Bildbereich

English translation: frequency domain

19:02 Nov 8, 2017
German to English translations [PRO]
Tech/Engineering - Mechanics / Mech Engineering
German term or phrase: Bildbereich
Da die Multiplikation im Bildbereich analog zur Differenziation im Zeitbereich ist, kann im Bildbereich für die DGL (9.1) eine Übertragungsfunktion ermittelt werden:
deutschenglisch
Local time: 02:07
English translation:frequency domain
Explanation:
I am sure, because I have obtained confirmation from a Math Wizard.

http://www.sinus-engineering.de/know-how/fachworterbuch/
Frequenzbereich (Bildbereich) > frequency domain

Zeitbereich und Frequenzbereich
https://www.ingenieurkurse.de/regelungstechnik/laplace-trans...
Wie Du ja bereits weißt, liegen bei den Berechnungen in der Regelungstechnik hauptsächlich Zeitfunktionen vor, weshalb man hier im Rahmen der LAPLACE-Transformation anstelle des Begriffes Originalbereich von einem Zeitbereich spricht. Gleiches gilt für den Bildbereich, dieser erhält den treffenderen Ersatzbegriff Frequenzbereich.

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Note added at 3 hrs (2017-11-08 22:15:22 GMT)
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https://ptolemy.eecs.berkeley.edu/eecs20/week12/multiplying....
We have seen that convolution in the time domain corresponds to multiplication in the frequency domain. It turns out that this relationship is symmetric, in that multiplication in the time domain corresponds to a peculiar form of convolution in the frequency domain

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Note added at 22 hrs (2017-11-09 17:23:09 GMT)
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@deutschenglish Thanks for letting me know that the EECS course is relevant. Any more info/details would help. Perhaps you could address Marcus on his Answer or in the Discussion, where he will be notified.
Selected response from:

Herbmione Granger
Germany
Local time: 03:07
Grading comment
Selected automatically based on peer agreement.
4 KudoZ points were awarded for this answer



Summary of answers provided
5 +2frequency domain
Herbmione Granger
5image
Marcus Malabad
5s domain (complex variable domain)
Johannes Gleim


Discussion entries: 15





  

Answers


14 hrs   confidence: Answerer confidence 5/5
s domain (complex variable domain)


Explanation:
"We have seen that convolution in the time domain corresponds to multiplication in the frequency domain" ist nicht das gleiche, sondern eine Laplace-Transformation, die auch bildlich anders aussieht.
Y(p) = Integral (y(t) e-pt) dt
(Leonhard, Einführung in die Regelungstechnik)

4.1 Impulsfunktion und Impulsantwort
:
Transformiert man die Anregungs- und Antwortfunktion des im Bild 4.1 gezeigten linearen System in den Bildbereich, so gilt für y(t) = δ(t)
L(δ(t)) = I · s
L(g(t) = G(p) = F(p) · 1 · s.
Die Bildfunkfunktion der Impulsantwort ist also, abgesehen von einem Dimensionsfaktor, gleich der Übertragungsfunktion.

range [MATH.] der Bildbereich Pl.: die Bildbereiche
complex variable domain [MATH.] der Bildbereich Pl.: die Bildbereiche
https://dict.leo.org/englisch-deutsch/bildbereich

frequency domain [MATH.][TECH.] der Frequenzbereich
https://dict.leo.org/englisch-deutsch/frequenzbereich

response function [TELEKOM.] die Antwortfunktion
transfer function [TELEKOM.] die Antwortfunktion
transmittance [TELEKOM.] die Antwortfunktion
https://dict.leo.org/englisch-deutsch/Antwortfunktion

impulse response [TELEKOM.] die Impulsantwort Pl.: die Impulsantworten
pulse response [ELEKT.] die Impulsantwort Pl.: die Impulsantworten
unit impulse response [TELEKOM.] die Impulsantwort Pl.: die Impulsantworten
https://dict.leo.org/englisch-deutsch/Impulsantwort


Definition der Variablen s
s = δ + j ω ist die unabhängige Variable im komplexen Frequenzbereich (Bildbereich, s-Bereich) mit δ als Realteil und j ω als Imaginärteil.

Für die Berechnung des Zeitverhaltens von Übertragungssystemen G(s) mit der Übertragungsfunktion müssen die Eingangssignale (Testsignale) im s-Bereich definiert werden.

Für die Berechnung der Sprungantwort eines Systems im Zeitbereich lautet der normierte Sprung 1(t) als Laplace-transformiertes Test-Eingangssignal U(s) = 1 / s.

