Aufgaben:Exercise 3.4Z: GSM Full-Rate Voice Codec - Revision history

Hwang at 11:25, 23 January 2023

2023-01-23T11:25:03Z

Guenter at 11:25, 2 January 2023

2023-01-02T11:25:28Z

Javier: Text replacement - "Category:Exercises for Mobile Communications" to "Category:Mobile Communications: Exercises"

2021-03-23T12:38:04Z

Text replacement - "Category:Exercises for Mobile Communications" to "Category:Mobile Communications: Exercises"

Guenter at 12:17, 20 February 2021

2021-02-20T12:17:01Z

Guenter at 13:21, 21 January 2021

2021-01-21T13:21:41Z

Guenter at 13:20, 21 January 2021

2021-01-21T13:20:48Z

Guenter at 12:58, 21 January 2021

2021-01-21T12:58:26Z

Guenter at 17:18, 20 January 2021

2021-01-20T17:18:51Z

Javier: Text replacement - "===Sample solution===" to "===Solution==="

2020-12-16T13:16:19Z

Text replacement - "===Sample solution===" to "===Solution==="

Javier: Text replacement - "Mobile Kommunikation/Gemeinsamkeiten von GSM und UMTS" to "Mobile_Communications/Similarities_Between_GSM_and_UMTS"

2020-12-15T14:02:40Z

Text replacement - "Mobile Kommunikation/Gemeinsamkeiten von GSM und UMTS" to "Mobile_Communications/Similarities_Between_GSM_and_UMTS"

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 }}
-[[File:EN_Mob_A_3_4_Z.png|right|frame|LPC, LTP and RPE parameters in the GSM Full-Rate Vocoder]]
+[[File:EN_Mob_A_3_4_Z.png|right|frame|LPC, LTP and RPE parameters in the GSM Full Rate Vocoder]]
-This codec called "GSM Full-Rate Vocoder"&nbsp; (which was standardized for the GSM system in 1991)&nbsp;  stands for a joint realization of coder and decoder and combines three methods for the compression of speech signals:
+This codec called "GSM Full Rate Vocoder"&nbsp; (which was standardized for the GSM system in 1991)&nbsp;  stands for a joint realization of coder and decoder and combines three methods for the compression of speech signals:
 *Linear Predictive Coding&nbsp; $\rm (LPC)$,
@@ Line 14: / Line 14: @@
-The numbers shown in the graphic indicate the number of bits generated by the three units of this Full-Rate speech codec per frame of&nbsp; $20$&nbsp; millisecond duration each.
+The numbers shown in the graphic indicate the number of bits generated by the three units of this Full Rate speech codec per frame of&nbsp; $20$&nbsp; millisecond duration each.
 It should be noted that LTP and RPE, unlike LPC, do not work frame by frame, but with sub-blocks of&nbsp; $5$&nbsp; milliseconds.&nbsp; However, this has no influence on solving the task.
@@ Line 38: / Line 38: @@
 *The task belongs to the chapter&nbsp; [[Mobile_Communications/Similarities_Between_GSM_and_UMTS|Similarities between GSM and UMTS]].
-*Reference is also made to the Chapter&nbsp;  [[Examples_of_Communication_Systems/Voice_Coding|Voice Coding]]&nbsp;  of the book "Examples of Communication Systems".
+*Reference is also made to the Chapter&nbsp;  [[Examples_of_Communication_Systems/Voice_Coding|Speech Coding]]&nbsp;  of the book "Examples of Communication Systems".
@@ Line 100: / Line 100: @@
 *From this the output data rate is calculated as
 :$$R_{\rm Out} = \frac{260}{20 \,{\rm ms}} \hspace{0.15cm} \underline {= 13\,{\rm kbit/s}}\hspace{0.05cm}.$$
-*The compression factor achieved by the full-rate speech codec is thus&nbsp; $104/13 = 8$.
+*The compression factor achieved by the full rate speech codec is thus&nbsp; $104/13 = 8$.

@@ Line 8: / Line 8: @@
 This codec called "GSM Full-Rate Vocoder"&nbsp; (which was standardized for the GSM system in 1991)&nbsp;  stands for a joint realization of coder and decoder and combines three methods for the compression of speech signals:
 *Linear Predictive Coding&nbsp; $\rm (LPC)$,
 *Long Term Prediction&nbsp; $\rm (LTP)$, and
 *Regular Pulse Excitation&nbsp; $\rm (RPE)$.
@@ Line 20: / Line 22: @@
 This results from the analog speech signal&nbsp; $s(t)$&nbsp; by
 *a suitable limitation to the bandwidth $B$,
 *sampling at the sampling rate $f_{\rm A} = 8 \ \rm kHz$,
 *quantization with $13 \ \rm bit$,
 *following segmentation into blocks of each&nbsp;$20 \ \rm ms$.

