AMR-NB

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AMR-NB (Adaptive Multi-Rate Narrowband) is a vocoder employed in low-bitrate applications like mobile phones. It is a form of ACELP where A stands for algebraic.


The following text aims to be a simpler and more explicit document of the AMR narrow band decoding processes to aid in development of a decoder. Reference to sections of the specification will be made in the following format: (c.f. §5.2.5). Happy reading.


Contents

Nomenclature weirdness

Throughout the specification, a number of references are made to the same (or very similar) items with fairly confusing variation. They are listed below to aid understanding of the following text but efforts will be made to consistently use one item name throughout or to use both with the lesser used name in parenthesis.

  • Pitch / Adaptive codebook
  • Fixed / Innovative (also algebraic when referring to the codebook)
  • Quantified means quantized


Summary

  • Mode dependent bitstream parsing
  • Indices parsed from bitstream
  • Indices decoded to give LSF vectors, fractional pitch lags, innovative code vectors and the pitch and innovative gains
  • LSF vectors converted to LP filter coefficients at each subframe
  • Subframe decoding
    • Excitation vector = adaptive code vector * adaptive (pitch) gain + innovative code vector * innovative gain
    • Excitation vector filtered through an LP synthesis filter to reconstruct speech
    • Speech signal filtered with adaptive postfilter


Bit stream frame format

Specification (26.101) describes two possible frame types - interface formats 1 and 2 (often abbreviated IF1 and IF2). IF2 is byte-aligned. The following tables of data are taken from this specification unless otherwise stated. AMR-NB over GSM uses a third slightly different format whose bit-packing is tightly defined by the GSM specs.

IF1 format

bits low level meaning high level meaning
4 Frame type AMR header
1 Frame quality indicator (0 bad/1 good)
3 Mode indication AMR auxiliary information
3 Mode request
8 CRC
  Class A bits AMR core frame
  Class B bits
  Class C bits

IF2 format

bits low level meaning high level meaning
4 Frame type AMR header
  Class A bits AMR core frame
  Class B bits
  Class C bits
  Padding (called "Bit stuffing" in the specification)  

GSM OTA format

bits low level meaning high level meaning
4 Mode request AMR auxiliary information
1 F bit (0 good/1 unusual) AMR header
4 Frame Type
1 Frame quality indicator (0 bad/1 good)
  Class A bits AMR core frame
6 CRC
  Class B bits

Field meaning

Frame type Frame content
0 AMR 4.75kbps
1 AMR 5.15kbps
2 AMR 5.90kbps
3 AMR 6.70kbps (PDC-EFR)
4 AMR 7.40kbps (TDMA-EFR)
5 AMR 7.95kbps
6 AMR 10.2kbps
7 AMR 12.2kbps (GSM-EFR)
8 AMR SID
9 GSM-EFR SID
10 TDMA-EFR SID
11 PDC-EFR SID
12-14 Reserved for future use
15 No data (no transmission/no reception)

Classes

Class Importance explanation
A Data that is most sensitive to error. Any error in these bits leads to a corrupted speech frame that should not be decoded without appropriate error concealment. This class of bits is protected by an 8-bit CRC.
B Less sensitive data that are present in all speech frames.
C Least sensitive data present only in higher bit rate frames.
  • Class A is protected by an 8-bit CRC with polynomial x^8+x^6+x^5+x^4+1 computed over the Class A bits.
  • However for AMR-NB over GSM the CRC is a 6-bit with polynomial x^6+x^5+x^3+x^2+x+1 computed over the Class A bits, and it immediately follows the Class A bits, rather than preceding them. That is, it's between the Class A and Class B bits. [see 3GPP TS 05.03 sec 3.9.4.3]
  • There is no significant step-wise change in subjective importance at class boundaries.
  • The distribution of bits is ordered from most to least subjective importance at both the class level and within the classes.
Frame type Total bits Class A bits Class B bits Class C bits
0 95 42 53 0
1 103 49 54 0
2 118 55 63 0
3 134 58 76 0
4 148 61 87 0
5 159 75 84 0
6 204 65 99 40
7 244 81 103 60
8 39 39 0 0
9 43 43 0 0
10 38 38 0 0
11 37 37 0 0

For the specifics of the bit stream layout (i.e. for the bits to parameter mappings) see 26.101 AMR speech codec frame structure and 26.090 AMR speech codec transcoding functions.