Gesuchte Funktion im s-Bereich:
Y(s) = U( s) ⋅ (K ⋅ 1) / (T ⋅ s + 1) = (K ⋅ 1 s) / ( T ⋅ s + 1)

Zugehörige Funktion im Zeitbereich:
y( t ) = K ⋅ ( 1 − e − t / T )

Der Faktor K unterliegt nicht der Transformation und ist deshalb im s-Bereich wie auch im Zeitbereich gültig.
https://de.wikipedia.org/wiki/Regelungstechnik

There are two major divisions in control theory, namely, classical and modern, which have direct implications for the control engineering applications. The scope of classical control theory is limited to single-input and single-output (SISO) system design, except when analyzing for disturbance rejection using a second input. The system analysis is carried out in the time domain using differential equations, in the complex-s domain with the Laplace transform, or in the frequency domain by transforming from the complex-s domain. Many systems may be assumed to have a second order and single variable system response in the time domain.
;
The ultimate end goal is to meet requirements typically provided in the time-domain called the step response, or at times in the frequency domain called the open-loop response. The step response characteristics applied in a specification are typically percent overshoot, settling time, etc. The open-loop response characteristics applied in a specification are typically Gain and Phase margin and bandwidth.
:
Control engineering has diversified applications that include science, finance management, and even human behavior. Students of control engineering may start with a linear control system course dealing with the time and complex-s domain, which requires a thorough background in elementary mathematics and Laplace transform, called classical control theory. In linear control, the student does frequency and time domain analysis.
https://en.wikipedia.org/wiki/Control_engineering

Mathematical techniques for analyzing and designing control systems fall into two different categories:
• Frequency domain – In this type the values of the state variables, the mathematical variables representing the system's input, output and feedback are represented as functions of frequency. The input signal and the system's transfer function are converted from time functions to functions of frequency by a transform such as the Fourier transform, Laplace transform, or Z transform. The advantage of this technique is that it results in a simplification of the mathematics; the differential equations that represent the system are replaced by algebraic equations in the frequency domain which is much simpler to solve. However, frequency domain techniques can only be used with linear systems, as mentioned above.
• Time-domain state space representation – In this type the values of the state variables are represented as functions of time. With this model, the system being analyzed is represented by one or more differential equations. Since frequency domain techniques are limited to linear systems, time domain is widely used to analyze real-world nonlinear systems. Although these are more difficult to solve, modern computer simulation techniques such as simulation languages have made their analysis routine.
https://en.wikipedia.org/wiki/Control_theory#Analysis_techni...

In mathematics, the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace (/ləˈplɑːs/). It takes a function of a real variable t (often time) to a function of a complex variable s (frequency).
The Laplace transform is very similar to the Fourier transform. While the Fourier transform of a function is a complex function of a real variable (frequency), the Laplace transform of a function is a complex function of a complex variable.
:
Properties of the unilateral Laplace transform Time domain s domain Comment
:
Frequency-domain derivative tf(t) − F ′(s) F′ is the first derivative of F with respect to s.
https://en.wikipedia.org/wiki/Laplace_transform

"s-Domain equivalent circuits and impedances"
Anstelle von Laplace-Transformation können selbstverständlich auch andere Methoden zur Lösung von linearen DGL 1. Ordnung herbeigezogen werden
:
Ideale Spannungsquelle: v(t) = V·ε(t) (Einheitssprung)
Gesucht sei der Strom i(t). Die Masche liefert
v(t) = R·i(t) + L·i'(t)
°-• Transformation in den Bildbereich
http://www.uni-protokolle.de/foren/viewt/184198,0.html

What is the difference between the S domain and frequency domain in circuit analysis?
They are related. You’ll typically see s = j = j 2πf . Strictly this is only valid for steady-state signals. The full form is s = σ + j where the σ is a “transient response” term. This comes from Euler’s equation representing signals as e^( + j)t = e^t e^jt = e^t cos t.

Doing things in s instead of f allows certain simplifications such as being able to (complex) algebraically solve impedance circuits exactly the same way you solve resistor circuits (in terms of Thevenin/Norton reductions, parallel/series reductions, Ohm’s law, etc.) with simplified impedance terms like jsL and -js/C for inductors and capacitors. With fewer terms it’s more direct, less error-prone and more obvious algebra.

