wenn alle Lautsprecherchassis synchron, in Phase, einschwingen.
+
The synchronous transient of the tweeter with the midrange and woofer causes the full impulse dynamics. A bass drum, for example, sounds fast and crisp when all the drivers are in phase.
 +
The step response starts with the rise time of the tweeter. But the tweeter has its limit in the rise time and the energy that should actually be generated at the beginning is usually converted into sound with a slight delay. Then an exaggerated peak is produced.
 +
The low-frequency limitation of the transmission behaviour is noticeable in a more or less strong drop of the curve.
 +
If the curve drops steeply from the peak, the woofer can only develop the first half-wave in the bass range weakly.
 +
If the graph is flatter, this is more successful.
 +
Of course a loudspeaker should also show a decent step response under different listening angles.
 +
But to achieve this is a high art. A correct step response on the listening axis is, however, the absolute prerequisite for the correct conversion of the vibrations, the music.<br />
 +
Low, mid and high frequency drivers do not have any relevant immanent latency with regard to the temporal origin. And if it does exist, then the starting points must nevertheless be congruent in time. The maxima of envelopes are unsuitable for the evaluation of the time behaviour with regard to the impulses. That's why group running times only say something about the steady state. Also distorted (in itself deformed) wave groups can have the maximum of the envelope at the same point (e.g. if a wave propagating within the chassis or its surroundings comes back too short as a reflection and distorts the wave group, etc. typical non-linearities).<br />
 +
The transient processes (especially the impulses) can be distorted in a wave group and they are in "non-time-correct loudspeakers"! We are then dealing with energy shifts, e.g. from the first half-wave to the second and following half-waves, which do not necessarily have to affect the maximum, since there are other events, see reflections, which cause the maximum.
 +
|
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[[File:Spirit III.jpg]]<br />
 +
''[[Myro Spirit III]]''
 +
|}
  
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Die Sprungantwort startet mit der Anstiegszeit des Hochtöners. Der Hochtöner hat aber seine Grenze in der Anstiegszeit und die Energie, welche eigentlich am Anfang erzeugt werden müsste, wird zumeist leicht verzögert in Schall gewandelt. Dann entsteht eine überhöhte Spitze.
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Die tieffrequente Begrenzung des Übertragungsverhaltens macht sich in einem mehr oder weniger starken Abfallen der Kurve bemerkbar.
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|-
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Fällt die Kurve ab der Spitze steil ab, so kann der Tieftöner die erste Halbwelle im Bassbereich nur schwach ausbilden.
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Verläuft der Graph flacher, dann gelingt dies besser.
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[[File:35226580.jpg]]<br />
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Ein Lautsprecher sollte natürlich auch unter verschiedenen Hörwinkeln eine ordentliche Sprungantwort aufzeigen.
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''[[Myro Amur D]] Black Diamond''
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Das zu schaffen ist jedoch die hohe Kunst.
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|
  
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Eine korrekte Sprungantwort auf Hörachse ist allerdings die unbedingte Voraussetzung für die richtige Wandlung der Schwingungen, der Musik.
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== The phase response ==
 +
The frequency response is sometimes represented as a complex frequency response, which is used to represent the phase response.
 +
This phase response of a loudspeaker also describes the time relations in the ''steady state'', but not the impulse behaviour. The time relations in the transient state differ considerably from the time relations in the steady state. Even loudspeakers with inverted drivers can have a uniform (steady-state) phase response. When measured in the steady state, even the polarity change that leads to complete distortion of the signal during transients is not to be seen as a phase rotation. The impulse reproduction is nevertheless faulty.<br />
 +
As always, you have to know exactly what the measurement conditions of a measurement procedure are in order to know what to read from it. Phase considerations presuppose that measurement points are defined within the measurement model in a fixed frequency bandwidth, which are set in relation to each other under the aspect of temporal shifts. The relationship between phase angle and frequency is what these measurement diagrams show us. The evaluation refers either to a steady state or to a quasi-static state. This also explains why no conclusions can be drawn about the output signal from the phase response, because it is always what is not shown to us that is interesting:
 +
*We don't know the model specifications regarding the definition of the reference points.
 +
*we have no information about the polarity, the amplitude
 +
*and therefore no clues about the sound structure.
  
