.rs
.\" Troff code generated by TPS Convert from ITU Original Files
.\"                 Not Copyright ( c) 1991 
.\"
.\" Assumes tbl, eqn, MS macros, and lots of luck.
.TA 1c 2c 3c 4c 5c 6c 7c 8c
.ds CH
.ds CF
.EQ
delim @@
.EN
.nr LL 40.5P
.nr ll 40.5P
.nr HM 3P
.nr FM 6P
.nr PO 4P
.nr PD 9p
.po 4P

.rs
\v | 5i'
.IP
\fB7.2\fR 	\fBCoding\ of\ analogue\ signals\ by\ methods\ other\ than\ PCM\fR 
.sp 1P
.RT
.sp 2P
.LP
\fBRecommendation\ G.721\fR 
.RT
.sp 2P
.ce 1000
\fB32\ kbit/s\ \fR \fBADAPTIVE\ DIFFERENTIAL\ PULSE\ CODE\fR 
.EF '%	Fascicle\ III.4\ \(em\ Rec.\ G.721''
.OF '''Fascicle\ III.4\ \(em\ Rec.\ G.721	%'
.ce 0
.sp 1P
.ce 1000
\fBMODULATION\ (ADPCM)\fR 
.FS
This
Recommendation G.721 completely replaces the text of Recommendation\ G.721
published in Fascicle\ III.3 of the \fIRed Book\fR . It should be noted 
that systems designed in accordance with the present Recommendation will 
not be compatible with systems designed in accordance with the \fIRed Book\fR 
version. 
.FE
.ce 0
.sp 1P
.ce 1000
\fI(Melbourne, 1988)\fR 
.sp 9p
.RT
.ce 0
.sp 1P
.LP
\fB1\fR 	\fBGeneral\fR 
.sp 1P
.RT
.PP
The characteristics below are recommended for the conversion of a 64\ kbit/s 
A\(hylaw or \(*m\(hylaw PCM channel to and from a 32\ kbit/s channel. The 
conversion is applied to the PCM bit stream using an ADPCM transcoding
technique. The relationship between the voice frequency signals and the PCM
encoding/decoding laws is fully specified in Recommendation\ G.711.
.PP
Paragraphs 1.1 and 1.2 of this Recommendation provide an outline
description of the ADPCM transcoding algorithm, \(sc\(sc\ 2 and\ 3 provide the
principles and functional descriptions of the ADPCM encoding and decoding
algorithms respectively, whilst \(sc\ 4 is the precise specification for the
algorithm computations. Networking aspects and digital test sequences are
addressed in Apendices\ I and\ II respectively to this Recommendation.
.PP
Simplified block diagrams of both the ADPCM encoder and decoder are
shown in Figure\ 1/G.721.
.PP
In \(sc 4, each sub\(hyblock in the encoder and decoder is precisely defined 
using one particular logical sequence. If other methods of computation 
are 
used, extreme care should be taken to ensure that they yield \fIexactly\fR 
the same value for the output processing variables. Any further departures 
from the 
processes detailed in \(sc\ 4 will incur performance penalties which may be
severe.
.PP
\fINote 1\fR \ \(em\ For the time being, the 32 kbit/s ADPCM algorithm 
defined in this Recommendation is intended for transmission purposes since 
switching 
applications at this bit rate are a subject for further study by the CCITT.
.PP
\fINote 2\fR \ \(em\ Prior to the definition of this Recommendation, other 32
kbit/s ADPCM algorithms of similar performance have been incorporated in
equipment designs and used in national telecommunications networks.
.PP
\fINote 3\fR \ \(em\ In the short term, due to the limited availability of
32\ kbit/s ADPCM equipment, the use of 32\ kbit/s ADPCM in the international
network, when requested by one of the Administrations concerned, will require 
bilateral and/or multilateral agreement. 
.PP
\fINote 4\fR \ \(em\ Signalling and multiplexing considerations are beyond 
the scope of this Recommendation (see for example Recommendation\ G.761). 
.RT
.sp 1P
.LP
1.1
	\fIADPCM encoder\fR 
.sp 9p
.RT
.PP
Subsequent to the conversion of the A\(hylaw or \(*m\(hylaw PCM input signal 
to uniform PCM, a difference signal is obtained, by subtracting an estimate 
of the input signal from the input signal itself. An adaptative 15\(hylevel 
quantizer is used to assign four binary digits to the value of the difference 
signal for transmission to the decoder. An inverse quantizer produces a 
quantized 
difference signal from these same four binary digits. The 
signal
estimate
is added to this 
quantized difference signal
to produce
the reconstructed
.PP
version of the input signal. Both the reconstructed signal and the quantized
difference signal are operated upon by an 
adaptive predictor
which
produces the estimate of the input signal, thereby completing the 
feedback  loop
.
