Modulation Methods/Further AM Variants - Revision history

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	*For frequency and phase synchronous demodulation,  the signal in the upper branch before the low-pass  $H_{\rm E1}(f)$  is:		*For frequency and phase synchronous demodulation,  the signal in the upper branch before the low-pass  $H_{\rm E1}(f)$  is:
	:$$b_1(t) = q_1(t) \cdot 2 \cdot \cos^2 (\omega_{\rm T}\cdot t) - q_2(t) \cdot 2 \cdot		:$$b_1(t) = q_1(t) \cdot 2 \cdot \cos^2 (\omega_{\rm T}\cdot t) - q_2(t) \cdot 2 \cdot\cos (\omega_{\rm T}\cdot t)\cdot \sin (\omega_{\rm T}\cdot t) $$
	\cos (\omega_{\rm T}\cdot t)\cdot \sin (\omega_{\rm T}\cdot t) $$
	:$$\Rightarrow \hspace{0.3cm} b_1(t) = q_1(t)\cdot \big[ 1 + \cos (2 \omega_{\rm T}\cdot t) \big] - q_2(t)\cdot \sin (2 \omega_{\rm T}\cdot t) \hspace{0.05cm}.$$		:$$\Rightarrow \hspace{0.3cm} b_1(t) = q_1(t)\cdot \big[ 1 + \cos (2 \omega_{\rm T}\cdot t) \big] - q_2(t)\cdot \sin (2 \omega_{\rm T}\cdot t) \hspace{0.05cm}.$$

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	{{Display}}		{{Display}}
			[[de:Modulationsverfahren/Weitere_AM–Varianten]]

Guenter at 09:52, 13 January 2023

2023-01-13T09:52:43Z

Hwang at 22:08, 2 January 2023

2023-01-02T22:08:21Z

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	[[File:EN_Mod_T_2_5_S1b.png\|right\|frame\|Illustrating the Nyquist edge for PAL–B/G Television]]		[[File:EN_Mod_T_2_5_S1b.png\|right\|frame\|Illustrating the Nyquist edge for PAL–B/G Television]]
	In this schematic representation,  one ~~recognises~~:		In this schematic representation,  one recognizes:
	*The radiated spectrum  (only positive frequencies are drawn)  ranges from  $f_{\rm T} - 1.25 \ \rm MHz$  to  $f_{\rm T} + 5.75 \ \rm MHz$.  The lower vestigial sideband including Nyquist edge is  $\approx 1.25 \ \rm MHz$  wide.		*The radiated spectrum  (only positive frequencies are drawn)  ranges from  $f_{\rm T} - 1.25 \ \rm MHz$  to  $f_{\rm T} + 5.75 \ \rm MHz$.  The lower vestigial sideband including Nyquist edge is  $\approx 1.25 \ \rm MHz$  wide.
	*The green dashed line shows the receiver passband.  The image carrier  '''(B)'''  – abbreviation  "B"  from German "Bild"   ⇒   "image") –   at carrier frequency  $f_{\rm T}$  is centered on the Nyquist edge.		*The green dashed line shows the receiver passband.  The image carrier  '''(B)'''  – abbreviation  "B"  from German "Bild"   ⇒   "image") –   at carrier frequency  $f_{\rm T}$  is centered on the Nyquist edge.

Hwang at 22:02, 2 January 2023

2023-01-02T22:02:08Z

Reed at 14:21, 9 April 2022

2022-04-09T14:21:53Z

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	[[File:EN_Mod_T_2_5_S1.png\|right\|frame\|Spectrum  (of the analytical signal)  for vestigial sideband amplitude modulation]]		[[File:EN_Mod_T_2_5_S1.png\|right\|frame\|Spectrum  (of the analytical signal)  for vestigial sideband amplitude modulation]]
	The problem can be greatly mitigated if instead single-sideband AM one uses   "vestigial sideband amplitude modulation"  $\rm (VSB–AM)$,  as shown in the adjacent graph.		The problem can be greatly mitigated if instead of single-sideband AM one uses   "vestigial sideband amplitude modulation"  $\rm (VSB–AM)$,  as shown in the adjacent graph.