Thus because of the Laplace transform and using s you eliminate all the Ldi/dt and Cdv/dt terms (i.e. calculus) and replace them with complex algebra and eliminate the need for any time variables (in steady state).
https://www.quora.com/What-is-the-difference-between-the-S-d...

https://www.youtube.com/watch?v=crptDg_LC4U

Johannes Gleim
Local time: 03:07
Works in field
Native speaker of: Native in GermanGerman
PRO pts in category: 378
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2 hrs   confidence: Answerer confidence 5/5 peer agreement (net): +2
frequency domain


Explanation:
I am sure, because I have obtained confirmation from a Math Wizard.

http://www.sinus-engineering.de/know-how/fachworterbuch/
Frequenzbereich (Bildbereich) > frequency domain

Zeitbereich und Frequenzbereich
https://www.ingenieurkurse.de/regelungstechnik/laplace-trans...
Wie Du ja bereits weißt, liegen bei den Berechnungen in der Regelungstechnik hauptsächlich Zeitfunktionen vor, weshalb man hier im Rahmen der LAPLACE-Transformation anstelle des Begriffes Originalbereich von einem Zeitbereich spricht. Gleiches gilt für den Bildbereich, dieser erhält den treffenderen Ersatzbegriff Frequenzbereich.

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Note added at 3 hrs (2017-11-08 22:15:22 GMT)
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https://ptolemy.eecs.berkeley.edu/eecs20/week12/multiplying....
We have seen that convolution in the time domain corresponds to multiplication in the frequency domain. It turns out that this relationship is symmetric, in that multiplication in the time domain corresponds to a peculiar form of convolution in the frequency domain

--------------------------------------------------
Note added at 22 hrs (2017-11-09 17:23:09 GMT)
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@deutschenglish Thanks for letting me know that the EECS course is relevant. Any more info/details would help. Perhaps you could address Marcus on his Answer or in the Discussion, where he will be notified.

Herbmione Granger
Germany
Local time: 03:07
Native speaker of: Native in EnglishEnglish
PRO pts in category: 12
Grading comment
Selected automatically based on peer agreement.
Notes to answerer
Asker: plus points for referencing a UC Berkeley EECS course :)

Asker: Marcus you are going against some big guns here...please JUSTIFY your answer


Peer comments on this answer (and responses from the answerer)
agree  Annika Hogekamp
7 mins
  -> Thanks, Annika!

disagree  Johannes Gleim: Die Frage lautete: Wie übersetzt man Bildbereich? und nicht Frequenzbereich. Das kann man nicht gleichsetzen, auch wenn das manche tun. Nur ein Wörterbuch, das anderen zuverlässigen Quellen widerspricht (vereinfacht), sonst nur einsprachige Quellen.
12 hrs
  -> Interessant: https://www.proz.com/kudoz/german_to_english/electronics_ele...

agree  Lancashireman
13 hrs
  -> Thank you!

agree  Kim Metzger
15 hrs
  -> Thank you!

disagree  Marcus Malabad: Sorry this is wrong. The only thing you've done is cite an article where three words (convolution, frequency domain, multiplication) are co-located. Nothing more. No definitions, no A = B.
15 hrs
  -> That's interesting. The Math Wiz's doctoral dissertion was about Transformationen. BTW Bildbereich is Abbildung-Bereich.

agree  Harald 4711
2 days 2 mins
  -> Danke, Harald!
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18 hrs   confidence: Answerer confidence 5/5
image


Explanation:
Respectfully disagreeing with my colleagues above. This should be "image" as TonyT above writes (but just "image").

The operative word here is Übertragungsfunktion (transfer function). Transfer functions possess a domain (Bereich) and image (Bild).

A domain of a function is the set of input arguments which defines the function. A function's image is the output of the function from a subset of its domain. Set theory. Please google domain/image in the context of functions.

In German it's Definitionsbereich/Definitionsmenge (or just Bereich) and Bildbereich (or just Bild).

This should *NOT* be translated to 'domain'.

Your sentence:
Since the multiplication in the image is analogous to the differentiation in the time domain, a transfer function can be defined in the image for DGL.

In this context, image/Bild and time domain/Zeitbereich are sets of signals (referring to your other question).





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Note added at 1 day22 hrs (2017-11-10 17:15:28 GMT)
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Let us go back to the mathematics and math concepts in English and German since set theory is not your everyday subject.

A function is defined by its domain, codomain and image (or 'range' in some textbooks). A domain is a set of values that can go into a function. A codomain is a set of values that could come out of the function (output). An image is the set of values that are the actual output of the function.