Decoding of LP filter parameters

The received indices of LSP quantization are used to reconstruct the quantified LSP vectors. (c.f. §5.2.5)


12.2kbps mode summary

  • indices into code books are parsed from the bit stream
  • indices give elements of split matrix quantised (SMQ) residual LSF vectors from the relevant code books
  • prediction from the previous frame is added to obtain the mean-removed LSF vectors
  • the mean is added
  • the LSF vectors are converted to cosine domain LSP vectors

Decoding SMQ residual LSF vectors

The elements of the SMQ vectors are stored at an index into a code book that varies according to the mode. There are 5 code books for the 12.2kbps mode corresponding to the 5 indices. These tables will be referred to as:

lsf_m_n

the number of indices parsed according to the mode
the index 'position' i.e. 1 for the first index, etc

The 5 indices are stored using 7, 8, 8 + sign bit, 8, 6 bits respectively. The four elements of a 'split quantized sub-matrix' are stored at the index position in the appropriate code book are reassigned as follows:

lsf_5_1[index1] 
r1_1, r1_2, r2_1, r2_2
lsf_5_2[index2] 
r1_3, r1_4, r2_3, r2_4
lsf_5_3[index3] 
r1_5, r1_6, r2_5, r2_6
lsf_5_4[index4] 
r1_7, r1_8, r2_7, r2_8
lsf_5_5[index5] 
r1_9, r1_10, r2_9, r2_10

With rj_i :

the first or second residual lsf vector
the coefficient of a residual lsf vector ( i = 1, ..., 10 )
rj_i 
residual line spectral frequencies (LSFs) in Hz

Mean-removed LSF vector prediction

Amrnb lsfmeanrem.gif

z_j(n) 
the mean-removed LSF vector at the jth subframe
r_j(n) 
prediction residual vector of frame n at the jth subframe
^r_2(n-1) 
the quantified residual vector from the previous frame at the 2nd subframe

The mean is added

Amrnb lsfvec.gif

lsf_mean_m 
a table of the means of the LSF coefficients
the number of indices parsed according to the mode
fj 
the LSF vectors

LSF to LSP vector conversion

Amrnb lspvec.gif

q_k[i] 
the ith coefficient of the kth line spectral pair (LSP) in the cosine domain
the two lsf vectors give the LSP vectors q2, q4 at the 2nd and 4th subframes; k = 2*j
f_j[i] 
ith coefficient of the jth LSF vector; [0,4000] Hz
f_s 
sampling frequency in Hz (8kHz)

Other active modes summary

The process for the other modes is similar to that for the 12.2kbps mode.

  • indices into code books are parsed from the bit stream
  • indices give elements of a split matrix quantised (SMQ) residual LSF vector from the relevant code books
  • prediction from the previous frame is added to obtain the mean-removed LSF vector
  • the mean is added
  • the LSF vector is converted to a cosine domain LSP vector

Decoding the SMQ residual LSF vector

The 3 indices are stored with the following numbers of bits:

Mode (kbps) 1st index (bits) 2nd index (bits) 3rd index (bits)
10.2 8 9 9
7.95 9 9 9
7.40 8 9 9
6.70 8 9 9
5.90 8 9 9
5.15 8 8 7
4.75 8 8 7

The four elements of a 'split quantized sub-matrix' are stored at the index position in the appropriate code book are:

1st index in 1st code book 
r_1, r_2, r_3
2nd index in 2nd code book 
r_4, r_5, r_6
3rd index in 3rd code book 
r_7, r_8, r_9, r_10
r_i 
residual LSF vector (Hz)
the coefficient of vector ( i = 1, ..., 10 )

Mean-removed LSF vector prediction

Amrnb lsfmeanrem2.gif

z_j(n)[i] 
the ith coefficient of the mean-removed LSF vector at the jth subframe
r_j(n)[i] 
the ith coefficient of the prediction residual vector of frame n at the jth subframe
pred_fac[i] 
the ith coefficient of the prediction factor
^r_j(n-1)[i] 
the ith coefficient of the the quantified residual vector of the previous frame at the jth subframe