	The present description is based on the textbook   [Mäu88]<ref>Mäusl, R.:  Analoge Modulationsverfahren.  Heidelberg: Dr. Hüthig, 1988.</ref>.  According to it,  the VSB-AM can be characterized as follows:		The present description is based on the textbook   [Mäu88]<ref>Mäusl, R.:  Analoge Modulationsverfahren.  Heidelberg: Dr. Hüthig, 1988.</ref>.  According to it,  the VSB-AM can be characterized as follows:

Reed at 14:21, 9 April 2022

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	When transmitting signals using single-sideband modulation  $\rm (SSB–AM)$  the following problems occur:		When transmitting signals using single-sideband modulation  $\rm (SSB–AM)$  the following problems occur:
	*To suppress the unwanted sideband,  a filter with a very high edge slope must be used.		*To suppress the unwanted sideband,  a filter with a very high edge slope must be used.
	*Such a steep-edged filters exhibit strong group delay distortions,  especially at the limit of the passband.		*Such steep-edged filters exhibit strong group delay distortions,  especially at the limit of the passband.

Reed at 14:21, 9 April 2022

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	{{Header		{{Header
	\|Untermenü=Amplitude Modulation and Demodulation		\|Untermenü=Amplitude Modulation and Demodulation
	\|Vorherige Seite=~~Einseitenbandmodulation~~		\|Vorherige Seite=Single-Sideband Modulation
	\|Nächste Seite=~~Phasenmodulation~~ (PM)		\|Nächste Seite=Phase Modulation (PM)
	}}		}}
	==Vestigial sideband amplitude modulation==		==Vestigial sideband amplitude modulation==

Guenter at 13:34, 18 January 2022

2022-01-18T13:34:19Z

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	An example of an incoherent demodulator is the   [[Modulation_Methods/Envelope_Demodulation\|envelope demodulator]].		An example of an incoherent demodulator is the  [[Modulation_Methods/Envelope_Demodulation\|envelope demodulator]].

	{{GraueBox\|TEXT=		{{GraueBox\|TEXT=

Guenter at 13:28, 18 January 2022

2022-01-18T13:28:33Z

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	:$$v_2(t) = q_2(t)\hspace{0.05cm}.$$		:$$v_2(t) = q_2(t)\hspace{0.05cm}.$$
	*When there is a phase offset  $Δϕ_{\rm T}$  between the transmitted and received carrier signals,  in addition to attenuation of the intended participant,<br>crosstalk from the second participant occurs,  resulting in nonlinear distortion:		*When there is a phase offset  $Δϕ_{\rm T}$  between the transmitted and received carrier signals,  in addition to attenuation of the intended participant,<br>crosstalk from the second participant occurs,  resulting in nonlinear distortion:
	:$$v_1(t) = \alpha_{11} \cdot q_1(t)+ \alpha_{12} \cdot q_2(t) \hspace{0.05cm}, ~~\hspace{0.3cm}~~ v_2(t) = \alpha_{21} \cdot q_1(t)+ \alpha_{22} \cdot q_2(t)$$		:$$v_1(t) = \alpha_{11} \cdot q_1(t)+ \alpha_{12} \cdot q_2(t) \hspace{0.05cm}, $$
			:$$v_2(t) = \alpha_{21} \cdot q_1(t)+ \alpha_{22} \cdot q_2(t)$$
	:$$\Rightarrow\hspace{0.3cm}\alpha_{11} = \alpha_{22} = \cos(\Delta \phi_{\rm T}) \hspace{0.05cm}, \hspace{0.3cm} \alpha_{12} = -\alpha_{21} = \sin(\Delta \phi_{\rm T}) \hspace{0.05cm}.$$		:$$\Rightarrow\hspace{0.3cm}\alpha_{11} = \alpha_{22} = \cos(\Delta \phi_{\rm T}) \hspace{0.05cm}, \hspace{0.3cm} \alpha_{12} = -\alpha_{21} = \sin(\Delta \phi_{\rm T}) \hspace{0.05cm}.$$

	==Incoherent (non-coherent) Demodulation==		==Incoherent (non-coherent) Demodulation==
	<br>		<br>
	~~Demodulators can be classified in the following way:~~

	{{BlaueBox\|TEXT=		{{BlaueBox\|TEXT=
	$\text{Definition:}$  A demodulator is said to be  '''coherent''', if in addition to the required frequency synchronization, it requires accurate information about the phase of the transmit-side carrier signal  $z(t)$  to reconstruct the ~~message~~ signal.		$\text{Definition:}$  Demodulators can be classified in the following way:
			*A demodulator is said to be  '''coherent''',  if in addition to the required frequency synchronization,  it requires accurate information about the phase of the transmit-side carrier signal  $z(t)$  to reconstruct the source signal.

