Signal Representation/Principles of Communication - Revision history

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@@ Line 209: / Line 209: @@
 {{BlaueBox|TEXT=
-$\text{Definition:}$&nbsp; The transmission is&nbsp; &raquo;$\text{distortion&ndash;free}$&laquo;,&nbsp; if the sink signal is as follows:
+$\text{Definition:}$&nbsp; The transmission is&nbsp; &raquo;'''distortion&ndash;free'''&laquo;,&nbsp; if the sink signal is as follows:
 :: <math>v(t)=\alpha \cdot q(t-\tau)+n(t).</math>
 In this case the sink signal differs from the source signal except for the noise component&nbsp; $n(t)$&nbsp; only by
@@ Line 218: / Line 218: @@
 {{BlaueBox|TEXT=
-$\text{Definition:}$&nbsp;  If the equation&nbsp; $v(t)=\alpha \cdot q(t-\tau)+n(t)$&nbsp; is not fulfilled,&nbsp; then there are&nbsp; &raquo;$\text{distortions}$&laquo;.&nbsp;
+$\text{Definition:}$&nbsp;  If the equation&nbsp; $v(t)=\alpha \cdot q(t-\tau)+n(t)$&nbsp; is not fulfilled,&nbsp; then there are&nbsp; &raquo;'''distortions'''&laquo;.&nbsp;
-As described in the book&nbsp; [[Linear_and_Time_Invariant_Systems|"Linear and Time Invariant Systems"]]&nbsp; one distinguishes between
+As described in the book&nbsp; [[Linear_and_Time_Invariant_Systems|&raquo;Linear and Time Invariant Systems&laquo;]]&nbsp; one distinguishes between
-* &nbsp;[[Linear_and_Time_Invariant_Systems/Lineare_Verzerrungen|$\text{linear distortions}$]],&nbsp;
+* &nbsp;[[Linear_and_Time_Invariant_Systems/Lineare_Verzerrungen|&raquo;linear distortions&laquo;]],&nbsp;
-* &nbsp;[[Linear_and_Time_Invariant_Systems/Nonlinear_Distortions|$\text{nonlinear distortions}$]].
+* &nbsp;[[Linear_and_Time_Invariant_Systems/Nonlinear_Distortions|&raquo;nonlinear distortions&laquo;]].
 &rArr; &nbsp; In this context we refer to the&nbsp; $($German language$)$&nbsp; learning video&nbsp;
-:[[Lineare_und_nichtlineare_Verzerrungen_(Lernvideo)|"Lineare und nichtlineare Verzerrungen"]]&nbsp; &rArr; &nbsp; "Linear and nonlinear distortions".
+:[[Lineare_und_nichtlineare_Verzerrungen_(Lernvideo)|&raquo;Lineare und nichtlineare Verzerrungen&laquo;]]&nbsp; &rArr; &nbsp; "Linear and nonlinear distortions".
 }}
 Here again in slightly different words:
-*The attenuation factor&nbsp; $\alpha$&nbsp; only causes the signal&nbsp; $v(t)$&nbsp; to be slightly&nbsp; "quieter"&nbsp; than&nbsp; $q(t)$;&nbsp; but both signals have the same shape.
+*The attenuation factor&nbsp; $\alpha$&nbsp; only causes the signal&nbsp; $v(t)$&nbsp; to be slightly&nbsp; &raquo;quieter&laquo;&nbsp; than&nbsp; $q(t)$;&nbsp; but both signals have the same shape.
 *The delay&nbsp; $\tau$&nbsp; causes the signal&nbsp; $v(t)$&nbsp; to arrive at the receiver later than&nbsp; $q(t)$&nbsp; was sent.
@@ Line 246: / Line 246: @@
 $\text{Example 3:}$&nbsp; The terms used here shall now be clarified by an image signal.
-On the right you see as original image a color template with&nbsp; $291 × 218$&nbsp; pixels and&nbsp; $24$&nbsp; bit color depth.&nbsp; From the possible&nbsp; $2^{24} = 16\hspace{0.08cm} 777\hspace{0.08cm} 216$&nbsp; only a few colors are used here.
+On the right you see as original image a color template with&nbsp; $291 × 218$&nbsp; pixels and&nbsp; $24$&nbsp; bit color depth.&nbsp; From the possible&nbsp; $2^{24} = 16\hspace{0.08cm} 777\hspace{0.08cm} 216$&nbsp; colors only a few colors are used here.
 &rArr; &nbsp; In the lower left image,&nbsp; the signal is superposed with additive noise&nbsp; $n(t)$&nbsp; which is perceived as&nbsp; "snow".
