Applets:The Doppler Effect - Revision history

Maintenance script: Join split $$ formula lines for correct rendering

2026-03-16T13:49:05Z

Join split $$ formula lines for correct rendering

← Older revision		Revision as of 15:49, 16 March 2026
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	'''(1)'''  According to the exact, relativistic first equation:		'''(1)'''  According to the exact, relativistic first equation:
	:$$f_{\rm E} = f_{\rm S} \cdot \frac{\sqrt{1 - (v/c)^2} }{1 - v/c }		:$$f_{\rm E} = f_{\rm S} \cdot \frac{\sqrt{1 - (v/c)^2} }{1 - v/c }\hspace{0.3cm} \Rightarrow \hspace{0.3cm} f_{\rm D} = f_{\rm E} - f_{\rm S} = f_{\rm S} \cdot \left [ \frac{\sqrt{1 - (v/c)^2} }{1 - v/c } - 1 \right ]\hspace{0.3cm}\Rightarrow \hspace{0.3cm}{f_{\rm D} }/{f_{\rm S} } = \frac{\sqrt{1 - (v/c)^2} }{1 - v/c } - 1 \hspace{0.05cm}.$$
	\hspace{0.3cm} \Rightarrow \hspace{0.3cm} f_{\rm D} = f_{\rm E} - f_{\rm S} = f_{\rm S} \cdot \left [ \frac{\sqrt{1 - (v/c)^2} }{1 - v/c } - 1 \right ]\hspace{0.3cm}
	\Rightarrow \hspace{0.3cm}{f_{\rm D} }/{f_{\rm S} } = \frac{\sqrt{1 - (v/c)^2} }{1 - v/c } - 1 \hspace{0.05cm}.$$

	:$$\Rightarrow\hspace{0.3cm}v_1/c = 0.6\text{:}\hspace{0.5cm}{f_{\rm D} }/{f_{\rm S} } = \frac{\sqrt{1 - 0.6^2} }{1 - 0.6 } - 1 = \frac{0.8}{0.4 } - 1 = 1		:$$\Rightarrow\hspace{0.3cm}v_1/c = 0.6\text{:}\hspace{0.5cm}{f_{\rm D} }/{f_{\rm S} } = \frac{\sqrt{1 - 0.6^2} }{1 - 0.6 } - 1 = \frac{0.8}{0.4 } - 1 = 1\hspace{0.3cm}\Rightarrow\hspace{0.3cm} {f_{\rm E} }/{f_{\rm S} } = 2\hspace{0.05cm}.$$
	\hspace{0.3cm}\Rightarrow\hspace{0.3cm} {f_{\rm E} }/{f_{\rm S} } = 2
	\hspace{0.05cm}.$$

	:$$\Rightarrow\hspace{0.3cm}v_2/c = 10^{\rm -5}\text{:}\hspace{0.5cm}{f_{\rm D} }/{f_{\rm S} } = \frac{\sqrt{1 - (10^{-5})^2} }{1 - (10^{-5}) } - 1 \approx 1 + 10^{-5} - 1 = 10^{-5} \hspace{0.3cm}\Rightarrow\hspace{0.3cm} {f_{\rm E} }/{f_{\rm S} } = 1.00001		:$$\Rightarrow\hspace{0.3cm}v_2/c = 10^{\rm -5}\text{:}\hspace{0.5cm}{f_{\rm D} }/{f_{\rm S} } = \frac{\sqrt{1 - (10^{-5})^2} }{1 - (10^{-5}) } - 1 \approx 1 + 10^{-5} - 1 = 10^{-5} \hspace{0.3cm}\Rightarrow\hspace{0.3cm} {f_{\rm E} }/{f_{\rm S} } = 1.00001\hspace{0.05cm}.$$
	\hspace{0.05cm}.$$

