Exercise 3.4Z: GSM Full-Rate Voice Codec

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LPC-, LTP- und RPE-Parameter beim GSM-Vollraten-Codec

This codec called GSM Fullrate Vocoder  (which was standardized for the GSM system in 1991) stands for a joint realization of coder and decoder and combines three methods for the compression of speech signals:

• Linear Predictive Coding (LPC),
• Long Term Prediction (LTP), and
• Regular Pulse Excitation (RPE ).

The numbers shown in the graph indicate the number of bits generated by the three units of this FR speech codec per frame of  $20$  millisecond duration each.

It should be noted that LTP and RPE, unlike LPC, do not work frame by frame, but with sub-blocks of  $5$  milliseconds. However, this has no influence on solving the task.

The input signal in the above graphic is the digitalized speech signal  $s_{\rm R}(n)$.

This results from the analog speech signal  $s(t)$  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 $20 \ \rm ms$.

The further tasks of preprocessing will not be discussed in detail here.

Notes:

• This exercise belongs to the chapter  Gemeinsamkeiten von GSM und UMTS.
• Reference is also made to the Chapter  Sprachcodierung  des Buches „Beispiele von Nachrichtensystemen”.

Questionnaire

1

To which bandwidth  $B$  must the speech signal be limited?

$B \ = \ $ $\ \rm kHz$

2

Of How many samples  $(N_{\rm R})$  is there a language frame? How large is the input data rate  $R_{\rm In}$?

$N_{\rm R} \hspace{0.18cm} = \ $ $\ \rm samples$

$R_{\rm In} \hspace{0.15cm} = \ $ $\ \rm kbit/s$

3

What is the output data rate  $R_{\rm Out}$ of the GSM full rate codec?

$R_{\rm Out} \ = \ $ $\ \rm kbit/s$

4

Which statements apply to the block "LPC"?

	LPC makes a short-term prediction over one millisecond.
	The  $36$  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  $s_{\rm R}(t)$.

5

Which statements regarding the block „LTP” are true?

	LTP removes periodic structures of the speech signal.
	The long-term prediction is performed once per frame.
	The memory of the LTP predictor is up to  $15 \ \rm ms$.

6

Which statements apply to the block "RPE"?

	RPE delivers fewer bits than LPC and LTP.
	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.

Sample solution

Solution

(1)  To satisfy the sampling theorem, the bandwidth $B$ must not exceed $ f_{\rm A}/2 \hspace{0.15cm}\underline{= 4 \ \ \rm kHz}$.

(2)  The given sampling rate $f_{\rm A} = 8 \ \rm kHz$ results in a distance between individual samples of $T_{\rm A} = 0.125 \ \rm ms$.

• Thus a speech frame of $(20 {\rm ms})$ consists of $N_{\rm R} = 20/0.125 = \underline{160 \ \rm samples}$, each quantized with $13 \ \rm Bit$.
• The data rate is thus

$$R_{\rm In} = \frac{160 \cdot 13}{20 \,{\rm ms}} \hspace{0.15cm} \underline {= 104\,{\rm kbit/s}}\hspace{0.05cm}.$$

(3)  The graph shows that per speech frame $36 \ {\rm (LPC)} + 36 \ {\rm (LTP)} + 188 \ {\rm (RPE)} = 260 \ \ \rm Bit$ 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.

(4)  Only the first two statements are true:

• The 36 LPC–bits describe a total of eight filter coefficients of a non-recursive filter, whereby eight acf–values are determined from the short-term analysis and where these are converted into reflection factors $r_{k}$ after the so-called Schur recursion.
• From these the eight LAR–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.
• 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.

(5)  Correct are the the statements 1 and 3, but not the second:

• The LTP–analysis and –filtering is done blockwise every $5 \ \rm ms$ (40 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.
• 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 „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.

(6)  The statements 2 and 3 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).
• 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.
• The "RPE pulse" thus occupies $13 \cdot 12 = 156$ of the $260$ output bits.

More details about the RPE block can be found on the page RPE–Codierung des Buches „Beispiele von Nachrichtensystemen”.