-[[File:P_ID588_Sig_T_1_1_S7b.jpg|center|frame|Effects of&nbsp; "noise"&nbsp; and&nbsp; "distortion"&nbsp; on an image signal]]
+[[File:P_ID588_Sig_T_1_1_S7b.jpg|center|frame|Effects of&nbsp; &raquo;noise&laquo;&nbsp; and&nbsp; &raquo;distortion&laquo;&nbsp; on an image signal]]
 The lower right image shows the influence of&nbsp; $($nonlinear$)$&nbsp; distortions,&nbsp; which lead to a distortion of both brightness values and color information at the selected setting of the CCD camera.&nbsp; You can see:
-#In the marked field of the gray staircase,&nbsp; the brightness corresponds approximately to the original image&nbsp; $($above$)$.
+#In the marked field of the gray staircase,&nbsp; the brightness corresponds approximately to the original image&nbsp; $($above on the right $)$.
 #On the other hand,&nbsp; other fields appear as too light or too dark or filled with missing colors.
 #Noise effects play no role in the lower right image as opposed to the lower left image.

@@ Line 198: / Line 198: @@
 ==Signal distortions==
 <br>
-It has already been mentioned that ideallyv&nbsp; $v(t) = q(t)$v&nbsp; should be valid.&nbsp; However,&nbsp; as with any real transmission channel &nbsp; $r(t) \neq s(t)$,&nbsp; the sink signal&nbsp; $v(t)$&nbsp; will be different from the source signal&nbsp; $q(t)$.&nbsp; Here are some examples:
+It has already been mentioned that ideally&nbsp; $v(t) = q(t)$&nbsp; should be valid.&nbsp; However,&nbsp; as with any real transmission channel &nbsp; $r(t) \neq s(t)$,&nbsp; the sink signal&nbsp; $v(t)$&nbsp; will be different from the source signal&nbsp; $q(t)$.&nbsp; Here are some examples:
 {{BlaueBox|TEXT=
-$\text{Definition:}$&nbsp; One speaks of&nbsp; &raquo;$\text{noise}$&laquo;,&nbsp; if for the sink signal applies:
+$\text{Definition:}$&nbsp; One speaks of&nbsp; &raquo;'''noise'''&laquo;,&nbsp; if for the sink signal applies:
 :: <math> v(t)=q(t)+n(t).</math>
 *The additive noise component&nbsp; $n(t)$&nbsp; is always of stochastic nature and usually has no relation to the source signal&nbsp; $q(t)$.&nbsp;

@@ Line 57: / Line 57: @@
 In the following diagram a transmission system  is shown schematically.
-[[File:EN_Sig_T_1_1_S2_neu.png|center|frame| General block diagram of a message transmission system]]
+[[File:EN_Sig_T_1_1_S2_neu.png|center|frame| General block diagram of a transmission system]]
 The individual system components have the following tasks:
-*The&nbsp; &raquo;'''message source'''&laquo;&nbsp; returns the source signal&nbsp; $q(t)$,&nbsp; which shall be transmitted over the channel to the spatially distant sink.&nbsp; The source can be for example a computer,&nbsp; a radio station or a telephone participant.
+*The&nbsp; &raquo;'''message source'''&laquo;&nbsp; returns the&nbsp; &raquo;source signal&laquo;&nbsp; $q(t)$,&nbsp; which shall be transmitted over the channel to the spatially distant sink.&nbsp; The source can be for example a computer,&nbsp; a radio station or a telephone participant.
-*In most cases the source signal&nbsp; $q(t)$&nbsp; itself is unsuitable for transmission and must first be converted into the signal&nbsp; $s(t)$&nbsp; in a suitable manner.&nbsp; This process is called&nbsp; &raquo;modulation&laquo;&nbsp; and is performed by the&nbsp; &raquo;'''transmitter'''&laquo;.&nbsp;  In the following the signal &nbsp; $s(t)$&nbsp; is called&nbsp; &raquo;transmitted signal&laquo;.
+*In most cases the source signal&nbsp; $q(t)$&nbsp; itself is unsuitable for transmission and must first be converted into the signal&nbsp; $s(t)$&nbsp; in a suitable manner.&nbsp; This process is called&nbsp; &raquo;modulation&laquo;&nbsp; and is performed by the&nbsp; &raquo;'''transmitter'''&laquo;.&nbsp;  In the following,&nbsp; the signal&nbsp; $s(t)$&nbsp; is called&nbsp; &raquo;transmitted signal&laquo;.
 *During transmission over the&nbsp; &raquo;'''channel'''&laquo;&nbsp; the signal&nbsp; $s(t)$&nbsp; is changed in its form.&nbsp; At the same time,&nbsp; interference and noise signals are added.&nbsp; The signal at the channel output and simultaneously at the receiver input is called the&nbsp; &raquo;received signal&laquo;&nbsp; $r(t)$.