	:$$\Rightarrow\hspace{0.3cm}v_3/c = 10^{\rm -7}\text{:}\hspace{0.5cm}{f_{\rm D} }/{f_{\rm S} } = \frac{\sqrt{1 - (10^{-7})^2} }{1 - (10^{-7}) } - 1 \approx 1 + 10^{-7} - 1 = 10^{-7} \hspace{0.3cm}\Rightarrow\hspace{0.3cm} {f_{\rm E} }/{f_{\rm S} } = 1.0000001		:$$\Rightarrow\hspace{0.3cm}v_3/c = 10^{\rm -7}\text{:}\hspace{0.5cm}{f_{\rm D} }/{f_{\rm S} } = \frac{\sqrt{1 - (10^{-7})^2} }{1 - (10^{-7}) } - 1 \approx 1 + 10^{-7} - 1 = 10^{-7} \hspace{0.3cm}\Rightarrow\hspace{0.3cm} {f_{\rm E} }/{f_{\rm S} } = 1.0000001\hspace{0.05cm}.$$
	\hspace{0.05cm}.$$

	'''(2)'''  On the other hand, according to the approximation, i.e. without taking into account the theory of relativity:		'''(2)'''  On the other hand, according to the approximation, i.e. without taking into account the theory of relativity:
	:$$f_{\rm E} = f_{\rm S} \cdot \big [ 1 + {v}/{c} \big ]		:$$f_{\rm E} = f_{\rm S} \cdot \big [ 1 + {v}/{c} \big ]\Rightarrow \hspace{0.3cm}{f_{\rm D} }/{f_{\rm S} } = {v}/{c} \hspace{0.05cm}.$$
	\Rightarrow \hspace{0.3cm}{f_{\rm D} }/{f_{\rm S} } = {v}/{c} \hspace{0.05cm}.$$

	:$$\Rightarrow\hspace{0.3cm}v_1/c = 0.6\text{:}\hspace{0.7cm} f_{\rm D}/f_{\rm S} \ \ = \ 0.6 \hspace{0.5cm} ⇒ \ \ \ f_{\rm E}/f_{\rm S} = 1.6,$$		:$$\Rightarrow\hspace{0.3cm}v_1/c = 0.6\text{:}\hspace{0.7cm} f_{\rm D}/f_{\rm S} \ \ = \ 0.6 \hspace{0.5cm} ⇒ \ \ \ f_{\rm E}/f_{\rm S} = 1.6,$$
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	'''(1)'''  According to the exact, relativistic first equation with  ${\rm cos}(\alpha) = -1$:		'''(1)'''  According to the exact, relativistic first equation with  ${\rm cos}(\alpha) = -1$:

	:$$f_{\rm E} = f_{\rm S} \cdot \frac{\sqrt{1 - (v/c)^2} }{1 + v/c }		:$$f_{\rm E} = f_{\rm S} \cdot \frac{\sqrt{1 - (v/c)^2} }{1 + v/c }\hspace{0.3cm} \Rightarrow \hspace{0.3cm} f_{\rm D} = f_{\rm E} - f_{\rm S} = f_{\rm S} \cdot \left [ \frac{\sqrt{1 - (v/c)^2} }{1 + v/c } - 1 \right ] \hspace{0.3cm} \Rightarrow \hspace{0.3cm}{f_{\rm D} }/{f_{\rm S} } = \frac{\sqrt{1 - (v/c)^2} }{1 + v/c } - 1 \hspace{0.05cm}.$$
	\hspace{0.3cm} \Rightarrow \hspace{0.3cm} f_{\rm D} = f_{\rm E} - f_{\rm S} = f_{\rm S} \cdot \left [ \frac{\sqrt{1 - (v/c)^2} }{1 + v/c } - 1 \right ] \hspace{0.3cm} \Rightarrow \hspace{0.3cm}{f_{\rm D} }/{f_{\rm S} } = \frac{\sqrt{1 - (v/c)^2} }{1 + v/c } - 1 \hspace{0.05cm}.$$