	If this phase information is not required, the demodulator is said to be an  '''incoherent demodulator'''.}}		*If this phase information is not required,  the demodulator is said to be an  '''incoherent demodulator'''  or  "non-coherent demodulator".}}


	An example of an incoherent ~~(or non-coherent)~~ demodulator is the   [[Modulation_Methods/Envelope_Demodulation\|envelope demodulator]].		An example of an incoherent demodulator is the   [[Modulation_Methods/Envelope_Demodulation\|envelope demodulator]].

	{{GraueBox\|TEXT=		{{GraueBox\|TEXT=
	$\text{Example 2:}$  A second example is shown in the following block diagram.  In contrast to quadrature amplitude modulation, here the orthogonality between cosine and sine functions is not used for the simultaneous transmission of a second source signal, but rather to simplify the receiver-side device.		$\text{Example 2:}$  A second example is shown in the following block diagram.  In contrast to quadrature amplitude modulation,  here the orthogonality between cosine and sine functions is not used for the simultaneous transmission of a second source signal,  but rather to simplify the receiver-side device.

	[[File:P_ID1054__Mod_T_2_5_S3_neu.png \|~~center~~\|frame\|Incoherent demodulation with  $\rm DSB-AM$]]		[[File:P_ID1054__Mod_T_2_5_S3_neu.png \|right\|frame\|Incoherent demodulation with  $\rm DSB-AM$]]

	It should be further noted regarding this arrangement:		It should be further noted regarding this arrangement:
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	:$$b_1(t) = \cos(\Delta \phi_{\rm T}) \cdot q(t), $$		:$$b_1(t) = \cos(\Delta \phi_{\rm T}) \cdot q(t), $$
	:$$b_2(t) = -\sin(\Delta \phi_{\rm T}) \cdot q(t).$$		:$$b_2(t) = -\sin(\Delta \phi_{\rm T}) \cdot q(t).$$
	*This ensures that the sink signal  $v(t)$  matches the source signal  $q(t)$ ~~, at least~~ in magnitude, regardless of the phase offset  $Δϕ_{\rm T}$~~ ~~:		*This ensures that the sink signal  $v(t)$  matches the source signal  $q(t)$  in magnitude,  regardless of the phase offset  $Δϕ_{\rm T}$:
	:$$v(t) = \sqrt{ b_1^2(t) + b_2^2(t)} = \sqrt{ q^2(t) } = \vert q(t) \vert \hspace{0.05cm}.$$		:$$v(t) = \sqrt{ b_1^2(t) + b_2^2(t)} = \sqrt{ q^2(t) } = \vert q(t) \vert \hspace{0.05cm}.$$
	*A prerequisite for operability – that is, for the result  $v(t) = q(t)$  – is that at all times  $q(t) ≥ 0$ . In an analog ~~message~~ system, this fact could be enforced using the "DSB-AM with carrier" modulation method, for example.		*A prerequisite for operability  – that is,  for the result  $v(t) = q(t)$  –  is that at all times  $q(t) ≥ 0$.  In an analog transmission system,  this fact could be enforced using the  "DSB-AM with carrier"  modulation method,  for example.
	*This form of non-coherent demodulation - or modifications of it - is mainly applied in some '''digital modulation methods''', which are discussed in detail in the fourth chapter of [[Modulation_Methods\|this book]].}}		*This form of non-coherent demodulation  (or modifications of it)  is mainly applied in some  '''digital modulation methods''',  which are discussed in detail in the fourth chapter of  [[Modulation_Methods\|this book]].}}

	==Exercises for the chapter==		==Exercises for the chapter==

← Older revision		Revision as of 11:52, 13 January 2023
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	When transmitting signals using single-sideband modulation  $\rm (SSB–AM)$  the following problems occur:		When transmitting signals using single-sideband modulation  $\rm (SSB–AM)$  the following problems occur:
	*To suppress the unwanted sideband,  a filter with a very high edge slope must be used.		*To suppress the unwanted sideband,  a filter with a very high edge slope must be used.

