Applets:Linear Distortions of Periodic Signals - Revision history

Guenter at 15:16, 13 April 2023

2023-04-13T15:16:48Z

Guenter at 15:36, 10 April 2023

2023-04-10T15:36:22Z

Noah at 22:12, 26 March 2023

2023-03-26T22:12:21Z

Noah at 22:09, 26 March 2023

2023-03-26T22:09:15Z

Noah at 22:08, 26 March 2023

2023-03-26T22:08:45Z

Guenter at 14:30, 13 January 2023

2023-01-13T14:30:12Z

Javier: Text replacement - "„" to """

2021-05-28T14:45:47Z

Text replacement - "„" to """

Javier: Text replacement - "”" to """

2021-05-28T14:41:44Z

Text replacement - "”" to """

Guenter at 13:55, 6 February 2021

2021-02-06T13:55:50Z

Guenter at 13:52, 6 February 2021

2021-02-06T13:52:41Z

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 *'''Nonlinear distortions'''  occur, if at all times $t$ the nonlinear correlation $y = g(x) \ne {\rm const.}  \cdot x$ exists between the signal values $x = x(t)$ at the input and $y = y(t)$ at the output, whereby  $y = g(x)$ is defined as the system's nonlinear characteristic. By creating a cosine signal at the input with frequency $f_0$ the output signal includes  $f_0$, as well as  multiple harmonic waves. We conclude that new frequencies arise through nonlinear distortion.
-[[File:EN_LZI_T_2_2_S3.png|center|frame|For clarification of nonlinear distortions |class=fit]]
+[[File:EN_LZI_T_2_2_S3_v2.png|center|frame|For clarification of nonlinear distortions |class=fit]]
 [[File:P_ID899__LZI_T_2_3_S1_neu.png|right |frame| Description of a linear system|class=fit]]

@@ Line 44: / Line 44: @@
 *'''Nonlinear distortions'''  occur, if at all times $t$ the nonlinear correlation $y = g(x) \ne {\rm const.}  \cdot x$ exists between the signal values $x = x(t)$ at the input and $y = y(t)$ at the output, whereby  $y = g(x)$ is defined as the system's nonlinear characteristic. By creating a cosine signal at the input with frequency $f_0$ the output signal includes  $f_0$, as well as  multiple harmonic waves. We conclude that new frequencies arise through nonlinear distortion.
-[[File:LZI_T_2_2_S3_vers2.png|center|frame|For clarification of nonlinear distortions |class=fit]]
+[[File:EN_LZI_T_2_2_S3.png|center|frame|For clarification of nonlinear distortions |class=fit]]
 [[File:P_ID899__LZI_T_2_3_S1_neu.png|right |frame| Description of a linear system|class=fit]]

@@ Line 67: / Line 67: @@
 *The '''phase function''' $b(f)$ indicates the negative frequency&ndash;dependent angle of $H(f)$ in the complex plane based on the real axis:
 :$$b(f) = - {\rm arc} \hspace{0.1cm}H(f) \hspace{0.2cm}{\rm in
-\hspace{0.1cm}Radian \hspace{0.1cm}(rad)}.$$
+\hspace{0.1cm}Radians \hspace{0.1cm}(rad)}.$$

@@ Line 93: / Line 93: @@
 The frequency response of a realizable high&ndash;pass  (HP) of order $N$ is:
 :$$H(f) = \left [\frac{ {\rm j}\cdot f/f_0 }{1 + {\rm j}\cdot f/f_0 }\right ]^N\hspace{0.05cm}.$$
-For example the LC high pass is a first order high pass. Consequently we can obtain
+For example the LC high-pass is a first order high-pass. Consequently we can obtain
 *the attenuation function:
 :$$a(f) =N/2 \cdot \ln  [1+( f_0/f)^2] \hspace{0.05cm},$$

