Linear and Time Invariant Systems - Revision history

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@@ Line 5: / Line 5: @@
 # Indicator in frequency domain is the&nbsp; &raquo;frequency response&laquo;&nbsp; $ H(f)=Y(f)/X(f)$,&nbsp; in time domain the&nbsp; &raquo;impulse response&raquo;&nbsp; $ h(t)$,&nbsp; where&nbsp; $ y(t)=x(t)\star h(t)$.
 # System distortions &nbsp; &rArr; &nbsp; $ y(t)\ne K \cdot x(t - \tau)$;&nbsp; distortion-free system:&nbsp; output and input differ only by attenuation/gain and/or delay time.
-# Linear distortions &nbsp; &rArr; &nbsp; $ Y(f)=X(f)\cdot H(f)$&nbsp; $($possibly reversible$)$;&nbsp; non-linear distortions &nbsp; &rArr; &nbsp; emergence of new frequencies&nbsp; $($irreversible distortions$)$.
+# Linear distortions $($possibly reversible$)$ &nbsp; &rArr; &nbsp; $ Y(f)=X(f)\cdot H(f)$; &nbsp;  non-linear distortions &nbsp; &rArr; &nbsp; emergence of new frequencies&nbsp; $($irreversible distortions$)$.
 # Peculiarities of causal systems &nbsp; &rArr; &nbsp; $ h(t<0)\equiv 0$;&nbsp; Hilbert transform,&nbsp; Laplace transform; inverse Laplace  transform &nbsp; &rArr; &nbsp; residue theorem.
 #Some results of line transmission theory;&nbsp; coaxial cable systems &nbsp; &rArr; &nbsp; "white noise";&nbsp; copper twisted pairs &nbsp; &rArr; &nbsp; dominant is&nbsp; "near-end crosstalk".

@@ Line 2: / Line 2: @@
 {{BlaueBox|TEXT=Based on the book&nbsp; [[Signaldarstellung|&raquo;Signal Representation&laquo;]],&nbsp; here it is described how to mathematically capture the influence of a filter on deterministic signals.
-# System theory analyses a quadripole&nbsp; $($&raquo;system&laquo;$)$&nbsp; using&nbsp; "cause" &nbsp; &rArr; &nbsp; $[$input &nbsp; $ X(f)\bullet\! \!-\!-\!\!\circ\, x( t )]$&nbsp; and&nbsp; &raquo;effect&raquo; &nbsp; &rArr; &nbsp; $[$output&nbsp; $ Y(f)\bullet\!-\!-\!\circ\, y( t )]$.
+# System theory analyses a quadripole&nbsp; $($&raquo;system&laquo;$)$&nbsp; using&nbsp; &raquo;cause&laquo; &nbsp; &rArr; &nbsp; $[$input &nbsp; $ X(f)\ \bullet\!\!-\!\!\!-\!\!\!-\!\!\circ\,\ x(t)]$&nbsp; and&nbsp; &raquo;effect&laquo; &nbsp; &rArr; &nbsp; $[$output&nbsp; $ Y(f)\ \bullet\!\!-\!\!\!-\!\!\!-\!\!\circ\,\, y( t )]$.
 # Indicator in frequency domain is the&nbsp; &raquo;frequency response&laquo;&nbsp; $ H(f)=Y(f)/X(f)$,&nbsp; in time domain the&nbsp; &raquo;impulse response&raquo;&nbsp; $ h(t)$,&nbsp; where&nbsp; $ y(t)=x(t)\star h(t)$.
-# System distortions &nbsp; &rArr; &nbsp; $ y(t)\ne K \cdot x(t - \tau)$;&nbsp; distortion-free system:&nbsp; output and input differ by attenuation/gain and delay time.
+# System distortions &nbsp; &rArr; &nbsp; $ y(t)\ne K \cdot x(t - \tau)$;&nbsp; distortion-free system:&nbsp; output and input differ only by attenuation/gain and/or delay time.
 # Linear distortions &nbsp; &rArr; &nbsp; $ Y(f)=X(f)\cdot H(f)$&nbsp; $($possibly reversible$)$;&nbsp; non-linear distortions &nbsp; &rArr; &nbsp; emergence of new frequencies&nbsp; $($irreversible distortions$)$.
 # Peculiarities of causal systems &nbsp; &rArr; &nbsp; $ h(t<0)\equiv 0$;&nbsp; Hilbert transform,&nbsp; Laplace transform; inverse Laplace  transform &nbsp; &rArr; &nbsp; residue theorem.
@@ Line 10: / Line 10: @@
-The filter influence on a random signal is only dealt with in the last chapter of the book &nbsp;[[Theory_of_Stochastic_Signals|&raquo;Theory of Stochastic Signals&raquo;]].
+The filter influence on a random signal is only dealt with in the last chapter of the book &nbsp;[[Theory_of_Stochastic_Signals|&raquo;Theory of Stochastic Signals&laquo;]].
-&rArr; &nbsp; First a&nbsp; &raquo;'''content overview'''&laquo;&nbsp; on the basis of the&nbsp; &raquo;'''four main chapters'''&laquo;&nbsp; with a total of&nbsp; &raquo;'''twelve individual chapters'''&laquo;&nbsp; and&nbsp; &raquo;'''93 sections'''&laquo;.}}
+&rArr; &nbsp; First the&nbsp; &raquo;'''content overview'''&laquo;&nbsp; on the basis of the&nbsp; &raquo;'''four main chapters'''&laquo;&nbsp; with a total of&nbsp; &raquo;'''twelve individual chapters'''&laquo;&nbsp; and&nbsp; &raquo;'''93 sections'''&laquo;.}}