	*Such steep-edged filters exhibit strong group delay distortions,  especially at the limit of the passband.		*Such steep-edged filters exhibit strong group delay distortions,  especially at the limit of the passband.

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	The present description is based on the textbook   [Mäu88]<ref>Mäusl, R.:  Analoge Modulationsverfahren.  Heidelberg: Dr. Hüthig, 1988.</ref>.  According to it,  the VSB-AM can be characterized as follows:		The present description is based on the textbook   [Mäu88]<ref>Mäusl, R.:  Analoge Modulationsverfahren.  Heidelberg: Dr. Hüthig, 1988.</ref>.  According to it,  the VSB-AM can be characterized as follows:
	*A certain frequency range of the actually suppressed sideband – in the considered example of the LSB – is additionally used with a relatively flat decreasing transfer function.		*A certain frequency range of the actually suppressed sideband – in the considered example of the LSB – is additionally used with a relatively flat decreasing transfer function.

	*On the receiver side,  a selection curve linearly increasing in frequency with a so-called  "Nyquist edge"  is used in the transition range from the suppressed sideband to the transmitted sideband.		*On the receiver side,  a selection curve linearly increasing in frequency with a so-called  "Nyquist edge"  is used in the transition range from the suppressed sideband to the transmitted sideband.

	*The demodulation performs a convolution of the sidebands around the carrier,  so that as a result the message content of a band with the same amplitude for all frequencies is obtained.		*The demodulation performs a convolution of the sidebands around the carrier,  so that as a result the message content of a band with the same amplitude for all frequencies is obtained.

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	[[File:EN_Mod_T_2_5_S1b.png\|right\|frame\|Illustrating the Nyquist edge for PAL–B/G Television]]		[[File:EN_Mod_T_2_5_S1b.png\|right\|frame\|Illustrating the Nyquist edge for PAL–B/G Television]]
	In this schematic representation,  one recognizes:		In this schematic representation,  one recognizes:
	*The radiated spectrum  (only positive frequencies are drawn)  ranges from  $f_{\rm T} - 1.25 \ \rm MHz$  to  $f_{\rm T} + 5.75 \ \rm MHz$.  The lower vestigial sideband including Nyquist edge is  $\approx 1.25 \ \rm MHz$  wide.		*The radiated spectrum  (only positive frequencies are drawn)  ranges from  $f_{\rm T} - 1.25 \ \rm MHz$  to  $f_{\rm T} + 5.75 \ \rm MHz$.  The lower vestigial sideband including Nyquist edge is  $\approx 1.25 \ \rm MHz$  wide.
	*The green dashed line shows the receiver passband.  The image carrier  '''(B)'''  – abbreviation  "B"  from German "Bild"   ⇒   "image") –   at carrier frequency  $f_{\rm T}$  is centered on the Nyquist edge.
			*The green dashed line shows the receiver passband.  The image carrier  '''(B)'''  – abbreviation  "B"  from German "Bild"   ⇒   "image") –   at carrier frequency  $f_{\rm T}$  is centered on the Nyquist edge.

	*The luminance signal   '''(L)'''  goes up to about  $5 \ \rm MHz$.  It contains the information for the image brightness and for the color  "green".		*The luminance signal   '''(L)'''  goes up to about  $5 \ \rm MHz$.  It contains the information for the image brightness and for the color  "green".

	*The chrominance signal   '''(C)'''  is embedded in the upper part. Two orthogonal carriers are [[Modulation_Methods/Further_AM_Variants#Quadrature_Amplitude_Modulation_.28QAM.29\|$\text{QAM-modulated}$]]  at  $4.43 \ \rm MHz$  for  "red"  and  "blue";  the carrier is suppressed.		*The chrominance signal   '''(C)'''  is embedded in the upper part. Two orthogonal carriers are [[Modulation_Methods/Further_AM_Variants#Quadrature_Amplitude_Modulation_.28QAM.29\|$\text{QAM-modulated}$]]  at  $4.43 \ \rm MHz$  for  "red"  and  "blue";  the carrier is suppressed.