	:$$\Rightarrow\hspace{0.3cm}v_1/c = 0.6\text{:}\hspace{0.5cm}{f_{\rm D} }/{f_{\rm S} } = \frac{\sqrt{1 - 0.6^2} }{1 + 0.6 } - 1 = \frac{0.8}{1.6 } - 1 =-0.5		:$$\Rightarrow\hspace{0.3cm}v_1/c = 0.6\text{:}\hspace{0.5cm}{f_{\rm D} }/{f_{\rm S} } = \frac{\sqrt{1 - 0.6^2} }{1 + 0.6 } - 1 = \frac{0.8}{1.6 } - 1 =-0.5\hspace{0.3cm}\Rightarrow\hspace{0.3cm} {f_{\rm E} }/{f_{\rm S} } = 0.5\hspace{0.05cm}.$$
	\hspace{0.3cm}\Rightarrow\hspace{0.3cm} {f_{\rm E} }/{f_{\rm S} } = 0.5
	\hspace{0.05cm}.$$

	:$$\Rightarrow\hspace{0.3cm}v_2/c = 10^{\rm -5}\text{:}\hspace{0.5cm}{f_{\rm D} }/{f_{\rm S} } = \frac{\sqrt{1 - (10^{-5})^2} }{1 + (10^{-5}) } - 1 \approx - 10^{-5}		:$$\Rightarrow\hspace{0.3cm}v_2/c = 10^{\rm -5}\text{:}\hspace{0.5cm}{f_{\rm D} }/{f_{\rm S} } = \frac{\sqrt{1 - (10^{-5})^2} }{1 + (10^{-5}) } - 1 \approx - 10^{-5}\hspace{0.3cm}\Rightarrow\hspace{0.3cm} {f_{\rm E} }/{f_{\rm S} } = 0.99999\hspace{0.05cm}.$$
	\hspace{0.3cm}\Rightarrow\hspace{0.3cm} {f_{\rm E} }/{f_{\rm S} } = 0.99999
	\hspace{0.05cm}.$$
	'''(2)'''  On the other hand, according to the approximation, i.e. without taking into account the theory of relativity:		'''(2)'''  On the other hand, according to the approximation, i.e. without taking into account the theory of relativity:
	:$$f_{\rm E} = f_{\rm S} \cdot \big [ 1 - {v}/{c} \big ] \hspace{0.3cm}		:$$f_{\rm E} = f_{\rm S} \cdot \big [ 1 - {v}/{c} \big ] \hspace{0.3cm}\Rightarrow \hspace{0.3cm}{f_{\rm D} }/{f_{\rm S} } = - {v}/{c} \hspace{0.05cm}.$$
	\Rightarrow \hspace{0.3cm}{f_{\rm D} }/{f_{\rm S} } = - {v}/{c} \hspace{0.05cm}.$$