@@ Line 14: / Line 14: @@
-The next block in the model above is ''Matching'': The output signal $y(t)$ is adjusted in amplitude and phase with equal quantities $k_{\rm M}$ and $\tau_{\rm M}$ for all frequencies which means that this is not a frequency-dependent equalization. Using the signal $z(t)$, one can differentiate between:
+The next block in the model above is ''Matching'': The output signal $y(t)$ is adjusted in amplitude and phase with equal variables $k_{\rm M}$ and $\tau_{\rm M}$ for all frequencies which means that this is not a frequency-dependent equalization. Using the signal $z(t)$, one can differentiate between:
-*attenuation distortion and frequency&ndash;independant attenuation, as well as
+*attenuation distortion and frequency&ndash;independent attenuation, as well as
-*phase distortion and frequency&ndash;independant delay.
+*phase distortion and frequency&ndash;independent delay.
@@ Line 109: / Line 109: @@
 {{GraueBox|TEXT=
 $\text{Example:}$&nbsp;
-This graphic shows the phase function $b(f)$ with the cut&ndash;off frequency $f_0 = 1\ \rm kHz$ and order $N=1$
+This graphic shows the phase function $b(f)$ with the cutoff frequency $f_0 = 1\ \rm kHz$ and order $N=1$
 * of a low&ndash;pass (green curve),
 * of a high&ndash;pass (violet curve).
@@ Line 127: / Line 127: @@
-''Remark:'' The shown signals were created using the interactive applet [[Applets:Kausale_Systeme_-_Laplacetransformation|Causal systems &ndash; Laplace transform]]. }}
+''Remark:'' The shown signals were created using the interactive applet [[Applets:Kausale_Systeme_-_Laplacetransformation|"Causal systems &ndash; Laplace transform"]]. }}
 === Attenuation and Phase Distortions  ===
@@ Line 293: / Line 293: @@
 &nbsp; &nbsp; '''(C)''' &nbsp; &nbsp; Selction of channel parameters per slider: Dämpfungsfaktoren und Phasenlaufzeiten
-&nbsp; &nbsp; '''(D)''' &nbsp; &nbsp; Selection of channel parameters for High and Low pass: Order$n$, cut-off-frequency $f_0$
+&nbsp; &nbsp; '''(D)''' &nbsp; &nbsp; Selection of channel parameters for High and Low pass: Order$n$, cutoff frequency $f_0$
 &nbsp; &nbsp; '''(E)''' &nbsp; &nbsp; Selection of matching parameters $k_{\rm M}$ and $\varphi_{\rm M}$

← Older revision		Revision as of 14:30, 13 January 2023
Line 1:		Line 1:
−	{{~~LntAppletLinkEn~~\|~~linDistortions_en~~}}         [https://~~www~~.lntwww.de/Applets:~~Lineare_Verzerrungen_periodischer_Signale~~ '''English Applet with ~~German~~ WIKI description''']	+	{{LntAppletLink\|physAnSignal_en}}         [https://en.lntwww.de/Applets:Physical_Signal_%26_Analytic_Signal '''English Applet with English WIKI description''']

