Applets:Generation of Walsh functions - Revision history

Maintenance script: Join 1 split formula blocks

2026-03-16T14:17:14Z

Join 1 split formula blocks

← Older revision		Revision as of 16:17, 16 March 2026
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	*The orders of the Hadamard matrices are fixed to powers of two, i.e.  $J = 2^G$  applies to a natural number  $G$. Starting from $\mathbf{H}_1 = [+1]$ and		*The orders of the Hadamard matrices are fixed to powers of two, i.e.  $J = 2^G$  applies to a natural number  $G$. Starting from $\mathbf{H}_1 = [+1]$ and

	:$$		:$$\mathbf{H}_2 =\left[ \begin{array}{rr}+1 & +1\\+1 & -1 \\\end{array}\right]$$the following relationship applies to the generation of further Hadamard matrices::$$\mathbf{H}_{2N} =\left[ \begin{array}{rr}+\mathbf{H}_N & +\mathbf{H}_N\\+\mathbf{H}_N & -\mathbf{H}_N \\\end{array}\right]$$
	\mathbf{H}_2 =
	\left[ \begin{array}{rr}
	+1 & +1\\
	+1 & -1 \\
	\end{array}\right]
	$$the following relationship applies to the generation of further Hadamard matrices::$$
	\mathbf{H}_{2N} =
	\left[ \begin{array}{rr}
	+\mathbf{H}_N & +\mathbf{H}_N\\
	+\mathbf{H}_N & -\mathbf{H}_N \\
	\end{array}\right]
	$$
	<br>		<br>

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	This interactive calculation tool was designed and realized at the  [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik]  $\rm (LNT)$  of the  [https://www.tum.de/ Technical University of Munich]  $\rm (TUM)$.		This interactive calculation tool was designed and realized at the  [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik]  $\rm (LNT)$  of the  [https://www.tum.de/ Technical University of Munich]  $\rm (TUM)$.

	*The first German version was created in 2007 by  [[Biographies_and_Bibliographies/~~An_LNTwww_beteiligte_Studierende~~#Thomas_Gro.C3.9Fer_.28Diplomarbeit_LB_2006.2C_danach_freie_Mitarbeit_bis_2010.29\|Thomas Großer]]   in the context 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 German version was created in 2007 by  [[Biographies_and_Bibliographies/Students_involved_in_LNTwww#Thomas_Gro.C3.9Fer_.28Diplomarbeit_LB_2006.2C_danach_freie_Mitarbeit_bis_2010.29\|Thomas Großer]]   in the context 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]]).
	*2018/2019 the applet was converted on "HTML5" and redesigned by  [[Biographies_and_Bibliographies/~~An_LNTwww_beteiligte_Studierende~~#Carolin_Mirschina_.28Ingenieurspraxis_Math_2019.2C_danach_Werkstudentin.29\|Carolin Mirschina]]  (Engineering practice, 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]] ).		*2018/2019 the applet was converted on "HTML5" and redesigned by  [[Biographies_and_Bibliographies/Students_involved_in_LNTwww#Carolin_Mirschina_.28Ingenieurspraxis_Math_2019.2C_danach_Werkstudentin.29\|Carolin Mirschina]]  (Engineering practice, 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]] ).
	*2020 this English version was made by  [[Biographies_and_Bibliographies/~~An_LNTwww_beteiligte_Studierende~~#Carolin_Mirschina_.28Ingenieurspraxis_Math_2019.2C_danach_Werkstudentin.29\|Carolin Mirschina]]  (working student) and  [[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]].		*2020 this English version was made by  [[Biographies_and_Bibliographies/Students_involved_in_LNTwww#Carolin_Mirschina_.28Ingenieurspraxis_Math_2019.2C_danach_Werkstudentin.29\|Carolin Mirschina]]  (working student) and  [[Biographies_and_Bibliographies/LNTwww_members_from_LNT#Prof._Dr.-Ing._habil._Günter_Söder_(at_LNT_from_1974-2024)\|Günter Söder]].
	==Call the applet again==		==Call the applet again==
	<br>		<br>

