Applets:Digital Filters - Revision history

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	*By definition, the discrete-time impulse response is the same as the output sequence if there is a single "one" at $t =0$ at the input.		*By definition, the discrete-time impulse response is the same as the output sequence if there is a single "one" at $t =0$ at the input.
	:$$h(t)= \sum\limits_{\mu = 0}^\infty {a_0 \cdot {b_1} ^\mu \cdot \delta ( {t - \mu \cdot T_{\rm A} } )}\hspace{0.3cm}		:$$h(t)= \sum\limits_{\mu = 0}^\infty {a_0 \cdot {b_1} ^\mu \cdot \delta ( {t - \mu \cdot T_{\rm A} } )}\hspace{0.3cm}\Rightarrow \hspace{0.3cm}〈\hspace{0.05cm}h_\mu\hspace{0.05cm}〉= 〈\hspace{0.05cm}a_0, \ a_0\cdot {b_1}, \ a_0\cdot {b_1}^2 \ \text{...} \hspace{0.05cm}〉.$$
	\Rightarrow \hspace{0.3cm}〈\hspace{0.05cm}h_\mu\hspace{0.05cm}〉= 〈\hspace{0.05cm}a_0, \ a_0\cdot {b_1}, \ a_0\cdot {b_1}^2 \ \text{...} \hspace{0.05cm}〉.$$

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	<br>		<br>
	This interactive calculation tool was designed and implemented at the [http://www.lnt.ei.tum.de/startseite chair for communications engineering] at the [https://www.tum.de/ Technische Universität München].		This interactive calculation tool was designed and implemented at the [http://www.lnt.ei.tum.de/startseite chair for communications engineering] at the [https://www.tum.de/ Technische Universität München].
	*The first 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 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 2005 by [[Biographies_and_Bibliographies/Students_involved_in_LNTwww#Bettina_Hirner_.28Diplomarbeit_LB_2005.29\|Bettina Hirner]] as part of her 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==

	{{LntAppletLink\|digitalFilters_en}}		{{LntAppletLink\|digitalFilters_en}}

Maintenance script: Update domain links: en.lntwww.de → en.lntwww.lnt.ei.tum.de, www.lntwww.de → lntwww.lnt.ei.tum.de

2026-03-16T11:09:53Z

Update domain links: en.lntwww.de → en.lntwww.lnt.ei.tum.de, www.lntwww.de → lntwww.lnt.ei.tum.de

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	Each signal $x(t)$ can only be represented on a computer by the sequence $〈x_ν〉$ of its samples, where $x_ν$ stands for $x(ν · T_{\rm A})$.		Each signal $x(t)$ can only be represented on a computer by the sequence $〈x_ν〉$ of its samples, where $x_ν$ stands for $x(ν · T_{\rm A})$.
	[[File:P_ID552__Sto_T_5_2_S1_neu.png\|right \|frame\| Block diagram of a digital (IIR–) filter $M$–order]]		[[File:P_ID552__Sto_T_5_2_S1_neu.png\|right \|frame\| Block diagram of a digital (IIR–) filter $M$–order]]
	*The time interval $T_{\rm A}$ between two samples is limited by the [https://en.lntwww.de/Signal_Representation/Discrete-Time_Signal_Representation#Sampling_theorem\|"sampling theorem"].		*The time interval $T_{\rm A}$ between two samples is limited by the [https://en.lntwww.lnt.ei.tum.de/Signal_Representation/Discrete-Time_Signal_Representation#Sampling_theorem\|"sampling theorem"].
	*We limit ourselves here to causal signals and systems, which means that $x_ν \equiv 0$ for $ν \le 0$.		*We limit ourselves here to causal signals and systems, which means that $x_ν \equiv 0$ for $ν \le 0$.

Noah at 16:44, 26 April 2023

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	==Applet Manual==		==Applet Manual==

	'''(A)'''     ~~Auswahl des Eingangssignals~~  $($Dirac,  ~~Sprung oder Rechteck~~$)$		'''(A)'''     Input signal selection  $($Dirac delta,  unit step or rectangular$)$

	'''(B)'''     ~~Einstellungen für Abszisse~~, ~~Ordinate und Geschwindigkeit~~		'''(B)'''     Settings for abscissa, ordinate and velocity.