@@ Line 68: / Line 68: @@
 *The&nbsp; &raquo;'''receiver'''&laquo;&nbsp; must undo the conversion made by the transmitter.&nbsp; If,&nbsp; for example,&nbsp; the low-frequency source signal&nbsp; $q(t)$&nbsp; was converted to the higher-frequency transmitted signal&nbsp; $s(t)$&nbsp; the receiver must also contain a&nbsp; &raquo;demodulator&laquo;&nbsp; and undo this conversion.
-*The last block in the model above is the&nbsp; &raquo;'''message sink'''&laquo;.&nbsp; The sink signal&nbsp; $v(t)$&nbsp; is like the  source signal&nbsp; $q(t)$&nbsp; again low- frequency.&nbsp; In the ideal case,&nbsp; however,&nbsp; which in practice&nbsp; $($due to the unavoidable noise$)$&nbsp; can never be reached exactly,&nbsp; should apply for all times:&nbsp; $v(t) = q(t)$.
+*The last block in the model above is the&nbsp; &raquo;'''message sink'''&laquo;.&nbsp; The&nbsp; &raquo;sink signal&laquo;&nbsp; $v(t)$&nbsp; is like the  source signal&nbsp; $q(t)$&nbsp; low-frequency.&nbsp; In the ideal case should apply for all times:&nbsp; $v(t) = q(t)$.&nbsp; But in practice&nbsp; this can never be reached exactly&nbsp; $($due to the unavoidable noise$)$.
@@ Line 81: / Line 81: @@
-In general,&nbsp; a distinction is made between analog and digital sources.&nbsp;  The description presented in this book apply equally to analog and digital signals.&nbsp; The basic differences between analog and digital signals are discussed in the chapter&nbsp; [[Signal_Representation/Signal_classification|"Signal classification"]],&nbsp; and  clarified  with examples throughout the&nbsp; $($German language$)$&nbsp; learning video
+In general,&nbsp; a distinction is made between analog and digital sources.&nbsp;  The description presented in this book apply equally to analog and digital signals.&nbsp; The basic differences between analog and digital signals are discussed in the chapter&nbsp; [[Signal_Representation/Signal_classification|&raquo;Signal classification&laquo;]],&nbsp; and  clarified  with examples throughout the&nbsp; $($German language$)$&nbsp; learning video
-:[[Analoge und digitale Signale (Lernvideo)|"Analoge und digitale Signale"]] &nbsp; &rArr; &nbsp; "Analog and Digital Signals".
+:[[Analoge und digitale Signale (Lernvideo)|&raquo;Analoge und digitale Signale&laquo;]] &nbsp; &rArr; &nbsp; "Analog and Digital Signals".
 [[File:EN_Sig_T_1_1_S3.png|right|frame|Frequency-time representation of a speech signal]]
 {{GraueBox|TEXT=
 $\text{Example 2:}$&nbsp;
-On the right you see the frequency-time representation of a speech signal.
+On the right you see the frequency-time representation of a speech signal:
@@ Line 113: / Line 113: @@
 *a signal converter &ndash; for example from&nbsp; &raquo;analog&laquo;&nbsp; to&nbsp; &raquo;digital&laquo;&nbsp; using the components&nbsp; &raquo;sampling&laquo;,&nbsp; &raquo;quantization&raquo;&nbsp; and&nbsp; &raquo;PCM encoding&raquo;,
-*an encoder for removing redundancy to data compression &nbsp; $($&raquo;source coding&laquo;$)$&nbsp; or <br>for systematically adding redundancy,&nbsp; which can be used at the receiver for&nbsp; "error detection" &nbsp; and/or&nbsp; "error correction" &nbsp; $($&raquo;channel coding&laquo;$)$,
+*an encoder for removing redundancy to data compression &nbsp; $($&raquo;source coding&laquo;$)$&nbsp; or <br>for systematically adding redundancy,&nbsp; which can be used at the receiver for&nbsp; &raquo;error detection&laquo; &nbsp; and/or&nbsp; &raquo;error correction&laquo; &nbsp; $($&raquo;channel coding&laquo;$)$,
 *a modulator for adaptation to the transmission channel &ndash; for example a frequency conversion by means of amplitude,&nbsp; phase or frequency modulation or the corresponding digital methods ASK,&nbsp; PSK,&nbsp; FSK.
-Depending on the application, the&nbsp; &raquo;'''performance characteristics'''&laquo; mentioned above mean that very specific properties are required for signal transmission.
+Depending on the application,&nbsp; the&nbsp; &raquo;'''performance characteristics'''&laquo; mentioned above mean that very specific properties are required for signal transmission.