	*The audio carrier   '''(T)'''  – abbreviation  "T"  from German "Ton"   ⇒   "sound/audio") –   is at  $f_{\rm T} + 5.5 \ \rm MHz$  and is  $12 \ \rm dB$  lower than the image carrier.		*The audio carrier   '''(T)'''  – abbreviation  "T"  from German "Ton"   ⇒   "sound/audio") –   is at  $f_{\rm T} + 5.5 \ \rm MHz$  and is  $12 \ \rm dB$  lower than the image carrier.

	*If there is a two-channel sound  (stereo)  transmission   ⇒   a second   '''(T)'''  carrier at  $5.75 \ \rm MHz$.}}		*If there is a two-channel sound  (stereo)  transmission   ⇒   a second   '''(T)'''  carrier at  $5.75 \ \rm MHz$.}}

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	*The transmitted signal is composed of two mutually orthogonal components:		*The transmitted signal is composed of two mutually orthogonal components:
	:$$s(t) = q_1(t) \cdot \cos (\omega_{\rm T}\cdot t) - q_2(t) \cdot \sin (\omega_{\rm T}\cdot t)\hspace{0.05cm}.$$		:$$s(t) = q_1(t) \cdot \cos (\omega_{\rm T}\cdot t) - q_2(t) \cdot \sin (\omega_{\rm T}\cdot t)\hspace{0.05cm}.$$

	*For frequency and phase synchronous demodulation,  the signal in the upper branch before the low-pass  $H_{\rm E1}(f)$  is:		*For frequency and phase synchronous demodulation,  the signal in the upper branch before the low-pass  $H_{\rm E1}(f)$  is:
	:$$b_1(t) = q_1(t) \cdot 2 \cdot \cos^2 (\omega_{\rm T}\cdot t) - q_2(t) \cdot 2 \cdot		:$$b_1(t) = q_1(t) \cdot 2 \cdot \cos^2 (\omega_{\rm T}\cdot t) - q_2(t) \cdot 2 \cdot
	\cos (\omega_{\rm T}\cdot t)\cdot \sin (\omega_{\rm T}\cdot t) $$		\cos (\omega_{\rm T}\cdot t)\cdot \sin (\omega_{\rm T}\cdot t) $$
	:$$\Rightarrow \hspace{0.3cm} b_1(t) = q_1(t)\cdot \big[ 1 + \cos (2 \omega_{\rm T}\cdot t) \big] - q_2(t)\cdot \sin (2 \omega_{\rm T}\cdot t) \hspace{0.05cm}.$$		:$$\Rightarrow \hspace{0.3cm} b_1(t) = q_1(t)\cdot \big[ 1 + \cos (2 \omega_{\rm T}\cdot t) \big] - q_2(t)\cdot \sin (2 \omega_{\rm T}\cdot t) \hspace{0.05cm}.$$

	*Thus,  by limiting to frequencies  $\|f\| < f_{\rm T}$,  we obtain in the upper and lower branches,  resp.:		*Thus,  by limiting to frequencies  $\|f\| < f_{\rm T}$,  we obtain in the upper and lower branches,  resp.:
	:$$v_1(t) = q_1(t),$$		:$$v_1(t) = q_1(t),$$
	:$$v_2(t) = q_2(t)\hspace{0.05cm}.$$		:$$v_2(t) = q_2(t)\hspace{0.05cm}.$$

	*When there is a phase offset  $Δϕ_{\rm T}$  between the transmitted and received carrier signals,  in addition to attenuation of the intended participant,<br>crosstalk from the second participant occurs,  resulting in nonlinear distortion:		*When there is a phase offset  $Δϕ_{\rm T}$  between the transmitted and received carrier signals,  in addition to attenuation of the intended participant,<br>crosstalk from the second participant occurs,  resulting in nonlinear distortion:
	:$$v_1(t) = \alpha_{11} \cdot q_1(t)+ \alpha_{12} \cdot q_2(t) \hspace{0.05cm}, $$		:$$v_1(t) = \alpha_{11} \cdot q_1(t)+ \alpha_{12} \cdot q_2(t) \hspace{0.05cm}, $$
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	It should be further noted regarding this arrangement:		It should be further noted regarding this arrangement:
	*The receiver-side carrier signals can have an arbitrary and also time-dependent phase offset  $Δϕ_{\rm T}$  with respect to the carrier signals at the transmitter, as long as the phase difference between the two branches remains exactly  $90^\circ$ .		*The receiver-side carrier signals can have an arbitrary and also time-dependent phase offset  $Δϕ_{\rm T}$  with respect to the carrier signals at the transmitter, as long as the phase difference between the two branches remains exactly  $90^\circ$ .