These processes give the LSP vector at the 4th subframe (q4)

LSP vector interpolation (c.f. §5.2.6)

12.2 kbps mode

Amrnb lspinterpq1-1.gif

Amrnb lspinterpq3-1.gif

Other modes

Amrnb lspinterpq1-2.gif

Amrnb lspinterpq2.gif

Amrnb lspinterpq3-2.gif

LSP vector to LP filter coefficient conversion (c.f. §5.2.4)

 for i=1..5
   f1[i]  = 2*f1[i-2] - 2*q[2i-1]*f1[i-1]
   for j=i-1..1
     f1[j] +=   f1[j-2] - 2*q[2i-1]*f1[j-1]
   end
 end

f1[-1] = 0; f1[0] = 0;

Same for f2[i] with q[2i] instead of q[2i-1]

 for i=1..5
   f'1[i] = f1[i] + f1[i-1]
   f'2[i] = f2[i] - f2[i-1]
 end

Amrnb lpccoeff.gif

a_i 
the LP filter coefficients

Decoding of the pitch (adaptive codebook) vector

  • indices parsed from bitstream
  • indices give integer and fractional parts of the pitch lag
  • pitch vector v(n) is found by interpolating the past excitation u(n) at the pitch lag using an FIR filter. (c.f. §5.6)


Decode pitch lag

Note: division in this section is integer division!

12.2kbps mode - 1/6 resolution pitch lag

First and third subframes

In the first and third subframes, a fractional pitch lag is used with resolutions:

  • 1/6 in the range [17 3/6, 94 3/6]
  • 1 in the range [95, 143]

...encoded using 9 bits.

For [17 3/6, 94 3/6] the pitch index is encoded as:

 pitch_index = (pitch_lag_int - 17)*6 + pitch_lag_frac - 3;
pitch_lag_int 
integer part of the pitch lag in the range [17, 94]
pitch_lag_frac 
fractional part of the pitch lag in 1/6 units in the range [-2, 3]

so...

 if(pitch_index < (94 4/6 - 17 3/6)*6)
   // fractional part is encoded in range [17 3/6, 94 3/6]
   pitch_lag_int = (pitch_index + 5)/6 + 17;
   pitch_lag_frac = pitch_index - pitch_lag_int*6 + (17 3/6)*6;

And for [95, 143] the pitch index is encoded as:

 pitch_index = (pitch_lag_int - 95) + (94 4/6 - 17 3/6)*6;
pitch_lag_int 
integer pitch lag in the range [95, 143]

so...

 else
   // only integer part encoded in range [95, 143], no fractional part
   pitch_lag_int  = pitch_index - (94 4/6 - 17 3/6)*6 + 95;
   pitch_lag_frac = 0;
Second and fourth subframes

In the second and fourth subframes, a pitch lag resolution of 1/6 is always used in the range [T1 - 5 3/6, T1 + 4 3/6], where T1 is nearest integer to the fractional pitch lag of the previous (1st or 3rd) subframe. The search range is bounded by [18, 143]. In this case the pitch delay is encoded using 6 bits and is therefore in the range [0,63].

So the search range for the pitch lag is:

 search_range_min = max(pitch_lag_int_prev - 5, 18);
 search_range_max = search_range_min + 9;
 if(search_range_max > 143) {
   search_range_max = 143;
   search_range_min = search_range_max - 9;
 }
pitch_lag_int_prev 
the integer part of the pitch lag from the previous sub frame

The pitch index is encoded as:

 pitch_index = (pitch_lag_int - (search_range_min - 1))*6 + pitch_lag_frac - 3;
pitch_lag_int 
the integer part of the pitch lag in the range [search_range_min - 1, search_range_max]
pitch_lag_frac 
the fractional part of the pitch lag in the range [-2, 3]

The formula for the pitch_index has been chosen to map pitch_lag_int [search_range_min - 1, search_range_max] and pitch_lag_frac [-2, 3] to [0,60]. (pitch_index = [0, 10]*6 + [-2, 3] - 3 = [0, 6, ..., 60] + [-5, 0] = [0,60])