← Older revision		Revision as of 12:38, 23 March 2021
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−	[[Category:~~Exercises for~~ Mobile Communications\|^3.2 Similarities between GSM and UMTS	+	[[Category:Mobile Communications: Exercises\|^3.2 Similarities between GSM and UMTS
	^]]		^]]

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 *From this the output data rate is calculated as
 :$$R_{\rm Out} = \frac{260}{20 \,{\rm ms}} \hspace{0.15cm} \underline {= 13\,{\rm kbit/s}}\hspace{0.05cm}.$$
-*The compression factor achieved by the full-rate speech codec is thus&nbsp; $104/13 = $8.
+*The compression factor achieved by the full-rate speech codec is thus&nbsp; $104/13 = 8$.

← Older revision		Revision as of 13:21, 21 January 2021
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−	More details about the RPE block can be found on the page [[Examples_of_Communication_Systems/Voice_Coding#Regular_Pulse_Excitation_.E2.80.93_RPE_Coding\|RPE coding]] of the book "Examples of Communication Systems".	+	More details about the RPE block can be found on the page  [[Examples_of_Communication_Systems/Voice_Coding#Regular_Pulse_Excitation_.E2.80.93_RPE_Coding\|RPE coding]]  of the book  "Examples of Communication Systems".

	{{ML-Fuß}}		{{ML-Fuß}}

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 {{ML-Kopf}}
-'''(1)'''&nbsp; To satisfy the sampling theorem, the bandwidth $B$ must not exceed $ f_{\rm A}/2 \hspace{0.15cm}\underline{= 4 \ \ \rm kHz}$.
+'''(1)'''&nbsp; To satisfy the sampling theorem, the bandwidth $B$&nbsp; must not exceed&nbsp; $ f_{\rm A}/2 \hspace{0.15cm}\underline{= 4 \ \ \rm kHz}$.
-'''(2)'''&nbsp; The given sampling rate $f_{\rm A} = 8 \ \rm kHz$ results in a distance between individual samples of $T_{\rm A} = 0.125 \ \rm ms$.
+'''(2)'''&nbsp; The given sampling rate&nbsp; $f_{\rm A} = 8 \ \rm kHz$&nbsp; results in a distance between individual samples of&nbsp; $T_{\rm A} = 0.125 \ \rm ms$.
-*Thus a speech frame of $(20 {\rm ms})$ consists of $N_{\rm R} = 20/0.125 = \underline{160 \ \rm samples}$, each quantized with $13 \ \rm Bit$.
+*Thus a speech frame of&nbsp; $20 {\rm ms}$&nbsp; consists of&nbsp; $N_{\rm R} = 20/0.125 = \underline{160 \ \rm samples}$, each quantized with&nbsp; $13 \ \rm bit$.
 *The data rate is thus
 :$$R_{\rm In} = \frac{160 \cdot 13}{20 \,{\rm ms}} \hspace{0.15cm} \underline {= 104\,{\rm kbit/s}}\hspace{0.05cm}.$$
@@ Line 92: / Line 92: @@
-'''(3)'''&nbsp;  The graph shows that per speech frame $36 \ {\rm (LPC)} + 36 \ {\rm (LTP)} + 188 \ {\rm (RPE)} = 260 \ \ \rm Bit$ are output.
+'''(3)'''&nbsp;  The graph shows that per speech frame&nbsp; $36 \ {\rm (LPC)} + 36 \ {\rm (LTP)} + 188 \ {\rm (RPE)} = 260 \ \ \rm bit$&nbsp; are output.
 *From this the output data rate is calculated as
 :$$R_{\rm Out} = \frac{260}{20 \,{\rm ms}} \hspace{0.15cm} \underline {= 13\,{\rm kbit/s}}\hspace{0.05cm}.$$
-*The compression factor achieved by the full rate speech codec is thus $104/13 = $8.
+*The compression factor achieved by the full-rate speech codec is thus&nbsp; $104/13 = $8.
-'''(4)'''&nbsp; Only the <u> first two statements</u> are true:
+'''(4)'''&nbsp; The <u>first two statements</u> are true:
-*The 36 LPC&ndash;bits describe a total of eight filter coefficients of a non-recursive filter, whereby eight acf&ndash;values are determined from the short-term analysis and where these are converted into reflection factors $r_{k}$ after the so-called Schur recursion.
+*The 36 LPC bits describe a total of eight filter coefficients of a non-recursive filter, whereby eight&nbsp; $\rm ACF$ values are determined from the short-term analysis and where these are converted into reflection factors&nbsp; $r_{k}$&nbsp; after the so-called "Schur recursion".