Here's a very illustrative example:
https://www.mathsisfun.com/sets/domain-range-codomain.html

So, say, we have a set of values that we'll define as the domain:
A = {1, 2, 3} (where 1, 2, 3 are the x values that are inputted into our function)

Codomain:
B = {1, 2, 3, 4, 5, 6, 7, 8, 9}
(These are the possible values that could come out of our function)

Let's assume our function is:
f(x) = x2 (x to the second power)

So if we plug all our x values (from the domain) into our function we get:
I = {1, 4, 9}
This is the image of our function. The image being the actual output once the x values that we have are applied to our function. Notice that I is a subset of B (image is a subset of codomain) although it is possible for I = B (the image can also be a set equivalent to the codomain).

OK let's go to the German definitions:
"Statt Definitionsmenge A wird auch Definitionsbereich, Domain, Urbildmenge
oder schlicht Urbild gesagt. Insbesondere im Falle partieller Funktionen wird
zusätzlich von der Quellmenge gesprochen, diese heißt auch Quelle oder Source, salopp auch x ‐ Werte. Die Zielmenge B wird auch Wertemenge, Wertebereich, Codomain, Destination. Die Elemente von A heißen Funktionsargumente oder Urbilder, oder Target genannt, die Elemente von
B heißen Zielwerte oder Zielelemente, salopp auch y ‐ Werte. Funktionswerte,
Bildelemente oder schlicht Bilder heißen dagegen nur diejenigen Elemente von
B, die tatsächlich als Bild eines Arguments auftreten, die Menge der Funktionswerte heißt Bildmenge, Bild, Image oder Range von f.

(source: http://www.stksachs.uni-leipzig.de/tl_files/media/pdf/lehrbu...

So in the paragraph above even in German there are various terms used for these concepts. Let's look at the definition for Bild:

"Funktionswerte, Bildelemente oder schlicht Bilder heißen dagegen nur diejenigen Elemente von B, die tatsächlich als Bild eines Arguments auftreten, die Menge der Funktionswerte heißt Bildmenge, Bild, Image oder Range von f"

Translation:
Function values, image elements or just images are only those elements of B that actually come up as the image of an argument. The set of function values is called Bildmenge, Bild, Image oder Range von f".

This is exactly the definition of image. In the PDF above the author says there are several terms used for the same concept.

Here's a German math textbook that says that Bildmenge = Bildbereich = Bild (just as the Wikipedia article on Bild states):

https://books.google.com.ph/books?id=un_yCQAAQBAJ&pg=PT40&lp...

In no way is Bildbereich is any mathematical definition the same as "frequency domain". First of all why is there talk of frequency! And if it were a frequency domain then the German would be Frequenzbereich. Pulling out a reference where both words Bildbereich and Frequenzbereich are mentioned in the same article is not proof.

Rely on the definitions! I write confidently because I studied this in my advanced math courses. Math genius yeah right...let's invite the math genius to define the word in German. Sheesh

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Note added at 1 day22 hrs (2017-11-10 17:25:23 GMT)
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The first German reference came up erroneously:

http://www.stksachs.uni-leipzig.de/tl_files/media/pdf/lehrbu...

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Note added at 1 day22 hrs (2017-11-10 17:38:59 GMT)
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Ok so I had a look at the much-ballyhooed UBerkeley reference. The author mentions frequency domain and time domain because he's writing about *signals and frequencies*! And he has arrived at a similar conclusion as the asker's source author: there is a correlation between mathematical operations in two sets. The Berkeley author is writing about this correlation between two specific domains in his specific case with a specific function.

This is not proof that Bildbereich is frequency domain. If this is not clear to anyone, then I rest my case. Let this answer stand for future Kudoz askers.


    https://en.wikipedia.org/wiki/Image_(mathematics)
    https://de.wikipedia.org/wiki/Bild_(Mathematik)
Marcus Malabad
Canada
Local time: 03:07
Specializes in field
Native speaker of: Native in EnglishEnglish, Native in TagalogTagalog
PRO pts in category: 149

Peer comments on this answer (and responses from the answerer)
disagree  Lancashireman: If your answer is so obviously right, you don't need to vote down the alternatives. // Nothing to do with "hurt feelings". Let your own solution stand on its own merits. // The element of 'domain' (Bereich) is missing from this answer.
1 hr
  -> Voting down the alternatives, as you put it, must be done to arrive at the right answer and that is the only objective here. Hurt feelings are inconsequential

agree  Johannes Gleim: In no way is Bildbereich is any mathematical definition the same as "frequency domain", that's correct.
3 days 2 hrs
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