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== Der Phasengang ==
+
In particular, the first half-waves of the transient, which determine to the highest degree the location and identification of a sound event, are not represented by phase measurements. The phase response related to the first half-waves would look completely different from the phase response related to subsequent half-waves. Therefore, there can be no phase response that is generally meaningful.<br />
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Die Darstellung des Frequenzgangs erfolgt gelegentlich auch als komplexer Frequenzgang, mit dem der Phasengang abgebildet wird.
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To interpret the transducer behaviour of a loudspeaker from frequency and phase response is much less meaningful than the step response. This is due to the assumptions and exclusions on which these measurement models are based.
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Auch dieser Phasengang eines Lautsprechers beschreibt die Zeitbeziehungen im ''eingeschwungenen'' Zustand, nicht aber das Impulsverhalten. Die Zeitbeziehungen im Einschwingvorgang unterscheiden sich erheblich von den Zeitbeziehungen im eingeschwungenen Zustand. Selbst Lautsprecher mit invertierten Chassis können einen gleichmäßigen (eingeschwungenen) Phasengang aufweisen. Die Impulswiedergabe ist dabei trotzdem fehlerhaft.<br />
 
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Phasenbetrachtungen setzen voraus, dass innerhalb des Messmodells Bezugspunkte definiert sind, die unter dem Aspekt zeitlicher Verschiebungen in Relation zueinander gesetzt werden. Die Auswertung bezieht sich dabei entweder auf einen eingeschwungenen Zustand oder auf einen quasi-statischen Zustand. Das erklärt auch, weshalb aus dem Phasengang keine Rückschlüsse auf das Ausgangssignal gezogen werden können. Insbesondere die ersten Halbwellen des Einschwingvorgangs, die in höchstem Maße die Ortung und die Identifikation eines Schallereignisses bestimmen, werden durch Phasenmessungen nicht dargestellt. Der Phasengang bezogen auf die ersten Halbwellen sähe ganz anders aus als der Phasengang bezogen auf nachfolgende Halbwellen. Es kann also keinen Phasengang geben, der allgemeingültig aussagefähig ist.
 
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'''Beispiel:'''<br />
 
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Die Klangcharakteristik von Instrumenten wird neben deren Einschwingvorgängen vor allem durch ein charakteristisches Spektrum von Grundtönen und deren Vielfachen (Obertönen) bestimmt. Liegt der Grundton beispielsweise bei 440 Hz und die Obertöne bei 880, 1.760, 3520, 7.040 Hz usw., so ergibt sich eine Schalldruckstruktur aus der Überlagerung dieser Wellen. Bei Verpolung des Hochtöners überlagert sich dieses Gemisch aus Grundton und Obertönen ganz anders und führt zu einer lautsprechertypischen, künstlichen Schallstruktur. Die Überlagerung einer richtig gepolten 440 Hz-Schwingung mit einer invertierten 7.040 Hz-Schwingung ergibt definitiv eine deutlich vom Original abweichende Summe. Im Phasengang sind all diese Phänomene aber unsichtbar!<br />
 
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Der Modebegriff "Zeitrichtige Lautsprecher", der sich in der Regel auf einen halbwegs linearen Phasengang bezieht, sagt im Grunde gar nichts aus.
 