.RT
.LP
.sp 1
.bp
.sp 1P
.LP
1.2
	\fIADPCM decoder\fR 
.sp 9p
.RT
.PP
The decoder includes a structure identical to the feedback portion of the 
encoder, together with a uniform PCM to A\(hylaw or \(*m\(hylaw conversion 
and a 
synchronous coding adjustment
.
.PP
The synchronous coding adjustment prevents cumulative distortion
occurring on synchronous tandem codings (ADPCM\(hyPCM\(hyADPCM,\ etc. digital
connections) under certain conditions (see \(sc\ 3.7). The synchronous coding
adjustment is achieved by adjusting the 
PCM output codes
in a manner
which attempts to eliminate 
quantizing distortion
in the next 
ADPCM encoding stage
.
.RT
.LP
.rs
.sp 37P
.ad r
\fBFigure 1/G.721, p.\fR 
.sp 1P
.RT
.ad b
.RT
.sp 2P
.LP
\fB2\fR 	\fBADPCM encoder\fR \fBprinciples\fR 
.sp 1P
.RT
.PP
Figure 2/G.721 is a block schematic of the encoder. For each
variable to be described, \fIk\fR \ is the 
sampling index
and samples are
taken at 125\ \(*ms intervals. A fundamental description of each block is given
below in \(sc\(sc\ 2.1 to\ 2.8.
.bp
.RT
.LP
.rs
.sp 25P
.ad r
\fBFigure 2/G.721, p.\fR 
.sp 1P
.RT
.ad b
.RT
.sp 1P
.LP
2.1
	\fIInput PCM format conversion\fR 
.sp 9p
.RT
.PP
This block converts the input signal \fIs\fR (\fIk\fR ) from A\(hylaw or 
\(*m\(hylaw PCM to a uniform PCM signal \fIs\fR\d1\u(\fIk\fR ). 
.RT
.sp 1P
.LP
2.2
	\fIDifference signal\fR \fIcomputation\fR 
.sp 9p
.RT
.PP
This block calculates the difference signal \fId\fR (\fIk\fR ) from the 
uniform PCM signal \fIs\fR\d\fIl\fR\u(\fIk\fR ) and the signal 
estimate \fIs\fR\d\fIe\fR\u(\fIk\fR ):
\v'6p'
.RT
.ce 1000
\fId\fR (\fIk\fR ) = \fIs
\dl\u\fR (\fIk\fR ) \(em
\fIs
\de\u\fR (\fIk\fR )
.ce 0
.ad r
(2\(hy1)
.ad b
.RT
.LP
.sp 1
.sp 1P
.LP
2.3
	\fIAdaptive quantizer\fR 
.sp 9p
.RT
.PP
A 15\(hylevel non\(hyuniform adaptive quantizer is used to quantize the 
difference signal \fId\fR (\fIk\fR ). Prior to quantization, \fId\fR (\fIk\fR 
) is 
converted to
a base\ 2 logarithmic representation and scaled by \fIy\fR (\fIk\fR ) which is
computed by
the scale factor adaptation block. The normalized input/output characteristic 
(infinite precision values) of the quantizer is given in Table\ 1/G.721. 
Four 
binary digits are used to specify the quantized level representing
\fId\fR (\fIk\fR )
(three for the magnitude and one for the sign). The 4\(hybit quantizer output
\fII\fR (\fIk\fR ) forms the 32\ kbit/s output signal; it is also fed to 
the inverse adaptive quantizer, the adaptation speed control and the 
quantizer scale
factor
adaptation blocks.
.RT
.sp 1P
.LP
2.4
	\fIInverse adaptive quantizer\fR 
.sp 9p
.RT
.PP
A quantized version \fId\fR\d\fIq\fR\u(\fIk\fR ) of the difference signal 
is produced by scaling, using \fIy\fR (\fIk\fR ), specific values selected 
from the 
normalized quantizing characteristic given in Table\ 1/G.721 and then
transforming the result from the logarithmic domain.
.bp
.RT
.ce
\fBH.T. [T1.721]\fR 
.ce
TABLE\ 1/G.721
.ce
\fBQuantizer normalized input/output characteristic\fR 
.ps 9
.vs 11
.nr VS 11
.nr PS 9
.TS
center box;
cw(72p) | cw(30p) | cw(72p) .