	:$$\Rightarrow\hspace{0.3cm}v_1/c = 0.6\text{:}\hspace{0.7cm} f_{\rm D}/f_{\rm S} \ \underline {= \ 0.6} \ \ \ ⇒ \ \ \ f_{\rm E}/f_{\rm S} = 0.4,$$		:$$\Rightarrow\hspace{0.3cm}v_1/c = 0.6\text{:}\hspace{0.7cm} f_{\rm D}/f_{\rm S} \ \underline {= \ 0.6} \ \ \ ⇒ \ \ \ f_{\rm E}/f_{\rm S} = 0.4,$$
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	==About the Authors==		==About the Authors==
	This interactive calculation tool was designed and implemented at the  [https://www.ei.tum.de/en/lnt/home/ Institute for Communications Engineering]  at the  [https://www.tum.de/en Technical University of Munich].		This interactive calculation tool was designed and implemented at the  [https://www.ei.tum.de/en/lnt/home/ Institute for Communications Engineering]  at the  [https://www.tum.de/en Technical University of Munich].
	*The first version was created in 2009 by [[Biographies_and_Bibliographies/~~An_LNTwww_beteiligte_Studierende~~#Alexander_Happach_.28Diplomarbeit_EI_2009.29\|Alexander Happach]] as part of his diploma thesis with “FlashMX – 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 first version was created in 2009 by [[Biographies_and_Bibliographies/Students_involved_in_LNTwww#Alexander_Happach_.28Diplomarbeit_EI_2009.29\|Alexander Happach]] as part of his diploma thesis with “FlashMX – Actionscript” (Supervisor: [[Biographies_and_Bibliographies/LNTwww_members_from_LNT#Prof._Dr.-Ing._habil._Günter_Söder_(at_LNT_from_1974-2024)\|Günter Söder]]).
	*In 2020 the program was redesigned by [[Biographies_and_Bibliographies/~~An_LNTwww_beteiligte_Studierende~~#Andr.C3.A9_Schulz_.28Bachelorarbeit_LB_2020.29\|André Schulz]] (Bachelor thesis LB, Supervisors: [[Biographies_and_Bibliographies/~~Beteiligte_der_Professur_Leitungsgebundene_Übertragungstechnik~~#Benedikt_Leible.2C_M.Sc._.28bei_L.C3.9CT_seit_2017.29\|Benedikt Leible]] and [[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]] ) via "HTML5".		*In 2020 the program was redesigned by [[Biographies_and_Bibliographies/Students_involved_in_LNTwww#Andr.C3.A9_Schulz_.28Bachelorarbeit_LB_2020.29\|André Schulz]] (Bachelor thesis LB, Supervisors: [[Biographies_and_Bibliographies/LNTwww_members_from_LÜT#Benedikt_Leible.2C_M.Sc._.28bei_L.C3.9CT_seit_2017.29\|Benedikt Leible]] and [[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]] ) via "HTML5".

	==Once again: Open Applet in new Tab==		==Once again: Open Applet in new Tab==
	{{LntAppletLinkEnDe\|dopplereffect_en\|dopplereffect}}		{{LntAppletLinkEnDe\|dopplereffect_en\|dopplereffect}}

Noah at 21:05, 26 March 2023

2023-03-26T21:05:52Z

← Older revision		Revision as of 23:05, 26 March 2023
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	{{BlaueBox\|TEXT=		{{BlaueBox\|TEXT=
	$\text{Definition:}$  The  $\rm Doppler effect$  is the change in the perceived frequency of waves of any kind that occurs when the source (transmitter) and observer (receiver) move relative to each other. This was theoretically predicted by the Austrian mathematician, physicist and astronomer  [https://en.wikipedia.org/wiki/Christian_Doppler Christian Andreas Doppler]  in the middle of the 19th century and named after him.}}		$\text{Definition:}$  The  $\rm Doppler\:effect$  is the change in the perceived frequency of waves of any kind that occurs when the source (transmitter) and observer (receiver) move relative to each other. This was theoretically predicted by the Austrian mathematician, physicist and astronomer  [https://en.wikipedia.org/wiki/Christian_Doppler "Christian Andreas Doppler"]  in the middle of the 19th century and named after him.}}


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	*The graphics in  $\text{Example 3}$  apply to the unrealistically high speed  $v = c/5 = 60000\, {\rm km/s}$, which lead to the Doppler frequencies $f_{\rm D} = \pm 0.2\cdot f_{\rm S}$.		*The graphics in  $\text{Example 3}$  apply to the unrealistically high speed  $v = c/5 = 60000\, {\rm km/s}$, which lead to the Doppler frequencies $f_{\rm D} = \pm 0.2\cdot f_{\rm S}$.

	*In the case of mobile communications, the deviations between $f_{\rm S}$  and $f_{\rm E}$  are usually only a fraction of the transmission frequency.  At such realistic velocities  $(v \ll c)$  one can start from the following approximation, which does not take into account the effects described by the [https://en.wikipedia.org/wiki/Theory_of_relativity ~~Theory~~ of Relativity]:		*In the case of mobile communications, the deviations between $f_{\rm S}$  and $f_{\rm E}$  are usually only a fraction of the transmission frequency.  At such realistic velocities  $(v \ll c)$  one can start from the following approximation, which does not take into account the effects described by the [https://en.wikipedia.org/wiki/Theory_of_relativity "theory of Relativity"]:
	::<math>f_{\rm E} \approx f_{\rm S} \cdot \big [1 +{v}/{c} \cdot \cos(\alpha) \big ] \hspace{0.3cm} \Rightarrow \hspace{0.3cm}{\text{ Approach}}\hspace{0.05cm}.</math>		::<math>f_{\rm E} \approx f_{\rm S} \cdot \big [1 +{v}/{c} \cdot \cos(\alpha) \big ] \hspace{0.3cm} \Rightarrow \hspace{0.3cm}{\text{ Approach}}\hspace{0.05cm}.</math>

