Modulation Methods/Phase Modulation (PM) - Revision history

Hwang at 12:43, 18 January 2023

2023-01-18T12:43:56Z

Guenter at 16:43, 16 January 2023

2023-01-16T16:43:04Z

Guenter at 13:09, 13 January 2023

2023-01-13T13:09:40Z

Guenter at 13:03, 13 January 2023

2023-01-13T13:03:56Z

Hwang at 13:33, 9 January 2023

2023-01-09T13:33:05Z

Hwang at 13:32, 9 January 2023

2023-01-09T13:32:30Z

Hwang at 13:31, 9 January 2023

2023-01-09T13:31:43Z

Hwang at 13:28, 9 January 2023

2023-01-09T13:28:01Z

Hwang at 13:27, 9 January 2023

2023-01-09T13:27:38Z

Hwang at 22:16, 2 January 2023

2023-01-02T22:16:07Z

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← Older revision		Revision as of 12:43, 18 January 2023
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−	*The low-pass spectrum  $S_{\rm TP}(f) = B_1(f) \star B_2(f)$  consists of nine Dirac lines and is sketched in the diagram on the right.	+	*The low-pass spectrum  $S_{\rm TP}(f) = B_1(f) \star B_2(f)$  consists of nine Dirac delta lines and is sketched in the diagram on the right.

@@ Line 52: / Line 52: @@
 *on the right,&nbsp; the transmitted signal &nbsp;$s(t)$  ⇒  &nbsp; blue waveforms, compared to the carrier signal &nbsp;$z(t)$  &nbsp; ⇒  &nbsp; red waveforms,
 *on the left,&nbsp; the equivalent low-pass signal  &nbsp;$s_{\rm TP}(t)$&nbsp; in the complex plane.
-[[File:EN_Mod_T_3_1_S1b_v2.png|right|frame|Physical signal and equivalent low-pass signal for angle and amplitude modulation '''KORREKTUR: nachlaufend, vorlaufend''']]
+[[File:EN Mod T 3 1 S1b v3.png|right|frame|Physical signal and equivalent low-pass signal for angle and amplitude modulation]]