 Such features are for example:
-#&raquo;power limitation&laquo;&nbsp; &ndash; due to the discussions on the topic&nbsp; "electrosmog"&nbsp; highly topical,
+#&raquo;Power limitation&laquo;&nbsp; &ndash; due to the discussions on the topic&nbsp; "electrosmog"&nbsp; highly topical,
 #&raquo;bandwidth efficiency&laquo;&nbsp; &ndash; the UMTS auction in 2000 has shown what magnitudes are involved,
 #&raquo;distance&laquo;&nbsp; or&nbsp; &raquo;range&laquo;&nbsp; &ndash; unfavorable values increase the infrastructure costs,
@@ Line 134: / Line 134: @@
 Examples of transmission media are:
-#Electrical cables,&nbsp; e.g.&nbsp; copper wire,nbsp; twisted pair,
+#Electrical cables,&nbsp; e.g.&nbsp; copper wire,&nbsp; twisted pair,
 #coaxial cable,&nbsp; e.g.&nbsp; antenna line or cable network,
 #fiber optic cables,&nbsp; e.g.&nbsp; multi-mode and single-mode fiber optic,
-#radio channels,&nbsp; e.g.&nbsp; broadcasting,nbsp; mobile and satellite radio.
+#radio channels,&nbsp; e.g.&nbsp; broadcasting,&nbsp; mobile and satellite radio.
@@ Line 158: / Line 158: @@
 *pulse disturbances,&nbsp; e.g.&nbsp; from power lines,&nbsp; spark interference and discharges,
-*adjacent channel interference&nbsp; $($cros-stalk of other users,&nbsp; cross-modulation$)$.}}
+*adjacent channel interference&nbsp; $($cross-talk of other users,&nbsp; cross-modulation$)$.}}
 &nbsp; &rArr; &nbsp; You will find basic information about modeling the transmission channel in general and the simple&nbsp; &raquo;AWGN channel&laquo;&nbsp; in the the&nbsp; $($German language$)$&nbsp; learning video
-:[[Eigenschaften_des_Übertragungskanals_(Lernvideo)|"Eigenschaften des Übertragungskanals"]] &nbsp; &rArr; &nbsp; "Properties of the Transmission Channel".
+:[[Eigenschaften_des_Übertragungskanals_(Lernvideo)|&raquo;Eigenschaften des Übertragungskanals&laquo;]] &nbsp; &rArr; &nbsp; "Properties of the Transmission Channel".

@@ Line 12: / Line 12: @@
 This chapter describes in detail:
-#the&nbsp; &raquo;tasks  and the   basic structure&laquo;&nbsp;   of a transmission system,
+#The&nbsp; &raquo;tasks  and basic structure&laquo;&nbsp;   of a transmission system,
-#the&nbsp; &raquo;main functional units&laquo;&nbsp; &nbsp; $($source,&nbsp; transmitter,&nbsp; channel, receiver and sink$)$&nbsp; of such a system,&nbsp; and finally
+#the&nbsp; &raquo;main functional units&laquo;&nbsp; &nbsp; $($source,&nbsp; transmitter,&nbsp; channel,&nbsp; receiver,&nbsp; sink$)$&nbsp; of such a system,&nbsp; and finally
 #a&nbsp; &raquo;classification  of the signals&laquo;&nbsp; occurring in a transmission system according to several evaluation criteria: &nbsp; &nbsp; <br> &nbsp; &nbsp; &raquo;deterministic or stochastic, energy or power limited, continuous or discrete time, continuous or discrete value, analog or digital&laquo;.
@@ Line 27: / Line 27: @@
 {{GraueBox|TEXT=
 $\text{Example 1:}$&nbsp;
-An e&ndash;mail from Mr. Maier to Mrs. Miller is always a&nbsp; &raquo;message&laquo;.&nbsp; For Mrs. Miller,&nbsp; however,&nbsp; receiving this e&ndash;mail only means an information gain if she learns something new.&nbsp; The&nbsp; &raquo;information&laquo;&nbsp; transmitted by a message therefore depends to a great extent on the knowledge level of the recipient.&nbsp; In practice,&nbsp; the information contained in a message is rather small,&nbsp; especially in the field of telephony.}}
+An e&ndash;mail from Mr. Maier to Mrs. Miller is always a&nbsp; &raquo;message&laquo;.&nbsp;
@@ Line 42: / Line 45: @@
 {{BlaueBox|TEXT=
 $\text{Please note:}$&nbsp;
-*The signals used for&nbsp; &raquo;$\text{data transmissiion}$&raquo;&nbsp; are usually time functions.&nbsp; This means that&nbsp; $($at least$)$ one of the signal parameters is dependent on the time parameter&nbsp; $t$.&nbsp; Such parameters are for example for a signal tone the amplitude&nbsp; $($"volume"$)$&nbsp; and the frequency&nbsp; $($"pitch"$)$.