@@ Line 5: / Line 5: @@
 # Indicator in frequency domain is the&nbsp; &raquo;frequency response&laquo;&nbsp; $ H(f)=Y(f)/X(f)$,&nbsp; in time domain the&nbsp; &raquo;impulse response&raquo;&nbsp; $ h(t)$,&nbsp; where&nbsp; $ y(t)=x(t)\star h(t)$.
 # System distortions &nbsp; &rArr; &nbsp; $ y(t)\ne K \cdot x(t - \tau)$;&nbsp; distortion-free system:&nbsp; output and input differ by attenuation/gain and delay time.
-# Linear distortions &nbsp; &rArr; &nbsp; $ Y(f)=X(f)\cdot H(f)$&nbsp; $($possibly reversible$)$;&nbsp; non-linear distortions &nbsp; &rArr; &nbsp; emergence of new frequencies&nbsp; $($irreversible distortuions '''KORREKTUR: distortions'''$)$.
+# Linear distortions &nbsp; &rArr; &nbsp; $ Y(f)=X(f)\cdot H(f)$&nbsp; $($possibly reversible$)$;&nbsp; non-linear distortions &nbsp; &rArr; &nbsp; emergence of new frequencies&nbsp; $($irreversible distortions$)$.
 # Peculiarities of causal systems &nbsp; &rArr; &nbsp; $ h(t<0)\equiv 0$;&nbsp; Hilbert transform,&nbsp; Laplace transform; inverse Laplace  transform &nbsp; &rArr; &nbsp; residue theorem.
-#Some results of line theory '''KORREKTUR: line transmission theory''';&nbsp; coaxial cable systems &nbsp; &rArr; &nbsp; "white noise";&nbsp; copper twisted pairs &nbsp; &rArr; &nbsp; dominant is&nbsp; "near-end crosstalk".
+#Some results of line transmission theory;&nbsp; coaxial cable systems &nbsp; &rArr; &nbsp; "white noise";&nbsp; copper twisted pairs &nbsp; &rArr; &nbsp; dominant is&nbsp; "near-end crosstalk".

@@ Line 7: / Line 7: @@
 # Linear distortions &nbsp; &rArr; &nbsp; $ Y(f)=X(f)\cdot H(f)$&nbsp; $($possibly reversible$)$;&nbsp; non-linear distortions &nbsp; &rArr; &nbsp; emergence of new frequencies&nbsp; $($irreversible distortuions '''KORREKTUR: distortions'''$)$.
 # Peculiarities of causal systems &nbsp; &rArr; &nbsp; $ h(t<0)\equiv 0$;&nbsp; Hilbert transform,&nbsp; Laplace transform; inverse Laplace  transform &nbsp; &rArr; &nbsp; residue theorem.
-#Some results of line theory;&nbsp; coaxial cable systems &nbsp; &rArr; &nbsp; "white noise";&nbsp; copper twisted pairs &nbsp; &rArr; &nbsp; dominant is&nbsp; "near-end crosstalk".
+#Some results of line theory '''KORREKTUR: line transmission theory''';&nbsp; coaxial cable systems &nbsp; &rArr; &nbsp; "white noise";&nbsp; copper twisted pairs &nbsp; &rArr; &nbsp; dominant is&nbsp; "near-end crosstalk".

