Modulation Methods/Non-Linear Digital Modulation - Revision history

Guenter at 14:21, 17 January 2023

2023-01-17T14:21:03Z

Guenter at 16:55, 16 January 2023

2023-01-16T16:55:26Z

Guenter at 16:45, 16 January 2023

2023-01-16T16:45:06Z

Guenter at 13:54, 13 January 2023

2023-01-13T13:54:02Z

Hwang at 15:23, 11 January 2023

2023-01-11T15:23:04Z

Hwang at 13:39, 11 January 2023

2023-01-11T13:39:19Z

Hwang at 13:38, 11 January 2023

2023-01-11T13:38:13Z

Hwang at 13:35, 11 January 2023

2023-01-11T13:35:49Z

Hwang at 13:33, 11 January 2023

2023-01-11T13:33:21Z

Hwang at 13:19, 11 January 2023

2023-01-11T13:19:46Z

← Older revision		Revision as of 14:21, 17 January 2023
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	*This type of modulation is used,  for example,  in the [[Examples_of_Communication_Systems/General_Description_of_GSM\|$\text{GSM}$]]  mobile communications standard.		*This type of modulation is used,  for example,  in the [[Examples_of_Communication_Systems/General_Description_of_GSM\|$\text{GSM}$]]  mobile communications standard.

−	[[File:~~EN_Mod_T_4_4_S9~~.png \|right\|frame\| Signal waveforms in Gaussian Minimum Shift Keying  $\rm (GMSK)$ ~~'''KORREKTUR: Phasenmodulator'''~~]]	+	[[File:EN_Mod_T_4_4_S9_v3.png \|right\|frame\| Signal waveforms in Gaussian Minimum Shift Keying  $\rm (GMSK)$]]

← Older revision		Revision as of 16:55, 16 January 2023
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	*This type of modulation is used,  for example,  in the [[Examples_of_Communication_Systems/General_Description_of_GSM\|$\text{GSM}$]]  mobile communications standard.		*This type of modulation is used,  for example,  in the [[Examples_of_Communication_Systems/General_Description_of_GSM\|$\text{GSM}$]]  mobile communications standard.

−	[[File:~~EN_Mod_T_4_4_S9_v2~~.png \|right\|frame\| Signal waveforms in Gaussian Minimum Shift Keying  $\rm (GMSK)$]]	+	[[File:EN_Mod_T_4_4_S9.png \|right\|frame\| Signal waveforms in Gaussian Minimum Shift Keying  $\rm (GMSK)$ '''KORREKTUR: Phasenmodulator''']]

← Older revision		Revision as of 16:45, 16 January 2023
Line 312:		Line 312:
	*This type of modulation is used,  for example,  in the [[Examples_of_Communication_Systems/General_Description_of_GSM\|$\text{GSM}$]]  mobile communications standard.		*This type of modulation is used,  for example,  in the [[Examples_of_Communication_Systems/General_Description_of_GSM\|$\text{GSM}$]]  mobile communications standard.

−	[[File:~~EN_Mod_T_4_4_S9~~.png \|right\|frame\| Signal waveforms in Gaussian Minimum Shift Keying  $\rm (GMSK)$ ~~'''KORREKTUR: Phasenmodulator'''~~]]	+	[[File:EN_Mod_T_4_4_S9_v2.png \|right\|frame\| Signal waveforms in Gaussian Minimum Shift Keying  $\rm (GMSK)$]]

@@ Line 120: / Line 120: @@
 This demodulator operates according to following principle&nbsp; (see upper arrangement):
-#We are dealing with a&nbsp;[[Digital_Signal_Transmission/Optimal_Receiver_Strategies#Maximum-a-posteriori_and_maximum.E2.80.93likelihood_decision_rule|$\text{maximum–likelihood receiver}$]]&nbsp; $\rm (ML)$&nbsp; with&nbsp; [[Theory_of_Stochastic_Signals/Matched_Filter|$\text{Matched-Filter}$]]&nbsp; '''KORREKTUR: matched filter''' realization.&nbsp; This filter with frequency response&nbsp;$H_{\rm MF}(f)$&nbsp; can also be realized as an integrator with rectangular basic transmission pulse &nbsp;$g_s(t)$.
+#We are dealing with a&nbsp;[[Digital_Signal_Transmission/Optimal_Receiver_Strategies#Maximum-a-posteriori_and_maximum.E2.80.93likelihood_decision_rule|$\text{maximum–likelihood receiver}$]]&nbsp; $\rm (ML)$&nbsp; with&nbsp; [[Theory_of_Stochastic_Signals/Matched_Filter|$\text{matched filter}$]]&nbsp;  realization.&nbsp; This filter with frequency response&nbsp;$H_{\rm MF}(f)$&nbsp; can also be realized as an integrator with rectangular basic transmission pulse &nbsp;$g_s(t)$.
-#Both signals &nbsp;$b_{+1}(t)$&nbsp; and &nbsp;$b_{–1}(t)$&nbsp; before their corresponding matched–filters '''KORREKTUR: matched filters''' are obtained by phase-appropriate multiplication with the oscillations of the frequencies &nbsp;$f_{+1}$&nbsp; and &nbsp;$f_{–1}$,&nbsp; respectively.
+#Both signals &nbsp;$b_{+1}(t)$&nbsp; and &nbsp;$b_{–1}(t)$&nbsp; before their corresponding matched filters  are obtained by phase-appropriate multiplication with the oscillations of the frequencies &nbsp;$f_{+1}$&nbsp; and &nbsp;$f_{–1}$,&nbsp; respectively.
 #The maximum-likelihood receiver is known to decide on the branch&nbsp; (for the symbol)&nbsp; with the larger&nbsp; "metric",&nbsp; taking into account the following matched filter.&nbsp;
 #This means:   &nbsp;$a_ν = +1$&nbsp; was probably sent if the following condition is satisfied:
@@ Line 191: / Line 191: @@
 [[File:EN_Mod_T_4_4_S6.png | right|frame|  Block diagram for generating a MSK signal]]
-*the digital source signal at point&nbsp; '''(1)''',&nbsp; a sequence of Dirac impulses '''KORREKTUR: Dirac delta pulses''' spaced by &nbsp;$T$,&nbsp; weighted by the coefficients &nbsp;$a_ν ∈ \{–1, +1\}$:
+*the digital source signal at point&nbsp; '''(1)''',&nbsp; a sequence of Dirac delta pulses spaced by &nbsp;$T$,&nbsp; weighted by the coefficients &nbsp;$a_ν ∈ \{–1, +1\}$:
 :$$q_\delta(t) = \sum_{\nu = - \infty}^{+\infty}a_{ \nu} \cdot \delta (t - \nu
 \cdot T)\hspace{0.05cm};$$
@@ Line 295: / Line 295: @@
-The spectral calculation of CPM procedures '''KORREKTUR: methods''' is complicated in general.&nbsp; Only the special case&nbsp; "MSK"&nbsp; leads to equations which are easy to handle,&nbsp; as shown in &nbsp;[[Aufgaben:Exercise_4.14:_Phase_Progression_of_the_MSK|"Exercise 4.14"]].
+The spectral calculation of CPM methods is complicated in general.&nbsp; Only the special case&nbsp; "MSK"&nbsp; leads to equations which are easy to handle,&nbsp; as shown in &nbsp;[[Aufgaben:Exercise_4.14:_Phase_Progression_of_the_MSK|"Exercise 4.14"]].
 {{BlaueBox|TEXT=