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

2026-03-16T13:49:01Z

Join split $$ formula lines for correct rendering

← Older revision		Revision as of 15:49, 16 March 2026
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	+1 & -1 \\		+1 & -1 \\
	\end{array}\right]		\end{array}\right]
	$$		$$the following relationship applies to the generation of further Hadamard matrices::$$
	the following relationship applies to the generation of further Hadamard matrices:
	:$$
	\mathbf{H}_{2N} =		\mathbf{H}_{2N} =
	\left[ \begin{array}{rr}		\left[ \begin{array}{rr}

Maintenance script: Add German interlanguage link

2026-03-16T12:39:03Z

Add German interlanguage link

← Older revision		Revision as of 14:39, 16 March 2026
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	{{LntAppletLinkEnDe\|walsh_en\|walsh}}		{{LntAppletLinkEnDe\|walsh_en\|walsh}}
	<br><br>		<br><br>
			[[de:Applets:Generation_of_Walsh_functions]]

Hwang at 18:05, 21 March 2023

2023-03-21T18:05:15Z

← Older revision		Revision as of 20:05, 21 March 2023
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	*The first German version was created in 2007 by  [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Thomas_Gro.C3.9Fer_.28Diplomarbeit_LB_2006.2C_danach_freie_Mitarbeit_bis_2010.29\|Thomas Großer]]   in the context 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 German version was created in 2007 by  [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Thomas_Gro.C3.9Fer_.28Diplomarbeit_LB_2006.2C_danach_freie_Mitarbeit_bis_2010.29\|Thomas Großer]]   in the context 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]]).
	*2018/2019 the applet was converted on "HTML5" and redesigned by  [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Carolin_Mirschina_.28Ingenieurspraxis_Math_2019.2C_danach_Werkstudentin.29\|Carolin Mirschina]]  (Engineering practice, 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]] ).		*2018/2019 the applet was converted on "HTML5" and redesigned by  [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Carolin_Mirschina_.28Ingenieurspraxis_Math_2019.2C_danach_Werkstudentin.29\|Carolin Mirschina]]  (Engineering practice, 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]] ).
	*2020 this English version was made by  [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Carolin_Mirschina_.28Ingenieurspraxis_Math_2019.2C_danach_Werkstudentin.29\|Carolin Mirschina]]  (working student) and  [[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]].  ~~Translation using "www.DeepL.com/Translator" (free version).~~		*2020 this English version was made by  [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Carolin_Mirschina_.28Ingenieurspraxis_Math_2019.2C_danach_Werkstudentin.29\|Carolin Mirschina]]  (working student) and  [[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]].
	==Call the applet again==		==Call the applet again==
	<br>		<br>
	{{LntAppletLinkEnDe\|walsh_en\|walsh}}		{{LntAppletLinkEnDe\|walsh_en\|walsh}}
	<br><br>		<br><br>

Guenter at 13:28, 29 March 2021

2021-03-29T13:28:53Z

← Older revision		Revision as of 15:28, 29 March 2021
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	{{~~LntAppletLinkEn~~\|walsh_en}} ~~     ~~		{{LntAppletLinkEnDe\|walsh_en\|walsh}}
	~~[https://www.lntwww.de/Applets:Zur_Erzeugung_von_Walsh-Funktionen_(neues_Applet)       '''German Version''']~~

	== Program description==		== Program description==
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	==Call the applet again==		==Call the applet again==
	<br>		<br>
	{{~~LntAppletLinkEn~~\|walsh_en}} ~~     ~~		{{LntAppletLinkEnDe\|walsh_en\|walsh}}
	~~[https://www.lntwww.de/Applets:Zur_Erzeugung_von_Walsh-Funktionen_(neues_Applet)       '''German Version''']~~		<br><br>

Guenter at 12:45, 19 January 2021

2021-01-19T12:45:04Z

← Older revision		Revision as of 14:45, 19 January 2021
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	{{LntAppletLinkEn\|walsh_en}}		{{LntAppletLinkEn\|walsh_en}}
	[https://lntwww.de/Applets:Zur_Erzeugung_von_Walsh-Funktionen_(neues_Applet)       '''German Version''']		[https://www.lntwww.de/Applets:Zur_Erzeugung_von_Walsh-Funktionen_(neues_Applet)       '''German Version''']