 {
Normalized quantizer input range
log
 | fId\fR
(\fIk\fR
 | (em\fIy\fR
(\fIk\fR
)
 }	| fII\fR (\fIk\fR  |	 {
Normalized quantizer output
log
 | fId\fR
\fIq\fR
(\fIk\fR
 | (em\fIy\fR
(\fIk\fR
) 
 }
_
.T&
cw(72p) | cw(30p) | cw(72p) .
[3.12,\ +\(if)	7	3.32\ 
.T&
cw(72p) | cw(30p) | cw(72p) .
[2.72,\ \ 3.12)	6	2.91\ 
.T&
cw(72p) | cw(30p) | cw(72p) .
[2.34,\ \ 2.72)	5	2.52\ 
.T&
cw(72p) | cw(30p) | cw(72p) .
[1.91,\ \ 2.34)	4	2.13\ 
.T&
cw(72p) | cw(30p) | cw(72p) .
[1.38,\ \ 1.91)	3	1.66\ 
.T&
cw(72p) | cw(30p) | cw(72p) .
[0.62,\ \ 1.38)	2	1.05\ 
.T&
cw(72p) | cw(30p) | cw(72p) .
[\(em0.98,\ 0.62)	1	0.031
.T&
cw(72p) | cw(30p) | cw(72p) .
(\(em\(if,\ \(em0.98)	0	\(em\(if
.TE
.LP
\fINote\fR
\ \(em\ The convention used here is that \*Q[\*U indicates that the endpoint
value is included in the range, \*Q)\*U indicates that the endpoint value is
excluded from the range.
.nr PS 9
.RT
.ad r
\fBTable 1/G.721 [T1.721], p.\fR 
.sp 1P
.RT
.ad b
.RT
.sp 1P
.LP
2.5
	\fIQuantizer scale factor adaptation\fR 
.sp 9p
.RT
.PP
This block computes \fIy\fR (\fIk\fR ), the scaling factor for the
quantizer and the inverse quantizer. The inputs are the 4\(hybit quantizer 
output \fII\fR (\fIk\fR ) and the adaptation speed control parameter \fIa\fR\d\fIl\fR\u(\fIk\fR 
). 
.PP
The basic principle used in scaling the quantizer is 
bimodal
adaptation
:
.RT
.LP
	\(em
	fast for signals (e.g. speech) that produce difference
signals with large fluctuations;
.LP
	\(em
	slow for signals (e.g. voiceband data, tones) that produce
difference signals with small fluctuations.
.PP
The speed of adaptation is controlled by a combination of fast and slow 
scale factors. 
.PP
The 
fast (unlocked) scale factor
\fIy\fR\d\fIu\fR\u(\fIk\fR ) is
recursively computed in the base\ 2 logarithmic domain from the resultant
logarithmic scale factor \fIy\fR (\fIk\fR ):
\v'6p'
.RT
.ce 1000
\fIy
\du\u\fR (\fIk\fR ) = (1 \(em 2
\u\(em5
\d)\fIy\fR (\fIk\fR ) +
2
\u\(em5
\d\fIW\fR [\fII\fR (\fIk\fR )],
.ce 0
.ad r
(2\(hy2)
.ad b
.RT
.LP
.sp 1
where \fIy
\du\u\fR (\fIk\fR ) is limited by 1.06 \(= \fIy
\du\u\fR (\fIk\fR ) \(=  10.00.
.PP
The discrete function \fIW\fR (\fII\fR ) is defined as follows
(infinite precision values):
.ce
\fBH.T. [T2.721]\fR 
.ps 9
.vs 11
.nr VS 11
.nr PS 9
.TS
center box;
cw(24p) | cw(18p) | cw(18p) | cw(18p) | cw(18p) | cw(18p) | cw(18p) | cw(18p) | cw(18p) .
| (k |	7	6	5	4	3	2	1	0
_
.T&
cw(24p) | cw(18p) | cw(18p) | cw(18p) | cw(18p) | cw(18p) | cw(18p) | cw(18p) | cw(18p) .
W(I)	70.13	22.19	12.38	7.00	4.00	2.56	1.13	\(em0.75
.TE
.nr PS 9
.RT
.ad r
\fBTable [T2.721], p.\fR 
.sp 1P
.RT
.ad b
.RT
.PP
The factor (1 \(em 2\uD\dlF261\u5\d) introduces finite memory into the
adaptive process so that the states of the encoder and decoder converge
following transmission errors.