@@ Line 191: / Line 191: @@
 [[File:EN_Mod_T_4_4_S6.png | right|frame|  Block diagram for generating a MSK signal]]
-*the digital source signal at point&nbsp; '''(1)''',&nbsp; a sequence of Dirac impulses '''KORREKTUR: delta pulses''' spaced by &nbsp;$T$,&nbsp; weighted by the coefficients &nbsp;$a_ν ∈ \{–1, +1\}$:
+*the digital source signal at point&nbsp; '''(1)''',&nbsp; a sequence of Dirac impulses '''KORREKTUR: Dirac delta pulses''' spaced by &nbsp;$T$,&nbsp; weighted by the coefficients &nbsp;$a_ν ∈ \{–1, +1\}$:
 :$$q_\delta(t) = \sum_{\nu = - \infty}^{+\infty}a_{ \nu} \cdot \delta (t - \nu
 \cdot T)\hspace{0.05cm};$$

← Older revision		Revision as of 13:39, 11 January 2023
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	*This type of modulation is used,  for example,  in the [[Examples_of_Communication_Systems/General_Description_of_GSM\|$\text{GSM}$]]  mobile communications standard.		*This type of modulation is used,  for example,  in the [[Examples_of_Communication_Systems/General_Description_of_GSM\|$\text{GSM}$]]  mobile communications standard.

−	[[File:EN_Mod_T_4_4_S9.png \|right\|frame\| Signal waveforms in Gaussian Minimum Shift Keying  $\rm (GMSK)$]]	+	[[File:EN_Mod_T_4_4_S9.png \|right\|frame\| Signal waveforms in Gaussian Minimum Shift Keying  $\rm (GMSK)$ '''KORREKTUR: Phasenmodulator''']]

← Older revision		Revision as of 13:38, 11 January 2023
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−	The spectral calculation of CPM procedures is complicated in general.  Only the special case  "MSK"  leads to equations which are easy to handle,  as shown in  [[Aufgaben:Exercise_4.14:_Phase_Progression_of_the_MSK\|"Exercise 4.14"]].	+	The spectral calculation of CPM procedures '''KORREKTUR: methods''' is complicated in general.  Only the special case  "MSK"  leads to equations which are easy to handle,  as shown in  [[Aufgaben:Exercise_4.14:_Phase_Progression_of_the_MSK\|"Exercise 4.14"]].

	{{BlaueBox\|TEXT=		{{BlaueBox\|TEXT=

@@ Line 285: / Line 285: @@
 [[File:P_ID1735__Mod_T_4_4_S8_neu.png |right|frame|  Frequency pulse and phase pulse of some CPM variants]]
-#the individual graphs show the CPM frequency pulse&nbsp;$g(t)$&nbsp; above and the CPM phase pulse &nbsp;$g_ϕ(t)$&nbsp; below.
+#The individual graphs show the CPM frequency pulse&nbsp;$g(t)$&nbsp; above and the CPM phase pulse &nbsp;$g_ϕ(t)$&nbsp; below.
 #The two graphs on the left describe&nbsp; "$\rm MSK$".
 #The&nbsp; "$\rm 1–REC$"&nbsp; designation indicates that &nbsp;$g(t)$&nbsp; spans a single symbol duration &nbsp;$(T)$&nbsp; and is rectangular in shape.

← Older revision		Revision as of 13:33, 11 January 2023
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−	*The spacing of the individual Dirac pulses of the  "Dirac comb"  is now  $2T$  instead of  $T$  and the offset in the quadrature branch is no longer  $T/2$,  but  $T$.  In both cases,  the offset is equal to  $T_{\rm B}$.	+	*The spacing of the individual Dirac delta pulses of the  "Dirac comb"  is now  $2T$  instead of  $T$  and the offset in the quadrature branch is no longer  $T/2$,  but  $T$.  In both cases,  the offset is equal to  $T_{\rm B}$.