	*For the signals in the upper and lower branches – after the multiplier and low-pass filtering, respectively – it holds:		*For the signals in the upper and lower branches – after the multiplier and low-pass filtering, respectively – it holds:
	:$$b_1(t) = \cos(\Delta \phi_{\rm T}) \cdot q(t), $$		:$$b_1(t) = \cos(\Delta \phi_{\rm T}) \cdot q(t), $$
	:$$b_2(t) = -\sin(\Delta \phi_{\rm T}) \cdot q(t).$$		:$$b_2(t) = -\sin(\Delta \phi_{\rm T}) \cdot q(t).$$

	*This ensures that the sink signal  $v(t)$  matches the source signal  $q(t)$  in magnitude,  regardless of the phase offset  $Δϕ_{\rm T}$:		*This ensures that the sink signal  $v(t)$  matches the source signal  $q(t)$  in magnitude,  regardless of the phase offset  $Δϕ_{\rm T}$:
	:$$v(t) = \sqrt{ b_1^2(t) + b_2^2(t)} = \sqrt{ q^2(t) } = \vert q(t) \vert \hspace{0.05cm}.$$		:$$v(t) = \sqrt{ b_1^2(t) + b_2^2(t)} = \sqrt{ q^2(t) } = \vert q(t) \vert \hspace{0.05cm}.$$

	*A prerequisite for operability  – that is,  for the result  $v(t) = q(t)$  –  is that at all times  $q(t) ≥ 0$.  In an analog transmission system,  this fact could be enforced using the  "DSB-AM with carrier"  modulation method,  for example.		*A prerequisite for operability  – that is,  for the result  $v(t) = q(t)$  –  is that at all times  $q(t) ≥ 0$.  In an analog transmission system,  this fact could be enforced using the  "DSB-AM with carrier"  modulation method,  for example.

	*This form of non-coherent demodulation  (or modifications of it)  is mainly applied in some  »'''digital modulation methods'''«,  which are discussed in detail in the fourth chapter of  [[Modulation_Methods\|"this book"]].}}		*This form of non-coherent demodulation  (or modifications of it)  is mainly applied in some  »'''digital modulation methods'''«,  which are discussed in detail in the fourth chapter of  [[Modulation_Methods\|"this book"]].}}

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	{{GraueBox\|TEXT=		{{GraueBox\|TEXT=
	$\text{Example 1:}$  The vestigial sideband method is used for  (analog)  color television,  whose frequency spectrum according to the CCIR standard is shown in the graphic.  The frequencies given refer to the  [https://en.wikipedia.org/wiki/PAL PAL–B/G Television format]  used in Germany.		$\text{Example 1:}$  The vestigial sideband method is used for  (analog)  color television,  whose frequency spectrum according to the CCIR standard is shown in the graphic.  The frequencies given refer to the  [https://en.wikipedia.org/wiki/PAL $\text{PAL–B/G Television format}$]  used in Germany.