  
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'''Example:'''<br />
 +
The sound characteristics of instruments, in addition to their transient response, are determined primarily by a characteristic spectrum of fundamental tones and their multiples (overtones). For example, if the fundamental is at 440 Hz and the harmonics are at 880, 1,760, 3520, 7,040 Hz, etc., a sound pressure structure results from the superposition of these waves. If the polarity of the tweeter is reversed, this mixture of fundamental and overtones is superimposed in a completely different way, resulting in an artificial sound structure typical of loudspeakers. Superimposing a correctly poled 440 Hz oscillation with an inverted 7,040 Hz oscillation definitely results in a sum that differs significantly from the original. In the phase response, however, all these phenomena are invisible!<br />
 +
The fashionable term "time-corrected loudspeakers", which usually refers to a halfway linear phase response, basically says nothing at all.
 +
|}
  
  
 
<''zurück: [[Myroklopädie]]''><br />
 
<''zurück: [[Myroklopädie]]''><br />
 
<''zurück: [[Myro]]''>
 
<''zurück: [[Myro]]''>

Latest revision as of 13:01, 31 October 2020

Template:Delete candidate

The step response of a loudspeaker is generally associated with the aspect of time correctness. Although it is possible to mathematically extract the aspect time from the step response, as from any other signal, reducing the significance of the step response to this aspect misses the reality entirely. The step measurement is not a measurement of the time response. It is a measurement of the signal behavior. The graph of the step response relates the voltage values obtained from the sound pressure by the conversion by microphone to their temporal sequence in the same way as when using other signal forms or musical passages. Furthermore, the step response includes the frequency response of the transmission system, as well as all other extractable parameters. Not all parameters are optically differentiable, but they are still included. If you want to evaluate the behaviour of a loudspeaker at high volumes or under different dispersion angles, you can also do this with the help of the step response measurement.
The step response is therefore something like the genetic code of the loudspeaker. It shows how each cell ticks. The expert gets a clear indication of how this loudspeaker distorts all possible signals and sounds, because there is a clear correlation between the distortion of the step measurement and the distortion of all other signals/sounds.

The loudspeaker is an electroacoustic transducer. The elementary task of an electroacoustic transducer is to convert a signal structure fed to it into an equivalent sound structure. This includes frequency response linearity, low distortion, dynamics, phase response, impulse response, transient response, dispersion, etc. The step response of a loudspeaker describes its transmission behaviour and thus whether it performs this conversion correctly in principle. The basic requirement for the development of an electroacoustic transducer is thus defined. In addition, the electroacoustic transducer should generate the sound pressure required for its area of application and do so with as little distortion as possible. Furthermore, there is the requirement of a radiation pattern that is as uniform as possible. Not only quantitative aspects have to be considered. The quality of the sound radiated at different angles is also important. The quality (intelligibility) of the reflections depends on this. Therefore, the step response must also be measured in consideration of the radiation pattern.
The step response is not a typical parameter especially for a loudspeaker. It is a signal from control engineering and is used in any technical system to describe the behaviour between input and output.
It is a consensus among experts that the step response represents the transmission behaviour of a loudspeaker. Whether measured on axis, at an angle, from the rear or front, or inverted, it describes the transmission behaviour of loudspeakers more completely than any other test signal. It thus directly tells us how it sounds. Every slightest deviation from the ideal curve is an error, a non-linearity. One should take it seriously and know how to interpret it. Nevertheless, only a fraction of loudspeakers are capable of converting input signals into equivalent output signals (sound waves).
For other parameters, however, the following applies:

  • The frequency response on axis alone does not tell us how a speaker converts.

The frequency response under angle alone does not tell us how a loudspeaker converts. Group delay alone does not tell us how a loudspeaker performs. The linear and non-linear distortions alone do not tell us how a loudspeaker is transducing.

Ess series 450.jpg
ESS Connoisseur Series AMT 450'

Interpreting the transducer response of a loudspeaker from frequency and phase response is much less meaningful. This is due to the very assumptions and exclusions that underlie these measurement models. It is easy to prove with any signal shape / sound structure that a loudspeaker with a deformed step response also distorts other signals and that a loudspeaker with a step response very close to the ideal response also transforms any other signal very accurately. Our eardrum perceives a corresponding sound image due to these deviations in the pressure-time curve.