So the pitch lag is calculated through:

 // integer part of pitch lag = position in range [search_range_min - 1, search_range_max] + lower bound of range
 pitch_lag_int  = (pitch_index + 5)/6 + search_range_min - 1;
 // fractional part of pitch lag = pitch index - (integer part without offset)*6 - 1 3/6 offset to bring the values to the correct range
 pitch_lag_frac = pitch_index - ((pitch_index + 5)/6)*6 - 9;

Note that when using integers and integer division to conduct (pitch_index + 5)/6 the result is similar to taking the ceiling of pitch_index/6.0.

Others modes - 1/3 resolution pitch lag

First and third subframes

In the first and third subframes, a fractional pitch lag is used with resolutions:

  • 1/3 in the range [19 1/3, 84 2/3]
  • 1 in the range [85, 143]

...encoded using 8 bits.

For [19 1/3, 84 2/3] the pitch lag is encoded as:

 pitch_index = pitch_lag_int*3 + pitch_lag_frac - (19 1/3)*3;
pitch_lag_int 
integer part of the pitch lag in the range [19, 84]
pitch_lag_frac 
fractional part of the pitch lag in 1/3 units in the range [0, 2]

so...

 if(pitch_index < (85 - 19 1/3)*3)
   // fractional part is encoded in range [19 1/3, 84 2/3]
   pitch_lag_int = (pitch_index + 2)/3 + 19;
   pitch_lag_frac = pitch_index - pitch_lag_int*3 + (19 1/3)*3;

And for [85, 143] the pitch index is encoded as:

 pitch_index = pitch_lag_int - 85 + (85 - 19 1/3)*3;
pitch_lag_int 
integer pitch lag in the range [85, 143]

so...

 else
   // only integer part encoded in range [85, 143], no fractional part
   pitch_lag_int  = pitch_index - (85 - 19 1/3)*3 + 85;
   pitch_lag_frac = 0;
Second and fourth subframes

In the second and fourth subframes, the pitch lag resolution varies depending on the mode as follows:

  • 7.95 kbps mode
    • resolution of 1/3 is always used in the range [T1 - 10 2/3, T1 + 9 2/3]
    • encoded using 6 bits => pitch_index is in the range [0, 63]
  • 10.2 and 7.40 kbps modes
    • resolution of 1/3 is always used in the range [T1 - 5 2/3, T1 + 4 2/3]
    • encoded using 5 bits => pitch_index is in the range [0, 31]
  • 6.70, 5.90, 5.15 and 4.75 kbps modes
    • resolution of 1 is used in the range [T1 - 5, T1 + 4]
    • resolution of 1/3 is always used in the range [T1 - 1 2/3, T1 + 2/3]
    • encoded using 4 bits => pitch_index is in the range [0, 15]

Where T1 is nearest integer to the fractional pitch lag of the previous (1st or 3rd) subframe. The search range is bounded by [20, 143].

So the search range for the pitch lag is:

 lower_bound = 5;
 range = 9;
 if(mode == 7.95) {
   lower_bound = 10;
   range = 19;
 }
 search_range_min = max(pitch_lag_int_prev - lower_bound, 20);
 search_range_max = search_range_min + range;
 if(search_range_max > 143) {
   search_range_max = 143;
   search_range_min = search_range_max - range;
 }
pitch_lag_int_prev 
the integer part of the pitch lag from the previous sub frame


For modes 7.40, 7.95 and 10.2 the pitch index is encoded as:

 pitch_index = (pitch_lag_int - search_range_min)*3 + pitch_lag_frac + 2;
pitch_lag_int 
the integer part of the pitch lag in the range [search_range_min, search_range_max]
pitch_lag_frac 
the fractional part of the pitch lag in the range [-1, 1]

So the pitch lag is calculated through:

 // integer part of pitch lag = position of pitch lag in range [search_range_min, search_range_max] + lower bound of the range
 pitch_lag_int = (pitch_index + 2)/3 - 1 + search_range_min;
 // fractional part of pitch lag = pitch index - (integer part without offset)*3 - 2/3 to bring the values to the correct range
 pitch_lag_frac = pitch_index - ((pitch_index + 2)/3 - 1)*3 - 2;