	'''(C)'''     ~~Bedienfeld~~  $($Start, ~~Einzelschritt~~, ~~Gesamt~~, Pause, Reset$)$		'''(C)'''     Control panel  $($Start, Single step, Total, Pause, Reset$)$

	'''(D)'''     ~~Blockschaltbild mit schrittweiser Anpassung aller Werte~~		'''(D)'''     Block diagram with stepwise adjustment of all values.

	'''(E)'''     ~~Grafikfeld für Ausgabe der Ausgangsfolge~~		'''(E)'''     Graphic area for output of the output sequence

	'''(F)'''     ~~Aufgabenauswahl~~		'''(F)'''     Exercise selection

	'''(G)'''     ~~Fragen und Lösungen~~		'''(G)'''     Questions and solutions
	<br clear=all>		<br clear=all>
	==About the authors==		==About the authors==

Guenter at 15:02, 24 April 2023

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	[[File:~~Exercise_impuls_v2~~.png\|right \|frame\| Screenshot ~~'''Korrektur''' auch in Deutsch~~]]		[[File:EN_DIG_Fil_Mannt.png\|right \|frame\| Screenshot]]

	==Applet Manual==		==Applet Manual==

Guenter at 13:55, 21 April 2023

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			[[File:Exercise_impuls_v2.png\|right \|frame\| Screenshot '''Korrektur''' auch in Deutsch]]

	==Applet Manual==		==Applet Manual==

	~~[[File:Exercise_impuls_v2.png\|right \|frame\| Screenshot]]~~


	'''(A)'''     Auswahl des Eingangssignals  $($Dirac,  Sprung oder Rechteck$)$		'''(A)'''     Auswahl des Eingangssignals  $($Dirac,  Sprung oder Rechteck$)$

Guenter at 13:31, 21 April 2023

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	'''(B)'''     Einstellungen für Abszisse, Ordinate und Geschwindigkeit		'''(B)'''     Einstellungen für Abszisse, Ordinate und Geschwindigkeit

	'''(C)'''     ~~Einstellungen für den Programmablauf~~  $($		'''(C)'''     Bedienfeld  $($Start, Einzelschritt, Gesamt, Pause, Reset$)$

	'''(D)'''     ~~Berechnung der  "Running Digital Sum"~~		'''(D)'''     Blockschaltbild mit schrittweiser Anpassung aller Werte

	'''(E)'''     ~~Blockweise Bitänderung~~		'''(E)'''     Grafikfeld für Ausgabe der Ausgangsfolge

	'''(F)'''     ~~Grafikbereich für das Quellensignal  $q(t)$~~		'''(F)'''     Aufgabenauswahl

	'''(G~~)'''     Grafikbereich für das Codersignal  $c(t)$~~		'''(G)'''     Fragen und Lösungen
			<br clear=all>
	~~    '''(H)'''     Gesamtdarstellung der Werte  ${\it \Sigma}_0,\ {\it \Sigma}_1, \ {\it \Sigma}_2, \ {\it \Sigma}_4$  für  "MS43"  und  "MMS43"~~

	~~    '''(I)'''     Aufgabenauswahl~~

	~~    '''(I~~)'''     Fragen und Lösungen
	==About the authors==		==About the authors==
	<br>		<br>

Guenter at 13:22, 21 April 2023

2023-04-21T13:22:37Z

← Older revision		Revision as of 15:22, 21 April 2023
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	==Applet Manual==		==Applet Manual==
	~~<br>~~
	~~[[File:Exercise_impuls_v2.png\|right \|frame\| Screenshot '''Korrektur''']]~~

	~~    '''(A)'''     Auswahl der Quellensymbolfolge~~:~~  $\rm A$,  $\rm B$  oder  $\rm C$~~		[[File:Exercise_impuls_v2.png\|right \|frame\| Screenshot]]

	~~    '''(B)'''     Programmoptionen <br>                $($Zufallsfolge,  blockweise RDS-Berechnung,  Gesamtansicht,  Reset$)$~~

	'''(C)'''     ~~"MS43"~~  oder  ~~"MMS43"~~		'''(A)'''     Auswahl des Eingangssignals  $($Dirac,  Sprung oder Rechteck$)$

			'''(B)'''     Einstellungen für Abszisse, Ordinate und Geschwindigkeit

			'''(C)'''     Einstellungen für den Programmablauf  $($

	'''(D)'''     Berechnung der  "Running Digital Sum"		'''(D)'''     Berechnung der  "Running Digital Sum"