+*The signals used for&nbsp; &raquo;$\text{data transmission}$&laquo;&nbsp; are usually time functions.&nbsp; This means that&nbsp; $($at least$)$ one of the signal parameters is dependent on the time parameter&nbsp; $t$.&nbsp; Such parameters for a signal tone are e.g. the amplitude&nbsp; $($&raquo;volume&laquo;$)$&nbsp; and the frequency&nbsp; $($&raquo;pitch&laquo;$)$.
-*For storing messages &nbsp; &rArr; &nbsp; &raquo;$\text{data storage}$&laquo;&nbsp; the time functions are often mapped to spatial functions of suitable physical quantities such as magnetization&nbsp; $($"magnetic band"$)$&nbsp; or degree of blackening&nbsp; $($"film"$)$.}}
+*For storing messages &nbsp; &rArr; &nbsp; &raquo;$\text{data storage}$&laquo;&nbsp; the time functions are often mapped to spatial functions of suitable physical quantities such as magnetization&nbsp; $($&raquo;magnetic band&laquo;$)$&nbsp; or degree of blackening&nbsp; $($&raquo;film&laquo;$)$.}}

@@ Line 65: / Line 65: @@
 *The&nbsp; &raquo;'''receiver'''&laquo;&nbsp; must undo the conversion made by the transmitter.&nbsp; If,&nbsp; for example,&nbsp; the low-frequency source signal&nbsp; $q(t)$&nbsp; was converted to the higher-frequency transmitted signal&nbsp; $s(t)$&nbsp; the receiver must also contain a&nbsp; &raquo;demodulator&laquo;&nbsp; and undo this conversion.
-*The last block in the model above is the&nbsp; &raquo;'''message sink'''&laquo;.&nbsp; The sink signal&nbsp; $v(t)$&nbsp; is like the  source signal&nbsp; $q(t)$&nbsp; again low frequency.&nbsp; In the ideal case,&nbsp; however,&nbsp; which in practice&nbsp; $($due to the unavoidable noise$)$&nbsp; can never be reached exactly,&nbsp; should apply for all times:&nbsp; $v(t) = q(t)$.
+*The last block in the model above is the&nbsp; &raquo;'''message sink'''&laquo;.&nbsp; The sink signal&nbsp; $v(t)$&nbsp; is like the  source signal&nbsp; $q(t)$&nbsp; again low- frequency.&nbsp; In the ideal case,&nbsp; however,&nbsp; which in practice&nbsp; $($due to the unavoidable noise$)$&nbsp; can never be reached exactly,&nbsp; should apply for all times:&nbsp; $v(t) = q(t)$.
@@ Line 72: / Line 72: @@
 <br>
 As examples for message sources and for the source signal&nbsp; $q(t)$&nbsp; can be mentioned:
-*Audio signals, e.g. speech or music,
+#Audio signals,&nbsp; e.g.&nbsp; speech or music,
-*video signals, e.g. an analog television signal or an MPEG encoded streaming video,
+#video signals,&nbsp; e.g.&nbsp; an analog television signal or an MPEG encoded streaming video,
-*data signals, e.g. the data stream of a USB interface or an email on the Internet,
+#data signals,&nbsp; e.g.&nbsp; the data stream of a USB interface or an email on the Internet,
-*measure signals, e.g. for control or regulation in a production process.
+#measure signals,&nbsp; e.g.&nbsp; for control or regulation in a production process.
-In general, a distinction is made between analog and digital sources.&nbsp;  The description presented in this book apply equally to analog and digital signals.&nbsp; The basic differences between analog and digital signals are discussed in the chapter&nbsp; [[Signal_Representation/Signal_classification|"Signal classification"]],&nbsp; and  clarified  with examples throughout the (German language) learning video
+In general,&nbsp; a distinction is made between analog and digital sources.&nbsp;  The description presented in this book apply equally to analog and digital signals.&nbsp; The basic differences between analog and digital signals are discussed in the chapter&nbsp; [[Signal_Representation/Signal_classification|"Signal classification"]],&nbsp; and  clarified  with examples throughout the&nbsp; $($German language$)$&nbsp; learning video
 :[[Analoge und digitale Signale (Lernvideo)|"Analoge und digitale Signale"]] &nbsp; &rArr; &nbsp; "Analog and Digital Signals".
@@ Line 84: / Line 84: @@
 {{GraueBox|TEXT=
 $\text{Example 2:}$&nbsp;
 On the right you see the frequency-time representation of a speech signal.