For modes 4.75, 5.15, 5.90 and 6.70:

 t1_temp = max( min(pitch_lag_int_prev, search_range_min + 5), search_range_max - 4 );
t1_temp 
predicted pitch lag from the previous frame adjusted to fit into the 0 position of the search range

The pitch index is encoded as:

 // if pitch lag is below T1 - 1 2/3
 if( pitch_lag_int*3 + pitch_lag_frac <= (t1_temp - 2)*3 ) {
   // encode with resolution 1
   index = (pitch_lag_int - t1_temp) + 5;
 // else if pitch lag is below T1 + 1
 }else if( pitch_lag_int*3 + pitch_lag_frac < (t1_temp + 1)*3 ) {
   // encode with resolution 1/3
   index = ( pitch_lag_int*3 + pitch_lag_frac - (t1_temp - 2)*3 ) + 3;
 // else pitch lag is above T1 + 2/3
 }else {
   // encode with resolution 1
   index = (pitch_lag_int - t1_temp) + 11;
 }
pitch_lag_int 
the integer part of the pitch lag in the range [search_range_min, search_range_max]
pitch_lag_frac 
the fractional part of the pitch lag in the range [-1, 1]

The possible pitch indices and values are:

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
-5 -4 -3 -2 -1 2/3 -1 1/3 -1 -2/3 -1/3 0 1/3 2/3 1 2 3 4

So the pitch lag is calculated through:

 if(pitch_index < 4) {
   // integer part of pitch lag = pitch lag position in range [t1_temp - 5, t1_temp - 2] + lower bound of range
   pitch_lag_int = pitch_index + (t1_temp - 5);
   // this range is coded with resolution 1 so no fractional part
   pitch_lag_frac = 0;
 }else if(pitch_index < 12) {
   pitch_lag_int = (pitch_index - 2)/3 + (t1_temp - 2);
   pitch_lag_frac = (pitch_index - 4) - ((pitch_index - 2)/3)*3 - 11;
 }else {
   // integer part of pitch lag = pitch lag position in range [t1_temp + 1, t1_temp + 4] + lower bound of range
   pitch_lag_int = pitch_index - 12 + t1_temp + 1;
   // this range is coded with resolution 1 so no fractional part
   pitch_lag_frac = 0;
 }


Calculate pitch vector

Amrnb pitchvector.gif

integer pitch lag
sample position in the vectors 0, ..., 39
0, ..., 5 corresponding to fractions 0, 1/6, 2/6, 3/6, -2/6, -1/6 respectively

This equation can be used for both 1/3 and 1/6 resolution simply by multiplying t by 2 in the 1/3 case.

(Note: the coefficients b60 are in the reference source in an array called inter6)


Decoding of the fixed (innovative or algebraic) vector

  • the excitation pulse positions and signs are parsed from the bit stream
  • the pulse positions and signs are encoded differently depending on the mode
  • the fixed code book vector, c(n), is then constructed from the pulse positions and signs
  • if pitch_lag_int is less than the subframe size (40), the pitch sharpening procedure is applied


Decoding the pulse positions

12.2 kbps mode

  • 10 pulse positions each coded using 3 bit Gray codes
  • signs coded using 1 bit each for 5 pulse pairs


Pulse Positions
i0,i5 0, 5, 10, 15, 20, 25, 30, 35
i1,i6 1, 6, 11, 16, 21, 26, 31, 36
i2,i7 2, 7, 12, 17, 22, 27, 32, 37
i3,i8 3, 8, 13, 18, 23, 28, 33, 38
i4,i9 4, 9, 14, 19, 24, 29, 34, 39


10.2 kbps mode

  • 8 pulse positions, 4 pairs, coded as 3 values using 10, 10 and 7 bits
  • signs coded using 1 bit each for 4 pulse pairs


Pulse Positions
i0,i4 0, 4, 8, 12, 16, 20, 24, 28, 32, 36
i1,i5 1, 5, 9, 13, 17, 21, 25, 29, 33, 37
i2,i6 2, 6, 10, 14, 18, 22, 26, 30, 34, 38
i3,i7 3, 7, 11, 15, 19, 23, 27, 31, 35, 39