By far the greatest errors are made by loudspeakers when converting a dynamic signal structure. Errors and non-linearities that we recognize in a frequency response diagram are also reflected in the step response. Errors and nonlinearities that we see when measuring phase response or group delay are also reflected in the step response. And if we put enough energy into the step response, we will also see the compression and distortion of a transducer. By the way, this is also true for amplifiers. Here we can also see very well the intervention and the characteristics of protection circuits. But above all, the step response stands for the connecting, for the overall representation of many other measurements. A loudspeaker with a deformed step response never has a constant group delay or a uniform phase response. Furthermore, the step response is the only measurement signal that represents the transducer quality of a loudspeaker in a complex way and at the same time it is also relatively widespread. The step response is therefore ideally suited for the evaluation of the large number of loudspeaker models.

Kleine Elfe.jpg
Myro Little Elf'

Any professional knows that a speaker that converts properly is necessarily capable of a proper step response, that it can consequently also convert any input signal into the same output signal, whether a sine wave or any other waveform. And if the speaker can do this, and only then, it can properly convert a music signal. No loudspeaker that delivers a distorted step response is capable of input = output, that is, of reproducing music signals correctly, without distortion.
With a correctly shaped step response in the basic characteristic, one immediately recognizes the direct connection between frequency response linearity and shaping of the step response.
With a step response that is incorrectly shaped in the basic characteristic, the direct relationship between frequency response linearity and the shape of the step response is practically no longer recognizable, although it is presented here as well.

The step response has its uniform characteristic ONLY if:

  • the frequency response is linear on axis, whose border areas can also be seen very well. The same applies under angles.
  • the group delay is linear, or also the phase response.
  • the linear and non-linear distortions are minimal.

In the above cases, the reverse is not true! A linear frequency response does not indicate a correct step response. Neither does a uniform phase response. Thus "correct conversion" is not guaranteed! BUT: If the phase frequency response is correct (without phase rotations at the takeovers) and this not only in the steady state, but also in the transient state, then the step response is also correct, has the same linearity and thus also the correct basic characteristic (square wave over high and low pass filter).
Phase and amplitude interact, but the amplitude response can be improved even if the phase response deteriorates at the same time. (There are many examples of this in loudspeakers with 2nd or 3rd order filters etc.) This is the case when the measurement signal puts the loudspeaker in a steady state and the evaluations therefore only allow statements about this. For the step response, however, the phase in the transient, in the impulse dynamics, is important!

A short description can be found at the magazine Fairaudio about the step response and the impulse response.

Errors in the development of electroacoustic transducers mostly occur when the complex result of the step response is transferred into the mentioned differentiations and the developer develops further on this differentiated model level and optimizes his development object.
To improve the step response, the phase response and amplitude response must be improved together. Improving the amplitude response without improving the phase response, or more precisely the time relationships in the transient, does not improve the step response. Disregarding the correct polarity, for whatever reason, definitely leads to a wrong step response, to the wrong reproduction of transient response.

As a designer, you hear the sound responses of the loudspeaker during the measurement process and thus have a direct sound impression of what you can see on the screen. If you don't have this hearing experience, it takes some imagination to be able to imagine a sound formed from these sound waves. The loudspeaker delivers a sound similar in basic pattern every time it is stimulated with a signal. Anyone who was present during the measurement process would be able to hear this. The loudspeaker produces these transient noises in their characteristic typical of the loudspeaker regardless of whether we are listening to classical music, pop, rock or jazz over it or whether we want to listen to the soundtracks of films or understand the dialogues. It is easy to imagine, even for the layman, that the correct reproduction of vibrations results in fewer but distinct vibrations that are correct in their pitches. The sound image sounds clearer, more dynamic, less filled with artificial vibrations and more intelligible with a properly transducing speaker. There is a clear space between the tones and sounds, less filler, less distortion. The untrained listener would think it sounds thinner. But it doesn't in terms of energy content, only in terms of the nothingness between the tones! The comparison of a smeared, dusty disc with a freshly cleaned disc literally suggests itself here.
There are non-linearities in the transmission behaviour of loudspeakers, which basically result from the limited transmission bandwidth. These limits are also clearly visible in loudspeakers with largely correct step response.