 We thank&nbsp; Markus Kaindl<ref>Kaindl, M.: Kanalcodierung für Sprache und Daten in GSM-Systemen. Dissertation. <br>Lehrstuhl für Nachrichtentechnik, TU München. VDI Fortschritt-Berichte, Reihe 10, Nr. 764, 2005.</ref>, LNT/TUM, for providing the graphic.}}

@@ Line 12: / Line 12: @@
 This chapter describes in detail:
-#the&nbsp; &raquo;tasks  and the   basic structure&laquo;&nbsp;   of a communication system,
+#the&nbsp; &raquo;tasks  and the   basic structure&laquo;&nbsp;   of a transmission system,
-#the&nbsp; &raquo;main functional units&laquo;&nbsp; &nbsp; (source, transmitter, channel, receiver and sink)&nbsp; of such a system, and finally
+#the&nbsp; &raquo;main functional units&laquo;&nbsp; &nbsp; $($source,&nbsp; transmitter,&nbsp; channel, receiver and sink$)$&nbsp; of such a system,&nbsp; and finally
-#a&nbsp; &raquo;classification  of the signals&laquo;&nbsp; occurring in a communication system according to several evaluation criteria: &nbsp; &nbsp; <br> &nbsp; &nbsp; &raquo;deterministic or stochastic, energy or power limited, continuous or discrete time, continuous or discrete value, analog or digital&laquo;&nbsp;.
+#a&nbsp; &raquo;classification  of the signals&laquo;&nbsp; occurring in a transmission system according to several evaluation criteria: &nbsp; &nbsp; <br> &nbsp; &nbsp; &raquo;deterministic or stochastic, energy or power limited, continuous or discrete time, continuous or discrete value, analog or digital&laquo;.
-At the end of the chapter follows a short summary about &nbsp; &raquo;Calculating with complex numbers&laquo;.
+At the end of the chapter follows a short summary about&nbsp; &raquo;Calculating with complex numbers&laquo;.
@@ Line 23: / Line 23: @@
 ==Message - Information - Signal==
 <br>
-One distinguishes basically between the terms&nbsp; "message"&nbsp; and&nbsp; "information", which are often used synonymously nowadays.
+One distinguishes basically between the terms&nbsp; &raquo;message&laquo;&nbsp; and&nbsp; &raquo;information&laquo;,&nbsp; which are often used synonymously nowadays.
 {{GraueBox|TEXT=
 $\text{Example 1:}$&nbsp;
-An e&ndash;mail from Mr. Maier to Mrs. Miller is always a&nbsp; "message".&nbsp; For Mrs. Miller, however, receiving this e&ndash;mail only means an information gain if she learns something new.&nbsp; The&nbsp; "information"&nbsp; transmitted by a message therefore depends to a great extent on the knowledge level of the recipient. In practice, the information contained in a message is rather small, especially in the field of telephony.}}
+An e&ndash;mail from Mr. Maier to Mrs. Miller is always a&nbsp; &raquo;message&laquo;.&nbsp; For Mrs. Miller,&nbsp; however,&nbsp; receiving this e&ndash;mail only means an information gain if she learns something new.&nbsp; The&nbsp; &raquo;information&laquo;&nbsp; transmitted by a message therefore depends to a great extent on the knowledge level of the recipient.&nbsp; In practice,&nbsp; the information contained in a message is rather small,&nbsp; especially in the field of telephony.}}
-The transmission of messages &nbsp; &rArr; &nbsp; &raquo;'''communications'''&laquo;&nbsp; and their storage always requires an energetic or material carrier called&nbsp; "signal".&nbsp; Physically the representation of a message is done by signals, which can be of very different nature.
+The transmission of messages &nbsp;  and their storage always requires an energetic or material carrier called&nbsp; &raquo;signal&laquo;.&nbsp; Physically the representation of a message is done by signals,&nbsp; which can be of very different nature.
 Possible appearances are:
-*Electrical signals&nbsp; (for example current and voltage curve),
+#Electrical signals&nbsp; $($e.g.&nbsp; current and voltage curves$)$,
-*electromagnetic waves&nbsp; (for example in radio transmission),
+#electromagnetic waves&nbsp; $($e.g.&nbsp; in radio transmission$)$,
-*progression of pressure, temperature or other physical quantities,
+#progression of pressure,&nbsp; temperature or other physical quantities,
-*acoustic signals&nbsp; (for example, output signal of a loudspeaker),
+#acoustic signals&nbsp; $($e.g.&nbsp; output signal of a loudspeaker$)$,
-*optical signals&nbsp; (for example output signal of a laser).
+#optical signals&nbsp; $($e.g.&nbsp; output signal of a laser$)$.
 {{BlaueBox|TEXT=
 $\text{Please note:}$&nbsp;
-*The signals used for&nbsp; $\text{communication}$&nbsp; are usually time functions.&nbsp; This means that (at least) one of the signal parameters is dependent on the time parameter&nbsp; $t$.&nbsp; Such signal parameters are for example for a signal tone the amplitude ("volume") and the frequency ("pitch").