-*From these the eight LAR&ndash;coefficients are calculated according to the function ${\rm ln}[(1 - r_{k})/(1 + r_{k})]$, quantized with a different number of bits and sent to the receiver.
+*From these the eight LAR coefficients are calculated according to the function&nbsp; ${\rm ln}\big[(1 - r_{k})/(1 + r_{k})\big]$, quantized with a different number of bits and sent to the receiver.
-*The LPC output signal has a significantly lower amplitude than its input $s_{\rm R}(n)$, and it has a significantly reduced dynamic range and a flatter spectrum.
+*The LPC output signal has a significantly lower amplitude than its input&nbsp; $s_{\rm R}(n)$, and it has a significantly reduced dynamic range and a flatter spectrum.
-'''(5)'''&nbsp; Correct are the <u>the statements 1 and 3</u>, but not the second:
+'''(5)'''&nbsp; Correct are the <u>statements 1 and 3</u>, but not the second:
-*The LTP&ndash;analysis and &ndash;filtering is done blockwise every $5 \ \rm ms$ (40 samples), i.e. four times per speech frame.
+*The LTP analysis and  filtering is done blockwise every&nbsp; $5 \ \rm ms$&nbsp; &rArr; &nbsp; $(40$&nbsp; samples$)$, i.e. four times per speech frame.
-*The cross correlation function (CCF) between the current sub-block and the three previous sub-blocks is formed.
+*The cross correlation function&nbsp; $\rm (CCF)$&nbsp; between the current sub-block and the three previous sub-blocks is formed.
-*For each sub-block, an LTP&ndash;delay and an LTP&ndash;gain are determined which best match the sub-block.
+*For each sub-block, an LTP delay and an LTP gain are determined which best match the sub-block.
-*A correction signal of the following component &bdquo;RPE&rdquo; is also taken into account.
+*A correction signal of the following component "RPE" is also taken into account.
 *For the long-term prediction, as with the LPC, the output is reduced in redundancy compared to the input.
@@ Line 116: / Line 116: @@
 '''(6)'''&nbsp; The statements <u>2 and 3</u> are correct:
-*The fact that statement 1 is wrong can be seen from the graphic on the data page, because $188$ of the $260$ output bits come from the RPE. Language would be understandable with RPE alone (without LPC and LTP).
+*The fact that statement 1 is wrong can be seen from the graphic on the data page, because&nbsp; $188$&nbsp; of the&nbsp; $260$&nbsp; output bits come from the RPE.&nbsp; Voice would be understandable with RPE alone (without LPC and LTP).
-*Regarding the last statement: The RPE is of course looking for the subsequence with the '''maximum'' energy. The RPE pulses are a subsequence (13 of 40 samples) of three bits per subframe of $5 \ \rm ms$ and accordingly $12 \ \rm Bit$ per $20 \ \rm ms$ frame.
+*Regarding the last statement:&nbsp; The RPE is of course looking for the subsequence with the '''maximum''' energy.&nbsp; The RPE pulses are a subsequence&nbsp; $(13$&nbsp; of&nbsp; $40$&nbsp; samples$)$&nbsp; of three bits per subframe of&nbsp; $5 \ \rm ms$&nbsp; and accordingly&nbsp; $12$&nbsp; bits per&nbsp; $20 \ \rm ms$&nbsp; frame.
-*The "RPE pulse" thus occupies $13 \cdot 12 = 156$ of the $260$ output bits.
+*The "RPE pulse" thus occupies&nbsp; $13 \cdot 12 = 156$&nbsp; of the&nbsp; $260$&nbsp; output bits.
-More details about the RPE block can be found on the page [[Examples_of_Communication_Systems/Sprachcodierung#Regular_Pulse_Excitation_.E2.80.93_RPE.E2.80.93Codierung|RPE&ndash;Codierung]] des Buches „Beispiele von Nachrichtensystemen”.
+More details about the RPE block can be found on the page [[Examples_of_Communication_Systems/Voice_Coding#Regular_Pulse_Excitation_.E2.80.93_RPE_Coding|RPE coding]] of the book "Examples of Communication Systems".
 {{ML-Fuß}}