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	Outside the range between  $-f_{\rm D}$  and  $+f_{\rm D}$ , the probability density function is always zero.		Outside the range between  $-f_{\rm D}$  and  $+f_{\rm D}$ , the probability density function is always zero.

	[[Mobile_Communications/~~Statistische_Bindungen_innerhalb_des_Rayleigh-Prozesses~~#~~Dopplerfrequenz_und_deren_Verteilung~~\|$\text{Derivation}$]]  about the “nonlinear transformation of random quantities”.}}<br>		[[Mobile_Communications/Statistical_Bindings_within_the_Rayleigh_Process#Doppler_frequency_and_its_distribution\|$\text{"Derivation"}$]]  about the “nonlinear transformation of random quantities”.}}<br>


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	\hspace{0.05cm}.</math>		\hspace{0.05cm}.</math>

	This course is called  '''Jakes spectrum'''  named after  [http://ethw.org/William_C._Jakes,_Jr. William C. Jakes Jr.].  The doubling is necessary, because so far only the contribution of the real part  $x(t)$  has been considered.<br>		This course is called  '''Jakes spectrum'''  named after  [http://ethw.org/William_C._Jakes,_Jr. "William C. Jakes Jr."].  The doubling is necessary, because so far only the contribution of the real part  $x(t)$  has been considered.<br>

	[[File:P_ID2117__Mob_T_1_3_S4_v2.png\|right\|frame\|Doppler PDS and time function (magnitude in dB) for Rayleigh fading with Doppler effect]]		[[File:P_ID2117__Mob_T_1_3_S4_v2.png\|right\|frame\|Doppler PDS and time function (magnitude in dB) for Rayleigh fading with Doppler effect]]
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	In the  [[Examples_of_Communication_Systems/~~Allgemeine_Beschreibung_von_GSM~~#~~Zellularstruktur_von_GSM~~\|GSM–D network]]  $(f_{\rm S} = 900 \ \rm MHz)$  these values correspond to the speeds  $v = 60 \ \rm km/h$  and  $v = 120 \ \rm km/h$  respectively.		In the  [[Examples_of_Communication_Systems/General_Description_of_GSM#Cellular_structure_of_GSM\|"GSM–D network"]]  $(f_{\rm S} = 900 \ \rm MHz)$  these values correspond to the speeds  $v = 60 \ \rm km/h$  and  $v = 120 \ \rm km/h$  respectively.

	For the GSM–E network $(f_{\rm S} = 1.8 \ \rm GHz)$  these values apply to speeds that are half as high:   $v = 30 \ \rm km/h$  and  $v = 60 \ \rm km/h$  respectively.		For the GSM–E network $(f_{\rm S} = 1.8 \ \rm GHz)$  these values apply to speeds that are half as high:   $v = 30 \ \rm km/h$  and  $v = 60 \ \rm km/h$  respectively.

Hwang at 16:08, 23 January 2023

2023-01-23T16:08:23Z

← Older revision		Revision as of 18:08, 23 January 2023
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	=== Doppler frequency and its distribution===		=== Doppler frequency and its distribution===

	We briefly summarize the statements on the last ~~page~~, while we proceed with the second, the non – relativistic equation:		We briefly summarize the statements in the last section, while we proceed with the second, the non – relativistic equation:
	*A relative movement between transmitter (source) and receiver (observer) results in a shift by the Doppler frequency  $f_{\rm D} = f_{\rm E} - f_{\rm S}$.		*A relative movement between transmitter (source) and receiver (observer) results in a shift by the Doppler frequency  $f_{\rm D} = f_{\rm E} - f_{\rm S}$.