Basically:

  • The tweeter determines the maximum slew rate of an impulse.

The synchronous transient of the tweeter with the midrange and woofer causes the full impulse dynamics. A bass drum, for example, sounds fast and crisp when all the drivers are in phase. The step response starts with the rise time of the tweeter. But the tweeter has its limit in the rise time and the energy that should actually be generated at the beginning is usually converted into sound with a slight delay. Then an exaggerated peak is produced. The low-frequency limitation of the transmission behaviour is noticeable in a more or less strong drop of the curve. If the curve drops steeply from the peak, the woofer can only develop the first half-wave in the bass range weakly. If the graph is flatter, this is more successful. Of course a loudspeaker should also show a decent step response under different listening angles. But to achieve this is a high art. A correct step response on the listening axis is, however, the absolute prerequisite for the correct conversion of the vibrations, the music.
Low, mid and high frequency drivers do not have any relevant immanent latency with regard to the temporal origin. And if it does exist, then the starting points must nevertheless be congruent in time. The maxima of envelopes are unsuitable for the evaluation of the time behaviour with regard to the impulses. That's why group running times only say something about the steady state. Also distorted (in itself deformed) wave groups can have the maximum of the envelope at the same point (e.g. if a wave propagating within the chassis or its surroundings comes back too short as a reflection and distorts the wave group, etc. typical non-linearities).
The transient processes (especially the impulses) can be distorted in a wave group and they are in "non-time-correct loudspeakers"! We are then dealing with energy shifts, e.g. from the first half-wave to the second and following half-waves, which do not necessarily have to affect the maximum, since there are other events, see reflections, which cause the maximum.

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Myro Spirit III

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Myro Amur D Black Diamond

The phase response[edit]

The frequency response is sometimes represented as a complex frequency response, which is used to represent the phase response. This phase response of a loudspeaker also describes the time relations in the steady state, but not the impulse behaviour. The time relations in the transient state differ considerably from the time relations in the steady state. Even loudspeakers with inverted drivers can have a uniform (steady-state) phase response. When measured in the steady state, even the polarity change that leads to complete distortion of the signal during transients is not to be seen as a phase rotation. The impulse reproduction is nevertheless faulty.
As always, you have to know exactly what the measurement conditions of a measurement procedure are in order to know what to read from it. Phase considerations presuppose that measurement points are defined within the measurement model in a fixed frequency bandwidth, which are set in relation to each other under the aspect of temporal shifts. The relationship between phase angle and frequency is what these measurement diagrams show us. The evaluation refers either to a steady state or to a quasi-static state. This also explains why no conclusions can be drawn about the output signal from the phase response, because it is always what is not shown to us that is interesting:

  • We don't know the model specifications regarding the definition of the reference points.
  • we have no information about the polarity, the amplitude
  • and therefore no clues about the sound structure.

In particular, the first half-waves of the transient, which determine to the highest degree the location and identification of a sound event, are not represented by phase measurements. The phase response related to the first half-waves would look completely different from the phase response related to subsequent half-waves. Therefore, there can be no phase response that is generally meaningful.
To interpret the transducer behaviour of a loudspeaker from frequency and phase response is much less meaningful than the step response. This is due to the assumptions and exclusions on which these measurement models are based.

Example:
The sound characteristics of instruments, in addition to their transient response, are determined primarily by a characteristic spectrum of fundamental tones and their multiples (overtones). For example, if the fundamental is at 440 Hz and the harmonics are at 880, 1,760, 3520, 7,040 Hz, etc., a sound pressure structure results from the superposition of these waves. If the polarity of the tweeter is reversed, this mixture of fundamental and overtones is superimposed in a completely different way, resulting in an artificial sound structure typical of loudspeakers. Superimposing a correctly poled 440 Hz oscillation with an inverted 7,040 Hz oscillation definitely results in a sum that differs significantly from the original. In the phase response, however, all these phenomena are invisible!
The fashionable term "time-corrected loudspeakers", which usually refers to a halfway linear phase response, basically says nothing at all.


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