+*The signals used for&nbsp; &raquo;$\text{data transmissiion}$&raquo;&nbsp; are usually time functions.&nbsp; This means that&nbsp; $($at least$)$ one of the signal parameters is dependent on the time parameter&nbsp; $t$.&nbsp; Such parameters are for example for a signal tone the amplitude&nbsp; $($"volume"$)$&nbsp; and the frequency&nbsp; $($"pitch"$)$.
-*For storing messages &nbsp; &rArr; &nbsp; $\text{data storage}$&nbsp; the time functions are often mapped to spatial functions of suitable physical quantities such as magnetization (magnetic band) or degree of blackening (film).}}
+*For storing messages &nbsp; &rArr; &nbsp; &raquo;$\text{data storage}$&laquo;&nbsp; the time functions are often mapped to spatial functions of suitable physical quantities such as magnetization&nbsp; $($"magnetic band"$)$&nbsp; or degree of blackening&nbsp; $($"film"$)$.}}
-The set of all message signals can be cataloged by different criteria, as described in the chapter&nbsp; [[Signal_Representation/Signal_classification|"Signal classification"]].&nbsp;
+The set of all message signals can be cataloged by different criteria,&nbsp; as described in the chapter&nbsp; [[Signal_Representation/Signal_classification|&raquo;Signal classification&laquo;]].&nbsp;
-==Block diagram of a communications system==
+==Block diagram of a transmission system==
 <br>
-In the following diagram a communication system  is shown schematically.
+In the following diagram a transmission system  is shown schematically.
-[[File:EN_Sig_T_1_1_S2_neu.png|center|frame| General block diagram of a message transmission system &nbsp; &rArr; &nbsp; communication system]]
+[[File:EN_Sig_T_1_1_S2_neu.png|center|frame| General block diagram of a message transmission system]]
 The individual system components have the following tasks:
-*The&nbsp; &raquo;'''message source'''&laquo;&nbsp; returns the source signal&nbsp; $q(t)$, which shall be transmitted over the channel to the spatially distant sink.&nbsp; The source can be for example a computer, a radio station or a telephone participant.
+*The&nbsp; &raquo;'''message source'''&laquo;&nbsp; returns the source signal&nbsp; $q(t)$,&nbsp; which shall be transmitted over the channel to the spatially distant sink.&nbsp; The source can be for example a computer,&nbsp; a radio station or a telephone participant.
-*In most cases the source signal&nbsp; $q(t)$&nbsp; itself is unsuitable for transmission and must first be converted into the signal&nbsp; $s(t)$&nbsp; in a suitable manner.&nbsp; This process is called "modulation" and is performed by the&nbsp; &raquo;'''transmitter'''&laquo;.&nbsp;  In the following the signal &nbsp; $s(t)$&nbsp; is called&nbsp; "transmitted signal".
-*During transmission over the&nbsp; &raquo;'''channel'''&laquo;&nbsp; the signal&nbsp; $s(t)$&nbsp; is changed in its form.&nbsp; At the same time, interference and noise signals are added.&nbsp; The signal at the channel output and simultaneously at the receiver input is called the&nbsp; "received signal"&nbsp; $r(t)$.
+*In most cases the source signal&nbsp; $q(t)$&nbsp; itself is unsuitable for transmission and must first be converted into the signal&nbsp; $s(t)$&nbsp; in a suitable manner.&nbsp; This process is called&nbsp; &raquo;modulation&laquo;&nbsp; and is performed by the&nbsp; &raquo;'''transmitter'''&laquo;.&nbsp;  In the following the signal &nbsp; $s(t)$&nbsp; is called&nbsp; &raquo;transmitted signal&laquo;.
 *The&nbsp; &raquo;'''receiver'''&laquo;&nbsp; must undo the conversion made by the transmitter.&nbsp; If, for example, the low-frequency source signal&nbsp; $q(t)$&nbsp; was converted to the higher-frequency transmitted signal&nbsp; $s(t)$&nbsp; the receiver must also contain a demodulator and undo this conversion.
-*The last block in the model above is the&nbsp; &raquo;'''message sink'''&laquo;. The sink signal&nbsp; $v(t)$&nbsp; is like the  source signal&nbsp; $q(t)$&nbsp; again low frequency.&nbsp; In the ideal case, however, which in practice&nbsp; (due to the unavoidable noise)&nbsp; can never be reached exactly, should apply for all times&nbsp; $v(t) = q(t)$.
+*During transmission over the&nbsp; &raquo;'''channel'''&laquo;&nbsp; the signal&nbsp; $s(t)$&nbsp; is changed in its form.&nbsp; At the same time,&nbsp; interference and noise signals are added.&nbsp; The signal at the channel output and simultaneously at the receiver input is called the&nbsp; &raquo;received signal&laquo;&nbsp; $r(t)$.