Hwang at 01:10, 19 September 2022

2022-09-19T01:10:38Z

← Older revision		Revision as of 03:10, 19 September 2022
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	For the GSM–E network $(f_{\rm S} = 1.8 \ \rm GHz)$  these values apply to speeds that are half as high:   $v = 30 \ \rm km/h$  and  $v = 60 \ \rm km/h$  respectively.		For the GSM–E network $(f_{\rm S} = 1.8 \ \rm GHz)$  these values apply to speeds that are half as high:   $v = 30 \ \rm km/h$  and  $v = 60 \ \rm km/h$  respectively.

	The right picture shows the logarithmic ~~amount~~ of  $z(t)$:		The right picture shows the logarithmic magnitude of  $z(t)$:
	*You can see that the red curve is fading twice as fast as the blue one.		*You can see that the red curve is fading twice as fast as the blue one.
	*The Rayleigh – PDF (amplitude distribution) is independent of  $f_{\rm D, \hspace{0.05cm} max}$  and is therefore the same for both cases.}}<br>		*The Rayleigh – PDF (amplitude distribution) is independent of  $f_{\rm D, \hspace{0.05cm} max}$  and is therefore the same for both cases.}}<br>

Javier: Text replacement - "„" to """

2021-05-28T14:40:19Z

Text replacement - "„" to """

← Older revision		Revision as of 16:40, 28 May 2021
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	:* As in  $(6)$, only values between $f_{\rm D}=0.4$  and  $f_{\rm D}=-0.4$  are possible, but now all intermediate values $(-0.4 \le f_{\rm D} \le +0.4)$.		:* As in  $(6)$, only values between $f_{\rm D}=0.4$  and  $f_{\rm D}=-0.4$  are possible, but now all intermediate values $(-0.4 \le f_{\rm D} \le +0.4)$.
	:* With ~~&bdquo;~~Step" you can see:  $f_{\rm D}\equiv0$  only occurs if the receiver is exactly below the transmitter $(\alpha=\pm 90^\circ$, depending on the direction of travel$)$.		:* With "Step" you can see:  $f_{\rm D}\equiv0$  only occurs if the receiver is exactly below the transmitter $(\alpha=\pm 90^\circ$, depending on the direction of travel$)$.
	:* Doppler frequencies at the edges are much more common:  $\|f_{\rm D}\| = 0.4 -\varepsilon$, where  $\varepsilon$  indicates a small positive size.		:* Doppler frequencies at the edges are much more common:  $\|f_{\rm D}\| = 0.4 -\varepsilon$, where  $\varepsilon$  indicates a small positive size.
	:* The basic course of Doppler – PDF and Doppler – PDS   ⇒   ~~&bdquo;~~Jakes spectrum" can be explained from this experiment alone.		:* The basic course of Doppler – PDF and Doppler – PDS   ⇒   "Jakes spectrum" can be explained from this experiment alone.

	{{BlaueBox\|TEXT=		{{BlaueBox\|TEXT=
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	This interactive calculation tool was designed and implemented at the  [https://www.ei.tum.de/en/lnt/home/ Institute for Communications Engineering]  at the  [https://www.tum.de/en Technical University of Munich].		This interactive calculation tool was designed and implemented at the  [https://www.ei.tum.de/en/lnt/home/ Institute for Communications Engineering]  at the  [https://www.tum.de/en Technical University of Munich].
	*The first version was created in 2009 by [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Alexander_Happach_.28Diplomarbeit_EI_2009.29\|Alexander Happach]] as part of his diploma thesis with “FlashMX – 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 first version was created in 2009 by [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Alexander_Happach_.28Diplomarbeit_EI_2009.29\|Alexander Happach]] as part of his diploma thesis with “FlashMX – 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 2020 the program was redesigned by [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Andr.C3.A9_Schulz_.28Bachelorarbeit_LB_2020.29\|André Schulz]] (Bachelor thesis LB, Supervisors: [[Biographies_and_Bibliographies/Beteiligte_der_Professur_Leitungsgebundene_Übertragungstechnik#Benedikt_Leible.2C_M.Sc._.28bei_L.C3.9CT_seit_2017.29\|Benedikt Leible]] and [[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]] ) via ~~&bdquo;~~HTML5".		*In 2020 the program was redesigned by [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Andr.C3.A9_Schulz_.28Bachelorarbeit_LB_2020.29\|André Schulz]] (Bachelor thesis LB, Supervisors: [[Biographies_and_Bibliographies/Beteiligte_der_Professur_Leitungsgebundene_Übertragungstechnik#Benedikt_Leible.2C_M.Sc._.28bei_L.C3.9CT_seit_2017.29\|Benedikt Leible]] and [[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]] ) via "HTML5".