7.95 and 7.40 kbps modes

  • 4 pulse positions Gray coded using 3, 3, 3 and 4 bits
  • signs coded using 1 bit for each pulse


Pulse Positions
i0 0, 5, 10, 15, 20, 25, 30, 35
i1 1, 6, 11, 16, 21, 26, 31, 36
i2 2, 7, 12, 17, 22, 27, 32, 37
i3 3, 8, 13, 18, 23, 28, 33, 38

4, 9, 14, 19, 24, 29, 34, 39

6.70 kbps mode

  • 3 pulse positions coded using 3, 4 and 4 bits
  • signs coded using 1 bit for each pulse


Pulse Positions
i0 0, 5, 10, 15, 20, 25, 30, 35
i1 1, 6, 11, 16, 21, 26, 31, 36

3, 8, 13, 18, 23, 28, 33, 38

i2 2, 7, 12, 17, 22, 27, 32, 37

4, 9, 14, 19, 24, 29, 34, 39


5.90 kbps mode

  • 2 pulse positions coded using 4 and 5 bits
  • signs coded using 1 bit for each pulse


Pulse Positions
i0 1, 6, 11, 16, 21, 26, 31, 36

3, 8, 13, 18, 23, 28, 33, 38

i1 0, 5, 10, 15, 20, 25, 30, 35

1, 6, 11, 16, 21, 26, 31, 36
2, 7, 12, 17, 22, 27, 32, 37
4, 9, 14, 19, 24, 29, 34, 39

5.15 and 4.75 kbps modes

  • 2 pulse positions coded using 1 bit for the position subset and 3 bits per pulse
  • signs coded using 1 bit for each pulse


Subframe Subset Pulse Positions
1 1 i0 0, 5, 10, 15, 20, 25, 30, 35
i1 2, 7, 12, 17, 22, 27, 32, 37
2 i0 1, 6, 11, 16, 21, 26, 31, 36
i1 3, 8, 13, 18, 23, 28, 33, 38
2 1 i0 0, 5, 10, 15, 20, 25, 30, 35
i1 3, 8, 13, 18, 23, 28, 33, 38
2 i0 2, 7, 12, 17, 22, 27, 32, 37
i1 4, 9, 14, 19, 24, 29, 34, 39
3 1 i0 0, 5, 10, 15, 20, 25, 30, 35
i1 2, 7, 12, 17, 22, 27, 32, 37
2 i0 1, 6, 11, 16, 21, 26, 31, 36
i1 4, 9, 14, 19, 24, 29, 34, 39
4 1 i0 0, 5, 10, 15, 20, 25, 30, 35
i1 3, 8, 13, 18, 23, 28, 33, 38
2 i0 1, 6, 11, 16, 21, 26, 31, 36
i1 4, 9, 14, 19, 24, 29, 34, 39


Fixed codebook vector construction

All c(n) are zero if there is no pulse at position n. If there is a pulse at position n then it has the corresponding sign as parsed above.


Pitch sharpening

Amrnb fixvecpitshp.gif

β 
the decoded pitch gain, ^g_p, bounded by [0.0,1.0] for 12.2. kbps or [0.0,0.8] for other modes

Note: Only sharpen n in [pitch_lag_int-1, 39]. The reference source considers previous fixed vector elements (n<0) to be 0. I think this is also the reason pitch sharpening is not conducted for pitch_lag_int > 40 as all the sharpening contributions would be 0.

Decoding of the pitch and fixed codebook gains

Fixed gain prediction

A moving average prediction of the innovation (fixed) energy is conducted.


Amrnb fixedgainpred.gif

g_c' 
fixed gain prediction
\tilde{E} 
predicted energy [dB]
\bar{E} 
desired mean innovation (fixed) energy [dB]
E_I 
calculated mean innovation (fixed) energy [dB]


Amrnb predener.gif

4-tap MA prediction coefficients [0.68, 0.58, 0.34, 0.19]
^R(k) 
quantified prediction errors at subframe k 20*log10(^γ_gc(k))


Desired mean innovation (fixed) energy:

Mode (kbps) Mean energy (dB)
12.2 36
10.2 33
7.95 36
7.40 30
6.70 28.75
5.90 33
5.15 33
4.75 33


Amrnb meaniner.gif

E_I 
calculated mean innovation (fixed) energy [dB]
subframe size 40
c(n) 
fixed codebook vector

Dequantisation of the gains

12.2kbps and 7.95kbps - scalar quantised gains

The received indices are used to find the quantified pitch gain, ^g_p, and the quantified fixed gain correction factor, ^γ_gc.