@@ Line 5: / Line 5: @@
 # Indicator in frequency domain is the&nbsp; &raquo;frequency response&laquo;&nbsp; $ H(f)=Y(f)/X(f)$,&nbsp; in time domain the&nbsp; &raquo;impulse response&raquo;&nbsp; $ h(t)$,&nbsp; where&nbsp; $ y(t)=x(t)\star h(t)$.
 # System distortions &nbsp; &rArr; &nbsp; $ y(t)\ne K \cdot x(t - \tau)$;&nbsp; distortion-free system:&nbsp; output and input differ by attenuation/gain and delay time.
-# Linear distortions &nbsp; &rArr; &nbsp; $ Y(f)=X(f)\cdot H(f)$&nbsp; $($possibly reversible$)$;&nbsp; non-linear distortions &nbsp; &rArr; &nbsp; emergence of new frequencies&nbsp; $($irreversible distortuions$)$.
+# Linear distortions &nbsp; &rArr; &nbsp; $ Y(f)=X(f)\cdot H(f)$&nbsp; $($possibly reversible$)$;&nbsp; non-linear distortions &nbsp; &rArr; &nbsp; emergence of new frequencies&nbsp; $($irreversible distortuions '''KORREKTUR: distortions'''$)$.
 # Peculiarities of causal systems &nbsp; &rArr; &nbsp; $ h(t<0)\equiv 0$;&nbsp; Hilbert transform,&nbsp; Laplace transform; inverse Laplace  transform &nbsp; &rArr; &nbsp; residue theorem.
 #Some results of line theory;&nbsp; coaxial cable systems &nbsp; &rArr; &nbsp; "white noise";&nbsp; copper twisted pairs &nbsp; &rArr; &nbsp; dominant is&nbsp; "near-end crosstalk".

← Older revision		Revision as of 15:12, 23 February 2023
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	<br><br>		<br><br>

−
−	~~$(1)$    [[LNTwww:Bibliography_to_Linear_and_Time_Invariant_Systems\|$\text{Bibliography for the book}$]]~~
−
−	$(2)$    [[LNTwww:General_notes_about_"Linear_and_Time_Invariant_Systems"\|$\text{General notes about the book}$]]   (authors,  other participants,  materials as a starting point for the book,  references)
−	~~<br><br>~~


	{{Display}}		{{Display}}

@@ Line 61: / Line 61: @@
 $(4)$&nbsp; &nbsp; [[LNTwww:Bibliography_to_"Linear_and_Time_Invariant_Systems"|$\text{Bibliography}$]]
-$(5)$&nbsp; &nbsp; [[LNTwww:General_notes_about_Signal_Representation|$\text{Impressum}$]] }}
+$(5)$&nbsp; &nbsp; [[LNTwww:Imprint_for_the_book_"Linear_and_Time_Invariant_Systems"|$\text{Impressum}$]] }}
 <br><br>

← Older revision		Revision as of 14:46, 23 February 2023
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	The filter influence on a random signal is only dealt with in the last chapter of the book  [[Theory_of_Stochastic_Signals\|"Theory of Stochastic Signals"]].		The filter influence on a random signal is only dealt with in the last chapter of the book  [[Theory_of_Stochastic_Signals\|"Theory of Stochastic Signals"]].

−	⇒   First a  »'''content overview'''«  on the basis of the  »'''four main chapters'''«  with a total of  »'''twelve individual chapters'''«.}}	+	⇒   First a  »'''content overview'''«  on the basis of the  »'''four main chapters'''«  with a total of  »'''twelve individual chapters'''«  and  »'''93 sections'''«.}}