	== Program description==		== Program description==
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	<br>		<br>
	{{LntAppletLinkEn\|walsh_en}}		{{LntAppletLinkEn\|walsh_en}}
	[https://lntwww.de/Applets:Zur_Erzeugung_von_Walsh-Funktionen_(neues_Applet)       '''German Version''']		[https://www.lntwww.de/Applets:Zur_Erzeugung_von_Walsh-Funktionen_(neues_Applet)       '''German Version''']

Guenter at 12:37, 19 January 2021

2021-01-19T12:37:57Z

← Older revision		Revision as of 14:37, 19 January 2021
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	*Only  $J\hspace{-0.09cm} -\hspace{-0.09cm}1$, because the unspreaded sequence  $w_0(t)$  is usually not used.		*Only  $J\hspace{-0.09cm} -\hspace{-0.09cm}1$, because the unspreaded sequence  $w_0(t)$  is usually not used.
	*Please note the color assignment between the lines of the Hadamard matrix and the spreading sequences  $w_j(t)$.		*Please note the color assignment between the lines of the Hadamard matrix and the spreading sequences  $w_j(t)$.
	*The submatrix  $\mathbf H_4$  is highlighted in yellow.}}}		*The submatrix  $\mathbf H_4$  is highlighted in yellow.}}
	<br clear=all>		<br clear=all>

Guenter at 12:37, 19 January 2021

2021-01-19T12:37:20Z

← Older revision		Revision as of 14:37, 19 January 2021
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	{{LntAppletLinkEn\|walsh_en}}		{{LntAppletLinkEn\|walsh_en}}
	[https://~~en.~~lntwww.de/Applets:Zur_Erzeugung_von_Walsh-Funktionen_(neues_Applet)       '''German Version''']		[https://lntwww.de/Applets:Zur_Erzeugung_von_Walsh-Funktionen_(neues_Applet)       '''German Version''']

	== Program description==		== Program description==
Line 67:		Line 67:
	<br>		<br>
	{{LntAppletLinkEn\|walsh_en}}		{{LntAppletLinkEn\|walsh_en}}
	[https://~~en.~~lntwww.de/Applets:Zur_Erzeugung_von_Walsh-Funktionen_(neues_Applet)       '''German Version''']		[https://lntwww.de/Applets:Zur_Erzeugung_von_Walsh-Funktionen_(neues_Applet)       '''German Version''']

Guenter at 12:35, 19 January 2021

2021-01-19T12:35:35Z

← Older revision		Revision as of 14:35, 19 January 2021
Line 1:		Line 1:
	{{LntAppletLinkEn\|walsh_en}}		{{LntAppletLinkEn\|walsh_en}}
	[https://en.lntwww.de/Applets:~~Impulses_and_Spectra~~ '''~~English~~ Version''']		[https://en.lntwww.de/Applets:Zur_Erzeugung_von_Walsh-Funktionen_(neues_Applet)       '''German Version''']

	== Program description==		== Program description==
Line 66:		Line 66:
	==Call the applet again==		==Call the applet again==
	<br>		<br>
	{{LntAppletLinkEn\|walsh_en}}		{{LntAppletLinkEn\|walsh_en}}
	[https://en.lntwww.de/Applets:~~Impulses_and_Spectra~~ '''~~English~~ Version''']		[https://en.lntwww.de/Applets:Zur_Erzeugung_von_Walsh-Funktionen_(neues_Applet)       '''German Version''']

Guenter at 12:32, 19 January 2021

2021-01-19T12:32:22Z

← Older revision		Revision as of 14:32, 19 January 2021
Line 1:		Line 1:
	{{LntAppletLinkEn\|walsh_en}}		{{LntAppletLinkEn\|walsh_en}}
			[https://en.lntwww.de/Applets:Impulses_and_Spectra '''English Version''']

	== Program description==		== Program description==
Line 65:		Line 66:
	==Call the applet again==		==Call the applet again==
	<br>		<br>
	{{LntAppletLinkEn\|walsh_en}}		{{LntAppletLinkEn\|walsh_en}}
			[https://en.lntwww.de/Applets:Impulses_and_Spectra '''English Version''']