@@ Line 8: / Line 8: @@
 == # OVERVIEW OF THE THIRD MAIN CHAPTER # ==
 <br>
-The third chapter describes&nbsp; &raquo;'''angle modulation'''&laquo; &nbsp; $($short: "$\rm WM)$"&nbsp; from German &nbsp; "Winkelmodulation"$)$.&nbsp;
+The third chapter describes&nbsp; &raquo;'''angle modulation'''&laquo; &nbsp; $($short:&nbsp; "$\rm WM$"&nbsp; from German &nbsp; "Winkelmodulation"$)$.&nbsp;
 This is a generic term for
@@ Line 17: / Line 17: @@
 In detail,&nbsp; the chapter covers:
-#the&nbsp; &raquo;similarities and differences&laquo;&nbsp;  between phase and frequency modulation,
+#The&nbsp; &raquo;similarities and differences&laquo;&nbsp;  between phase and frequency modulation,
 #the&nbsp; &raquo;realization of the associated demodulators&laquo;,
 #the&nbsp; &raquo;signal characteristics and spectral functions&laquo;&nbsp; of angle-modulated signals and the influence of band limiting,
@@ Line 41: / Line 41: @@
 *The locus curve is an &nbsp; "arc"&nbsp; with radius &nbsp;$A_{\rm T}$.&nbsp; It follows that the envelope of an angle-modulated signal is always constant:
 :$$a(t) = |s_{\rm TP}(t)|= A_{\rm T}= {\rm const.}$$
-*The equivalent low-pass signal in angle modulation is always complex and determined by a time-dependent &nbsp; "phase function" &nbsp;$ϕ(t)$&nbsp; (in radians),&nbsp;  which determines the zero intercepts '''KORREKTUR: crossings''' of &nbsp;$s(t)$:
+*The equivalent low-pass signal in angle modulation is always complex and determined by a time-dependent &nbsp; "phase function" &nbsp;$ϕ(t)$&nbsp; (in radians),&nbsp;  which determines the zero crossings of &nbsp;$s(t)$:
 :$$s_{\rm TP}(t)= A_{\rm T} \cdot {\rm e}^{\hspace{0.05cm}{\rm j}\hspace{0.05cm}\cdot \hspace{0.05cm}\phi(t)}\hspace{0.05cm}.$$
 *For a symmetric source signal,&nbsp; &nbsp;$ϕ(t)$&nbsp; can take on all values between &nbsp;$±ϕ_{\rm max}$,&nbsp; where &nbsp;$ϕ_{\rm max}$&nbsp; indicates the &nbsp; &raquo;'''phase deviation'''&laquo;.&nbsp; The larger the phase deviation,&nbsp; the more intense the modulation.
@@ Line 59: / Line 59: @@
 The upper graph applies in the case of angle modulation &nbsp; $\rm (WM)$:
 *The equivalent low-pass signal&nbsp; $s_{\rm TP}(t) = A_{\rm T} · {\rm e}^{ \hspace{0.05cm}{\rm j}\hspace{0.05cm}· \hspace{0.05cm}ϕ(t)}$&nbsp; describes an arc &nbsp; &rArr; &nbsp;  constant envelope &nbsp; $a(t) = A_{\rm T}$.
-*Thus,&nbsp; the information about the source signal &nbsp;$q(t)$&nbsp; is exclusively found in the zero intercepts '''KORREKTUR: crossings''' of &nbsp;$s(t)$.
+*Thus,&nbsp; the information about the source signal &nbsp;$q(t)$&nbsp; is exclusively found in the zero crossings of &nbsp;$s(t)$.
 *Should &nbsp;$ϕ(t) < 0$&nbsp; hold,&nbsp; then the zero crossings of &nbsp;$s(t)$&nbsp; occur later than those of &nbsp;$z(t)$.&nbsp; Otherwise – when &nbsp;$ϕ(t) > 0$,&nbsp; the zero crossings of &nbsp;$s(t)$&nbsp; come before &nbsp;$z(t)$.
@@ Line 243: / Line 243: @@
 {{GraueBox|TEXT=
-[[File:EN_Mod_T_3_1_S3c.png |right|frame| Example of an equivalent low-pass–signal in phase modulation '''Korrektur''']]
+[[File:EN_Mod_T_3_1_S3c.png |right|frame| Example of an equivalent low-pass–signal in phase modulation]]
 $\rm Example\ 3\text{:}$&nbsp; The Bessel functions yield the following values for the modulation index&nbsp;$η = 1$:
 :$${\rm J}_0 = 0.765,\hspace{0.3cm}{\rm J}_1 = - {\rm J}_{ - 1} = 0.440, \hspace{0.3cm}{\rm J}_2 = {\rm J}_{ - 2} = 0.115,\hspace{0.3cm}{\rm J}_3 = - {\rm J}_{ - 3} = 0.020\hspace{0.05cm}.$$

@@ Line 8: / Line 8: @@
 == # OVERVIEW OF THE THIRD MAIN CHAPTER # ==
 <br>
-The third chapter describes&nbsp; &raquo;'''angle modulation'''&laquo; &nbsp; $\rm (WM)$ (from the German &nbsp; "Winkelmodulation"). This is a generic term for
+The third chapter describes&nbsp; &raquo;'''angle modulation'''&laquo; &nbsp; $($short: "$\rm WM)$"&nbsp; from German &nbsp; "Winkelmodulation"$)$.&nbsp;
-*&nbsp; "phase modulation"&nbsp; $\rm (PM)$,&nbsp;
-*&nbsp; "frequency modulation" &nbsp; $\rm (FM)$.&nbsp;
+This is a generic term for

@@ Line 60: / Line 60: @@
-The lower graph corresponds to &nbsp; [[Modulation_Methods/Double-Sideband_Amplitude_Modulation|$\text{Double-Sideband Amplitude Modulation}$]]&nbsp; $\rm (DSB-AM)$&nbsp; as described in Chapter 2,&nbsp; characterised by
+The lower graph corresponds to &nbsp; [[Modulation_Methods/Double-Sideband_Amplitude_Modulation|$\text{Double-Sideband Amplitude Modulation}$]]&nbsp; $\rm (DSB-AM)$&nbsp; as described in Chapter 2,&nbsp; characterized by
 *the time-dependent envelope &nbsp;$a(t)$&nbsp; according to the signal &nbsp;$q(t)$,
 *equidistant zero crossings of &nbsp;$s(t)$&nbsp; according to the carrier &nbsp;$z(t)$,&nbsp; and