@@ Line 139: / Line 139: @@
-You will find basic information about modeling the transmission channel in general and the simple AWGN channel in the the (German language) learning video
+&rArr; &nbsp; You will find basic information about modeling the transmission channel in general and the simple AWGN channel in the the (German language) learning video
 :[[Eigenschaften_des_Übertragungskanals_(Lernvideo)|"Eigenschaften des Übertragungskanals"]] &nbsp; &rArr; &nbsp; "Properties of the Transmission Channel".
@@ Line 197: / Line 197: @@
-In this context we refer to the (German language) learning video&nbsp;
+&rArr; &nbsp; In this context we refer to the (German language) learning video&nbsp;
 :[[Lineare_und_nichtlineare_Verzerrungen_(Lernvideo)|"Lineare und nichtlineare Verzerrungen"]]&nbsp; &rArr; &nbsp; "Linear and nonlinear distortions".
 }}

@@ Line 8: / Line 8: @@
 == # OVERVIEW OF THE FIRST MAIN CHAPTER # ==
 <br>
-This first chapter serves as an introduction to the whole topic, which is covered by the nine books of the series&nbsp; $\rm LNTwww$.
+This first chapter serves as an&nbsp; &raquo;introduction to the whole topic&laquo;,&nbsp; which is covered by the nine books of the&nbsp; $\rm LNTwww$&nbsp; series.
 This chapter describes in detail:
-*the&nbsp; &raquo;tasks  and the   basic structure&laquo;&nbsp;   of a communication system,
+#the&nbsp; &raquo;tasks  and the   basic structure&laquo;&nbsp;   of a communication system,
+#the&nbsp; &raquo;main functional units&laquo;&nbsp; &nbsp; (source, transmitter, channel, receiver and sink)&nbsp; of such a system, and finally
-*the&nbsp; &raquo;main functional units&laquo;&nbsp; &nbsp; (source, transmitter, channel, receiver and sink)&nbsp; of such a system, and finally
+#a&nbsp; &raquo;classification  of the signals&laquo;&nbsp; occurring in a communication system according to several evaluation criteria: &nbsp; &nbsp; <br> &nbsp; &nbsp; &raquo;deterministic or stochastic, energy or power limited, continuous or discrete time, continuous or discrete value, analog or digital&laquo;&nbsp;.

@@ Line 129: / Line 129: @@
 *the channel attenuation,
 *delays on the channel,
-*linear and non-linear '''KORREKTUR: nonlinear''' distortions.
+*linear and nonlinear distortions.
@@ Line 137: / Line 137: @@
 In addition, the&nbsp; &raquo;'''interfering signals'''&laquo;&nbsp; that occur during signal transmission must always be taken into account.&nbsp; The following are examples of this:
 *Noise signals - e.g. resistance and semiconductor noise,
-*Pulse '''KORREKTUR: intersymbol''' interference - e.g. power lines, spark interference and discharges,
+*Intersymbol interference - e.g. power lines, spark interference and discharges,
 *Adjacent channel interference&nbsp; (crosstalk of other users, interference, cross modulation).
@@ Line 163: / Line 163: @@
-Another important task of the receiver is to eliminate as much as possible the signal distortions and interference '''KORREKTUR: noise''' that occur during transmission.&nbsp; The realization of such system components for transmitters and receivers is done by different electrical networks and assemblies.
+Another important task of the receiver is to eliminate as much as possible the signal distortions and noise that occur during transmission.&nbsp; The realization of such system components for transmitters and receivers is done by different electrical networks and assemblies.
 Here, too, some functional units can be named as examples:
@@ Line 180: / Line 180: @@
 :: <math> v(t)=q(t)+n(t).</math>
 *The additive noise component&nbsp; $n(t)$&nbsp; is always of stochastic nature and usually has no relation to the source signal&nbsp; $q(t)$.&nbsp;
-*Such a noise term '''KORREKTUR: component''' is inevitable for every transmission.}}
+*Such a noise component is inevitable for every transmission.}}
@@ Line 221: / Line 221: @@
 *In the lower left image, the signal is superposed with additive noise&nbsp; $n(t)$&nbsp; which is perceived as "snow".
-*The lower right image shows the influence of (non&ndash;linear '''KORREKTUR: nonlinear''') distortions, which lead to a distortion of both brightness values and color information at the selected setting of the CCD camera.
+*The lower right image shows the influence of (nonlinear) distortions, which lead to a distortion of both brightness values and color information at the selected setting of the CCD camera.
 *In the marked field of the gray staircase, the brightness corresponds approximately to the original image (above).
 *On the other hand, other fields appear as too light or too dark or filled with missing colors.