	==Once again: Open Applet in new Tab==		==Once again: Open Applet in new Tab==
	{{LntAppletLinkEnDe\|dopplereffect_en\|dopplereffect}}		{{LntAppletLinkEnDe\|dopplereffect_en\|dopplereffect}}

Javier: Text replacement - "”" to """

2021-05-28T14:40:19Z

Text replacement - "”" to """

← Older revision		Revision as of 16:40, 28 May 2021
Line 280:		Line 280:

	:* As in  $(6)$, only values between $f_{\rm D}=0.4$  and  $f_{\rm D}=-0.4$  are possible, but now all intermediate values $(-0.4 \le f_{\rm D} \le +0.4)$.		:* As in  $(6)$, only values between $f_{\rm D}=0.4$  and  $f_{\rm D}=-0.4$  are possible, but now all intermediate values $(-0.4 \le f_{\rm D} \le +0.4)$.
	:* With &bdquo;Step~~”~~ you can see:  $f_{\rm D}\equiv0$  only occurs if the receiver is exactly below the transmitter $(\alpha=\pm 90^\circ$, depending on the direction of travel$)$.		:* With &bdquo;Step" you can see:  $f_{\rm D}\equiv0$  only occurs if the receiver is exactly below the transmitter $(\alpha=\pm 90^\circ$, depending on the direction of travel$)$.
	:* Doppler frequencies at the edges are much more common:  $\|f_{\rm D}\| = 0.4 -\varepsilon$, where  $\varepsilon$  indicates a small positive size.		:* Doppler frequencies at the edges are much more common:  $\|f_{\rm D}\| = 0.4 -\varepsilon$, where  $\varepsilon$  indicates a small positive size.
	:* The basic course of Doppler – PDF and Doppler – PDS   ⇒   &bdquo;Jakes spectrum~~”~~ can be explained from this experiment alone.		:* The basic course of Doppler – PDF and Doppler – PDS   ⇒   &bdquo;Jakes spectrum" can be explained from this experiment alone.

	{{BlaueBox\|TEXT=		{{BlaueBox\|TEXT=
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	This interactive calculation tool was designed and implemented at the  [https://www.ei.tum.de/en/lnt/home/ Institute for Communications Engineering]  at the  [https://www.tum.de/en Technical University of Munich].		This interactive calculation tool was designed and implemented at the  [https://www.ei.tum.de/en/lnt/home/ Institute for Communications Engineering]  at the  [https://www.tum.de/en Technical University of Munich].
	*The first version was created in 2009 by [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Alexander_Happach_.28Diplomarbeit_EI_2009.29\|Alexander Happach]] as part of his diploma thesis with “FlashMX – 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 first version was created in 2009 by [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Alexander_Happach_.28Diplomarbeit_EI_2009.29\|Alexander Happach]] as part of his diploma thesis with “FlashMX – 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 2020 the program was redesigned by [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Andr.C3.A9_Schulz_.28Bachelorarbeit_LB_2020.29\|André Schulz]] (Bachelor thesis LB, Supervisors: [[Biographies_and_Bibliographies/Beteiligte_der_Professur_Leitungsgebundene_Übertragungstechnik#Benedikt_Leible.2C_M.Sc._.28bei_L.C3.9CT_seit_2017.29\|Benedikt Leible]] and [[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]] ) via &bdquo;HTML5~~”~~.		*In 2020 the program was redesigned by [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Andr.C3.A9_Schulz_.28Bachelorarbeit_LB_2020.29\|André Schulz]] (Bachelor thesis LB, Supervisors: [[Biographies_and_Bibliographies/Beteiligte_der_Professur_Leitungsgebundene_Übertragungstechnik#Benedikt_Leible.2C_M.Sc._.28bei_L.C3.9CT_seit_2017.29\|Benedikt Leible]] and [[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]] ) via &bdquo;HTML5".