Guenter at 13:15, 21 April 2023

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 [[File:Exercise_impuls_v2.png|right |frame| Screenshot '''Korrektur''']]
-Exercise_impuls_v2.png
+&nbsp; &nbsp; '''(A)''' &nbsp; &nbsp; Auswahl der Quellensymbolfolge:&nbsp; $\rm A$,&nbsp; $\rm B$&nbsp; oder&nbsp; $\rm C$
 ==About the authors==
 <br>

Guenter at 15:58, 20 April 2023

2023-04-20T15:58:40Z

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	==Applet Manual==		==Applet Manual==
	<br>		<br>
	'''Korrektur'''		[[File:Exercise_impuls_v2.png\|right \|frame\| Screenshot '''Korrektur''']]

			Exercise_impuls_v2.png
	==About the authors==		==About the authors==
	<br>		<br>

Noah at 19:46, 16 April 2023

2023-04-16T19:46:41Z

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	$\text{Example 2:}$ Consider a non-recursive filter with the filter coefficients $a_0 = 1,\hspace{0.5cm} a_1 = 2,\hspace{0.5cm} a_2 = 1.$		$\text{Example 2:}$ Consider a non-recursive filter with the filter coefficients $a_0 = 1,\hspace{0.5cm} a_1 = 2,\hspace{0.5cm} a_2 = 1.$
	[[File:P_ID608__Sto_Z_5_3.png\|right\|frame\|~~Nichtrekursives Filter~~]]		[[File:P_ID608__Sto_Z_5_3.png\|right\|frame\|Non-recursive filter]]

	'''(1)''' The conventional impulse response is: $h(t) = \delta (t) + 2 \cdot \delta ( {t - T_{\rm A} } ) + \delta ( {t - 2T_{\rm A} } ).$ <br>        ⇒   discrete-time impulse response: $〈h_\mu〉= 〈1,\ 2,\ 1〉 .$		'''(1)''' The conventional impulse response is: $h(t) = \delta (t) + 2 \cdot \delta ( {t - T_{\rm A} } ) + \delta ( {t - 2T_{\rm A} } ).$ <br>        ⇒   discrete-time impulse response: $〈h_\mu〉= 〈1,\ 2,\ 1〉 .$
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	[[File:Sto_T_5_2_S3_version2.png \|frame\| Discrete-time impulse response ~~\| rechts~~]]		[[File:Sto_T_5_2_S3_version2.png \|frame\| Discrete-time impulse response]]
	$\text{Example 3:}$  The graphic opposite shows the discrete-time impulse response $〈\hspace{0.05cm}h_\mu\hspace{0.05cm}〉$ of a recursive filter of the first order with the parameters $a_0 = 1$ and $b_1 = 0.6$.		$\text{Example 3:}$  The graphic opposite shows the discrete-time impulse response $〈\hspace{0.05cm}h_\mu\hspace{0.05cm}〉$ of a recursive filter of the first order with the parameters $a_0 = 1$ and $b_1 = 0.6$.
	*The (discrete-time) course is exponentially falling and extends to infinity.		*The (discrete-time) course is exponentially falling and extends to infinity.
	*The ratio of the weights of two successive ~~Diracs~~ is $b_1 = 0.6$.		*The ratio of the weights of two successive Dirac deltas is $b_1 = 0.6$.
	}}		}}

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	'''(6)'''  Consider and interpret the impulse response and the step response for the filter coefficients  $a_0=1$,  $b_1=1$,  $a_1=a_2= b_2=0$.  }}		'''(6)'''  Consider and interpret the impulse response and the step response for the filter coefficients  $a_0=1$,  $b_1=1$,  $a_1=a_2= b_2=0$.  }}

	:*  '''The system is unstable''':   A discrete-time Dirac delta function at input $($at time  $t=0)$  causes an infinite number of ~~Diracs~~ of the same height in the output signal.		:*  '''The system is unstable''':   A discrete-time Dirac delta function at input $($at time  $t=0)$  causes an infinite number of Dirac deltas of the same height in the output signal.
	:*  A discrete-time step function at the input causes an infinite number of ~~Diracs~~ with monotonically increasing weights (to infinity) in the output signal.		:*  A discrete-time step function at the input causes an infinite number of Dirac deltas with monotonically increasing weights (to infinity) in the output signal.

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