	==Applet Description==		==Applet Description==

@@ Line 163: / Line 163: @@
 *An exercise description is displayed.
 *Parameter values are adjusted to the respective exercises.
-*Click &bdquo;Hide solution" to display the solution.
+*Click "Hide solution" to display the solution.
-Number &bdquo;0" is a &bdquo;Reset" button:
+Number "0" is a "Reset" button:
 *Sets parameters to initial values (when loading the page).
-*Displays a &bdquo;Reset text" to describe the applet further.
+*Displays a "Reset text" to describe the applet further.
@@ Line 313: / Line 313: @@
 &nbsp; &nbsp; '''(M)''' &nbsp; &nbsp; Variation possibilities for the graphic display
-$\hspace{1.5cm}$Zoom&ndash;functions &bdquo;$+$" (scale up), &bdquo;$-$" (scale down) und $\rm o$ (reset)
+$\hspace{1.5cm}$Zoom&ndash;functions "$+$" (scale up), "$-$" (scale down) und $\rm o$ (reset)
-$\hspace{1.5cm}$Move with &bdquo;$\leftarrow$" (section to the left, ordinate to the right),  &bdquo;$\uparrow$" &bdquo;$\downarrow$" und &bdquo;$\rightarrow$"
+$\hspace{1.5cm}$Move with "$\leftarrow$" (section to the left, ordinate to the right),  "$\uparrow$" "$\downarrow$" und "$\rightarrow$"
 $\hspace{1.5cm}$'''Other options'':
@@ Line 325: / Line 325: @@
 ==About the Authors==
 This interactive calculation was designed and realized at the [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik] of the [https://www.tum.de/ Technische Universität München].
-*The original version was created in 2005 by [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Bettina_Hirner_.28Diplomarbeit_LB_2005.29|Bettina Hirner]] as part of her Diploma thesis using &bdquo;FlashMX&ndash;Actionscript" (Supervisor: [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]] ).
+*The original version was created in 2005 by [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Bettina_Hirner_.28Diplomarbeit_LB_2005.29|Bettina Hirner]] as part of her Diploma thesis using "FlashMX&ndash;Actionscript" (Supervisor: [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]] ).
-*In 2018 this Applet was redesigned and updated to &bdquo;HTML5" by [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Jimmy_He_.28Bachelorarbeit_2018.29|Jimmy He]] as part of his Bachelor's thesis (Supervisor: [[Biographies_and_Bibliographies/Beteiligte_der_Professur_Leitungsgebundene_%C3%9Cbertragungstechnik#Tasn.C3.A1d_Kernetzky.2C_M.Sc._.28bei_L.C3.9CT_seit_2014.29|Tasnád Kernetzky]]) .
+*In 2018 this Applet was redesigned and updated to "HTML5" by [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Jimmy_He_.28Bachelorarbeit_2018.29|Jimmy He]] as part of his Bachelor's thesis (Supervisor: [[Biographies_and_Bibliographies/Beteiligte_der_Professur_Leitungsgebundene_%C3%9Cbertragungstechnik#Tasn.C3.A1d_Kernetzky.2C_M.Sc._.28bei_L.C3.9CT_seit_2014.29|Tasnád Kernetzky]]) .
 ==Once again: Open Applet in new Tab==
 {{LntAppletLinkEn|linDistortions_en}} &nbsp; &nbsp; &nbsp; &nbsp; [https://www.lntwww.de/Applets:Lineare_Verzerrungen_periodischer_Signale '''English Applet with German WIKI description''']

← Older revision		Revision as of 13:55, 6 February 2021
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	The ''Distortion Power'' $P_{\rm D}$ is used to measure the strength of the linear distortion and is defined as:		The ''Distortion Power'' $P_{\rm D}$ is used to measure the strength of the linear distortion and is defined as:
	:$$P_{\rm D} = \min_{k_{\rm M}, \ \tau_{\rm M}} P_\varepsilon.$$		:$$P_{\rm D} = \min_{k_{\rm M}, \ \tau_{\rm M}} P_\varepsilon.$$
−
−	~~[[Applets:Lineare_Verzerrungen_periodischer_Signale\|'''German description''']]~~

@@ Line 1: / Line 1: @@
-{{LntAppletLinkEn|linDistortions_en}} &nbsp; &nbsp; &nbsp; &nbsp; [https://www.lntwww.de/Applets:Lineare_Verzerrungen_periodischer_Signale '''Englisches Applet mit englischer WIKI–Beschreibung''']
+{{LntAppletLinkEn|linDistortions_en}} &nbsp; &nbsp; &nbsp; &nbsp; [https://www.lntwww.de/Applets:Lineare_Verzerrungen_periodischer_Signale '''English Applet with German WIKI description''']
 ==Applet Description==
@@ Line 332: / Line 332: @@
 ==Once again: Open Applet in new Tab==
-{{LntAppletLinkEn|linDistortions_en}} &nbsp; &nbsp; &nbsp; &nbsp; [https://www.lntwww.de/Applets:Lineare_Verzerrungen_periodischer_Signale '''Englisches Applet mit englischer WIKI–Beschreibung''']
+{{LntAppletLinkEn|linDistortions_en}} &nbsp; &nbsp; &nbsp; &nbsp; [https://www.lntwww.de/Applets:Lineare_Verzerrungen_periodischer_Signale '''English Applet with German WIKI description''']