	[[File:EN_Mod_T_2_5_S1b.png\|right\|frame\|Illustrating the Nyquist edge for PAL–B/G Television]]		[[File:EN_Mod_T_2_5_S1b.png\|right\|frame\|Illustrating the Nyquist edge for PAL–B/G Television]]
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	*The green dashed line shows the receiver passband.  The image carrier  '''(B)'''  – abbreviation  "B"  from German "Bild"   ⇒   "image") –   at carrier frequency  $f_{\rm T}$  is centered on the Nyquist edge.		*The green dashed line shows the receiver passband.  The image carrier  '''(B)'''  – abbreviation  "B"  from German "Bild"   ⇒   "image") –   at carrier frequency  $f_{\rm T}$  is centered on the Nyquist edge.
	*The luminance signal   '''(L)'''  goes up to about  $5 \ \rm MHz$.  It contains the information for the image brightness and for the color  "green".		*The luminance signal   '''(L)'''  goes up to about  $5 \ \rm MHz$.  It contains the information for the image brightness and for the color  "green".
	*The chrominance signal   '''(C)'''  is embedded in the upper part. Two orthogonal carriers are [[Modulation_Methods/Further_AM_Variants#Quadrature_Amplitude_Modulation_.28QAM.29\|QAM-modulated]]  at  $4.43 \ \rm MHz$  for  "red"  and  "blue";  the carrier is suppressed.		*The chrominance signal   '''(C)'''  is embedded in the upper part. Two orthogonal carriers are [[Modulation_Methods/Further_AM_Variants#Quadrature_Amplitude_Modulation_.28QAM.29\|$\text{QAM-modulated}$]]  at  $4.43 \ \rm MHz$  for  "red"  and  "blue";  the carrier is suppressed.
	*The audio carrier   '''(T)'''  – abbreviation  "T"  from German "Ton"   ⇒   "sound/audio") –   is at  $f_{\rm T} + 5.5 \ \rm MHz$  and is  $12 \ \rm dB$  lower than the image carrier.		*The audio carrier   '''(T)'''  – abbreviation  "T"  from German "Ton"   ⇒   "sound/audio") –   is at  $f_{\rm T} + 5.5 \ \rm MHz$  and is  $12 \ \rm dB$  lower than the image carrier.
	*If there is a two-channel sound  (stereo)  transmission   ⇒   a second   '''(T)'''  carrier at  $5.75 \ \rm MHz$.}}		*If there is a two-channel sound  (stereo)  transmission   ⇒   a second   '''(T)'''  carrier at  $5.75 \ \rm MHz$.}}
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	$\text{Definition:}$  Demodulators can be classified in the following way:		$\text{Definition:}$  Demodulators can be classified in the following way:
	*A demodulator is said to be  '''coherent''',  if in addition to the required frequency synchronization,  it requires accurate information about the phase of the transmit-side carrier signal  $z(t)$  to reconstruct the source signal.		*A demodulator is said to be  »'''coherent'''«,  if in addition to the required frequency synchronization,  it requires accurate information about the phase of the transmit-side carrier signal  $z(t)$  to reconstruct the source signal.

	*If this phase information is not required,  the demodulator is said to be an  '''incoherent demodulator'''  or  "non-coherent demodulator".}}		*If this phase information is not required,  the demodulator is said to be an  »'''incoherent demodulator'''«  or  "non-coherent demodulator".}}


	An example of an incoherent demodulator is the  [[Modulation_Methods/Envelope_Demodulation\|envelope demodulator]].		An example of an incoherent demodulator is the  [[Modulation_Methods/Envelope_Demodulation\|$\text{envelope demodulator}$]].

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	:$$v(t) = \sqrt{ b_1^2(t) + b_2^2(t)} = \sqrt{ q^2(t) } = \vert q(t) \vert \hspace{0.05cm}.$$		:$$v(t) = \sqrt{ b_1^2(t) + b_2^2(t)} = \sqrt{ q^2(t) } = \vert q(t) \vert \hspace{0.05cm}.$$
	*A prerequisite for operability  – that is,  for the result  $v(t) = q(t)$  –  is that at all times  $q(t) ≥ 0$.  In an analog transmission system,  this fact could be enforced using the  "DSB-AM with carrier"  modulation method,  for example.		*A prerequisite for operability  – that is,  for the result  $v(t) = q(t)$  –  is that at all times  $q(t) ≥ 0$.  In an analog transmission system,  this fact could be enforced using the  "DSB-AM with carrier"  modulation method,  for example.
	*This form of non-coherent demodulation  (or modifications of it)  is mainly applied in some  '''digital modulation methods''',  which are discussed in detail in the fourth chapter of  [[Modulation_Methods\|this book]].}}		*This form of non-coherent demodulation  (or modifications of it)  is mainly applied in some  »'''digital modulation methods'''«,  which are discussed in detail in the fourth chapter of  [[Modulation_Methods\|"this book"]].}}

	==Exercises for the chapter==		==Exercises for the chapter==