	==Once again: Open Applet in new Tab==		==Once again: Open Applet in new Tab==
	{{LntAppletLinkEnDe\|dopplereffect_en\|dopplereffect}}		{{LntAppletLinkEnDe\|dopplereffect_en\|dopplereffect}}

Tasnad at 14:21, 1 April 2021

2021-04-01T14:21:36Z

← Older revision		Revision as of 16:21, 1 April 2021
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	{{~~LntAppletLink~~\|dopplereffect_en}} ~~     ~~		{{LntAppletLinkEnDe\|dopplereffect_en\|dopplereffect}}
	~~[https://www.lntwww.de/Applets:Zur_Verdeutlichung_des_Dopplereffekts '''German Version''']~~

	==Applet Description==		==Applet Description==
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	==Once again: Open Applet in new Tab==		==Once again: Open Applet in new Tab==
			{{LntAppletLinkEnDe\|dopplereffect_en\|dopplereffect}}
	{{~~LntAppletLink~~\|dopplereffect_en}} ~~     ~~
	~~[https://www.lntwww.de/Applets:Zur_Verdeutlichung_des_Dopplereffekts '''German Version''']~~
	~~<br><br>~~

Guenter at 16:38, 21 January 2021

2021-01-21T16:38:45Z

← Older revision		Revision as of 18:38, 21 January 2021
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	==Exercises==		==Exercises==

	~~[[File:Exercises_binomial_fertig.png\|right]]~~		* First select the number  $(1, 2, \text{...})$  of the exercise.  The number  $0$  corresponds to a "Reset":  Same setting as at program start.
	* First select the number  $(1,\text{...}~~, 9~~)$  of the exercise. ~~<br>~~		*A task description is displayed.  The parameter values are adjusted.  Solution after pressing "Show solution". <br>
	*A task description is displayed. The parameter values are adjusted.
	*Solution after pressing "Show solution". <br>
	*The number  $0$  corresponds to a "Reset":  Same setting as at program start.
	*In the following descriptions, $f_{\rm S}$, $f_{\rm E}$  and$f_{\rm D}$  are each normalized to the reference frequency $f_{\rm 0}$.		*In the following descriptions, $f_{\rm S}$, $f_{\rm E}$  and$f_{\rm D}$  are each normalized to the reference frequency $f_{\rm 0}$.
	<br clear=all>		<br clear=all>

Guenter at 12:32, 8 August 2020

2020-08-08T12:32:01Z

← Older revision		Revision as of 14:32, 8 August 2020
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	:* Protanopia:   for users with pronounced red visual impairment		:* Protanopia:   for users with pronounced red visual impairment

	'''(B)'''     ~~Starting~~ position of the transmitter   ⇒   $(S_x,\ S_Y)$		'''(B)'''     Start position of the transmitter   ⇒   $(S_x,\ S_Y)$

	'''(C)'''     Input parameters		'''(C)'''     Input parameters

Guenter at 14:58, 7 August 2020

2020-08-07T14:58:40Z

← Older revision		Revision as of 16:58, 7 August 2020
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	'''(K)'''     Selection of the exercise according to the numbers		'''(K)'''     Selection of the exercise according to the numbers

	'''(L)'''     Task description and ~~question~~		'''(L)'''     Task description and questions

	'''(M)'''     Show and hide sample solution		'''(M)'''     Show and hide sample solution