@@ Line 12: / Line 12: @@
-The numbers shown in the graph indicate the number of bits generated by the three units of this FR speech codec per frame of&nbsp; $20$&nbsp; millisecond duration each.
+The numbers shown in the graphic indicate the number of bits generated by the three units of this Full-Rate speech codec per frame of&nbsp; $20$&nbsp; millisecond duration each.
 It should be noted that LTP and RPE, unlike LPC, do not work frame by frame, but with sub-blocks of&nbsp; $5$&nbsp; milliseconds.&nbsp; However, this has no influence on solving the task.
@@ Line 19: / Line 19: @@
 This results from the analog speech signal&nbsp; $s(t)$&nbsp; by
-*a suitable limitation to the bandwidth&nbsp; $B$,
+*a suitable limitation to the bandwidth $B$,
-*sampling at the sampling rate&nbsp; $f_{\rm A} = 8 \ \rm kHz$,
+*sampling at the sampling rate $f_{\rm A} = 8 \ \rm kHz$,
-*quantization with&nbsp; $13 \ \rm Bit$,
+*quantization with $13 \ \rm bit$,
 *following segmentation into blocks of each&nbsp;$20 \ \rm ms$.
 The further tasks of preprocessing will not be discussed in detail here.
@@ Line 34: / Line 32: @@
 ''Notes:''
-*This exercise belongs to the chapter&nbsp;   [[Mobile_Communications/Gemeinsamkeiten_von_GSM_und_UMTS|Gemeinsamkeiten von GSM und
+*The task belongs to the chapter&nbsp; [[Mobile_Communications/Similarities_Between_GSM_and_UMTS|Similarities between GSM and UMTS]].
- UMTS]].
+*Reference is also made to the Chapter&nbsp;  [[Examples_of_Communication_Systems/Voice_Coding|Voice Coding]]&nbsp;  of the book "Examples of Communication Systems".
@@ Line 45: / Line 42: @@
 <quiz display=simple>
-{To which bandwidth&nbsp; $B$&nbsp; must the speech signal be limited?
+{To which bandwidth $B$&nbsp; must the speech signal be limited?
 |type="{}"}
 $B \ = \ $ { 4 3% } $\ \rm kHz$
-{Of How many samples&nbsp; $(N_{\rm R})$&nbsp; is there a language frame? How large is the input data rate&nbsp; $R_{\rm In}$?
+{Of how many samples&nbsp; $(N_{\rm R})$&nbsp; is there a speech frame?&nbsp; How large is the input data rate $R_{\rm In}$?
 |type="{}"}
 $N_{\rm R} \hspace{0.18cm} = \ $ { 160 3% } $\ \rm samples$
 $R_{\rm In} \hspace{0.15cm} = \ $ { 104 3% } $\ \rm kbit/s$
-{What is the output data rate&nbsp; $R_{\rm Out}$ of the GSM full rate codec?
+{What is the output data rate $R_{\rm Out}$ of the GSM&ndash;full rate codec?
 |type="{}"}
 $R_{\rm Out} \ = \ $ { 13 3% } $\ \rm kbit/s$
@@ Line 64: / Line 61: @@
 + The&nbsp; $36$&nbsp; LPC bits specify coefficients that the receiver uses to undo the LPC filtering.
 - The filter for short-term prediction is recursive.
-- The LPC output signal is identical to the input&nbsp;  $s_{\rm R}(t)$.
+- The LPC output signal is identical to the input signal&nbsp;  $s_{\rm R}(t)$.
-{Which statements regarding the block „LTP” are true?
+{Which statements regarding the block "LTP" are true?
 |type="[]"}
 + LTP removes periodic structures of the speech signal.
@@ Line 77: / Line 74: @@
 + RPE removes unimportant parts for the subjective impression.
 + RPE subdivides each sub-block into four sub-sequences.
-- RPE selects the subsequence with the minimum energy.
+- RPE selects the sub-sequence with the minimum energy.
 </quiz>

← Older revision		Revision as of 14:02, 15 December 2020
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−	{{quiz-Header\|Buchseite=~~Mobile Kommunikation~~/~~Gemeinsamkeiten von GSM und UMTS~~	+	{{quiz-Header\|Buchseite=Mobile_Communications/Similarities_Between_GSM_and_UMTS

	}}		}}