Pitch gain

The parsed gain index is used to obtain the quantified pitch gain, ^g_p, from the corresponding codebook. (qua_gain_pitch in the reference source.)

Fixed gain correction factor

The parsed gain index is used to obtain the quantified fixed gain, ^g_c, from the corresponding codebook. (qua_gain_code in the reference source.) The table stores ^γ_gc, and the quantised energy error in two forms (these are needed for the moving average calculation of the predicted fixed gain):

qua_ener_MR122 = log2(^γ_gc) qua_ener = 20*log10(^γ_gc)

^γ_gc is stored at Q11 (i.e. it's multiplied by 2^11.) qua_ener_MR122 and qua_ener are stored at Q10.

Other modes - vector quantised gains

The received index gives both the quantified adaptive codebook gain, ^g_p, and the quantified algebraic codebook gain correction factor, ^γ_gc.

The tables contains the following data:

^g_p           (Q14),
^γ_gc          (Q12), (^g_c = g_c'*^γ_gc),
qua_ener_MR122 (Q10), (log2(^γ_gc))
qua_ener       (Q10)  (20*log10(^γ_gc))

The log2() and log10() values are calculated on the fixed point value
(g_fac Q12) and not on the original floating point value of g_fac
to make the quantizer/MA predictdor use corresponding values.

The codebook used depends on the mode:

6.70, 7.40, 10.2 kbps modes - table_gain_highrates in the reference source Four consecutive entries give ^g_p, ^γ_gc, qua_ener_MR122 and qua_ener. Apparently the values for qua_ener are the original ones from IS641 to ensure bit-exactness but are not exactly the rounded value of 20log10(^γ_gc).

5.15, 5.90 kbps modes - table_gain_lowrates Similar to table_gain_highrates, four consecutive entries give ^g_p, ^γ_gc, qua_ener_MR122 and qua_ener. There are no special notes for this table.

4.75 kbps mode - table_gain_MR475 Unlike the above mentioned tables, four consecutive values give ^g_p, ^γ_gc for subframes 0,2, and then ^g_p, ^γ_gc for subframes 1,3.

At the very least I think these tables could be redesigned a little.

Calculation of the quantified fixed gain

Amrnb fixedgain.gif

Smoothing of the fixed codebook gain

10.2, 6.70, 5.90, 5.15, 4.75 kbit/s modes only


Calculate averaged LSP vector

Amrnb lspsmooth.gif

\bar{q}(n) 
averaged LSP vector at frame n
^q_4(n) 
quantified LSP vector for the 4th subframe at frame n


Calculate fixed gain smoothing factor

Amrnb lspdiff.gif

diff_m 
difference measure at subframe m
loops over LSPs
loops over subframes
^q_m 
quantified LSP vector at subframe m

Note: I think the sum over the subframes is an error in the specification and they actually mean to use the quantified LSP vector from subframe m for the calculation of diff for subframe m. I think this is what they do in the reference source and the sum over m is an error.


Amrnb smoothfac.gif

k_m 
fixed gain smoothing factor
K_1 
0.4
K_2 
0.25
diff_m 
difference measure at subframe m

If diff_m has been greater than 0.65 for 10 subframes, k_m is set to 1.0 (i.e. no smoothing) for 40 subframes.

Calculate mean fixed gain

Amrnb meangc.gif

\bar{g_c}(m) 
mean fixed gain at subframe m
^g_c(k) 
quantified fixed gain at subframe k

Calculate smoothed fixed gain

Amrnb gcsmooth.gif

^g_c 
quantified fixed gain
\bar{g_c} 
averaged fixed gain

Anti-sparseness processing

7.95, 6.70, 5.90, 5.15, 4.75 kbit/s modes only


Evaluate impulse response filter strength

The fixed vector, c(n), has only a few pulses per subframe. In certain conditions, to reduce perceptual artifacts arising from this, the vector is circularly convolved with a predefined impulse response. The selection of the strength of filter is made based on the decoded gains.

 if ^g_p < 0.6
   impNr = 0
 else if ^g_p < 0.9
   impNr = 1
 else
   impNr = 2
impNr = 0 
strong impulse response filter
impNr = 1 
medium impulse response filter
impNr = 2 
no filtering
 if ^g_c(k) > 2 * ^g_c(k-1)
   impNr = min( impNr + 1, 2 )
 else if impNr = 0 AND median of last five ^g_p >= 0.6
   impNr = min( impNr(k), min(impNr(k-1) + 1, 2) )


Circular convolution of fixed vector and impulse response filter

Amrnb circconv.gif

(c * h) 
convolution of vectors c and h, in this case circular convolution
h[n] 
nth coefficient of the impulse response used for filtering
c[n] 
nth coefficient of the fixed vector

n = 0, ..., 39

To make the convolution circular, make the impulse response circular by taking h[-m] = h[39-m]

Computing the reconstructed speech

Construct excitation

Amrnb excitation.gif

u(n) 
excitation vector
^g_p 
quantified pitch gain
v(n) 
pitch vector
^g_c 
quantified fixed gain
c(n) 
fixed vector


Emphasise pitch vector contribution

This is apparently a post-processing technique.

Amrnb pitchvecemph.gif

^u(n) 
excitation vector with emphasised pitch vector contribution
β 
^g_p bounded by [0.0, 0.8] or [0.0, 1.0] depending on mode


Apply adaptive gain control (AGC) through gain scaling

Amrnb gainfac.gif

η 
gain scaling factor for emphasised excitation

Amrnb gainscalexc.gif

^u'(n) 
gain-scaled emphasised excitation


Calculate reconstructed speech samples

Amrnb synthfilter.gif

^s(n) 
reconstructed speech samples
^a_i 
LP filter coefficients

Note: for n-i < 0, ^s(n-i) should be take from previous speech samples if existing, else we will consider them 0 as this behaviour is undefined the specification.

Additional instability protection

If an overflow occurs during synthesis, the pitch vector, v(n), is scaled down by a factor of 4 and synthesis is conducted again bypassing emphasising the pitch vector contribution and adaptive gain control.

Q: What classifies an overflow? A: s(n) < -32768 or s(n) > 32767 (i.e. 16-bit signed int)

Post-processing

Adaptive post-filtering

(c.f. §6.2.1)

IIR filtering

The speech samples, ^s(n), are filtered through a formant filter and a tilt compensation filter.

Amrnb pfformant.gif

γ_n, γ_d 
control the amount of formant post-filtering

The speech samples, ^s(n), are filtered through ^A(z/γ_n) to produce the residual signal ^r(n).

Amrnb residual.gif

^r(n) is filtered through 1/^A(z/γ_d).

Amrnb fmntfilt.gif

The output is filtered through H_t(z) (the tilt compensation filter) resulting in the post-filtered speech signal, ^s_f(n).

Amrnb pftilt.gif

Amrnb mu.gif

Amrnb reffac.gif

Amrnb r h.gif

L_h 
22 - the truncation of the impulse response
h_f 
impulse response of the formant filter H_f

So, in summation notation:

Amrnb pftiltsum.gif

12.2 and 10.2 kbps modes

γ_n = 0.7

γ_d = 0.75

γ_t = 0.8 if k_1' > 0; 0 otherwise

Other modes

γ_n = 0.55

γ_d = 0.7

γ_t = 0.8

Adaptive gain control

Adaptive gain control is used to compensate for the gain difference between the filtered and synthesised speech signals.

Amrnb gainscalfac.gif

Amrnb gainscalfacwtd.gif

Amrnb gainscalspch.gif

\alpha 
adaptive gain control factor equal to 0.9

High-pass filtering and upscaling

(c.f. §6.2.2)

Amrnb highpass.gif

After completing all filtering, the samples are scaled up by a factor of 2.