.bp
.PP
The 
slow (locked) scale factor
\fIy\fR\d\fIl\fR\u(\fIk\fR ) is derived from \fIy\fR\d\fIu\fR\u(\fIk\fR 
) with a low pass filter operation: 
\v'6p'
.RT
.ce 1000
\fIy
\dl\u\fR (\fIk\fR ) = (1 \(em 2
\u\(em6
\d)\fIy
\dl\u\fR (\fIk\fR \(em 1) +
2
\u\(em6
\d\fIy
\du\u\fR (\fIk\fR )
.ce 0
.ad r
(2\(hy3)
.ad b
.RT
.PP
.sp 1
The fast and slow scale factors are then combined to form the
resultant scale factor:
\v'6p'
.ce 1000
\fIy\fR (\fIk\fR ) = \fIa
\dl\u\fR (\fIk\fR )\fIy
\du\u\fR (\fIk\fR \(em 1) + [1 \(em
\fIa
\dl\u\fR (\fIk\fR )]\fIy
\dl\u\fR (\fIk\fR \(em 1),
.ce 0
.ad r
(2\(hy4)
.ad b
.RT
.LP
.sp 1
.LP
where 0 \(= \fIa
\dl\u\fR (\fIk\fR ) \(= 1 (see \(sc 2.6).
.sp 1P
.LP
2.6
	\fIAdaptation speed control\fR 
.sp 9p
.RT
.PP
The controlling parameter \fIa\fR\d\fIl\fR\u(\fIk\fR ) can assume values 
in the range [0,\ 1]. It tends towards unity for speech signals and towards 
zero 
for voiceband data signals and tones. It is derived from a measure of the
rate\(hyof\(hychange of the difference signal values.
.PP
Two measures of the average magnitude of \fII\fR (\fIk\fR ) are
computed:
\v'6p'
.RT
.ce 1000
\fId
\dms
\u\fR (\fIk\fR ) = (1 \(em 2
\u\(em5
\d)\fId
\dms
\u\fR (\fIk\fR \(em 1)  + 2
\u\(em5
\d\fIF\fR [\fII\fR (\fIk\fR )],
.ce 0
.ad r
(2\(hy5)
.ad b
.RT
.LP
and
.ce 1000
\fId
\dml
\u\fR (\fIk\fR ) = (1 \(em 2
\u\(em7
\d)\fId
\dml
\u\fR (\fIk\fR \(em 1)  + 2
\u\(em7
\d\fIF\fR [\fII\fR (\fIk\fR )],
.ce 0
.ad r
(2\(hy6)
.ad b
.RT
.LP
.sp 1
where \fIF\fR [\fII\fR (\fIk\fR )] is defined by
.ce
\fBH.T. [T3.721]\fR 
.ps 9
.vs 11
.nr VS 11
.nr PS 9
.TS
center box;
cw(24p) | cw(18p) | cw(18p) | cw(18p) | cw(18p) | cw(18p) | cw(18p) | cw(18p) | cw(18p) .
| (k |	7	6	5	4	3	2	1	0
_
.T&
cw(24p) | cw(18p) | cw(18p) | cw(18p) | cw(18p) | cw(18p) | cw(18p) | cw(18p) | cw(18p) .
F[I(k)]  	7	3	1	1	1	0	0	0
.TE
.nr PS 9
.RT
.ad r
\fBTable [T3.721], p.\fR 
.sp 1P
.RT
.ad b
.RT
.LP
\fId\fR\d\fIm\fR\\d\fIs\fR\u(\fIk\fR ) is thus a relatively short term 
average of 
\fIF\fR [\fII\fR (\fIk\fR )]
and \fId\fR\d\fIm\fR\\d\fIl\fR\u(\fIk\fR ) is a relatively long term average of
\fIF\fR [\fII\fR (\fIk\fR )].
.PP
Using these two averages, the variable \fIa\fR\d\fIp\fR\u(\fIk\fR ) is
defined:
\v'6p'
.LP
\fIa
\dp\u\fR (\fIk\fR ) = 
\ (1 \(em
2
\u\(em4
\d)\fIa
\dp\u\fR (\fIk\fR \(em 1) + 2
\u\(em3
\d,
\ if 
@ left | fId~\dms~\u\fR (\fIk\fR ) \(em~\fId~\dml~\u\fR (\fIk\fR ) right | @ 
\(>=" 2
\u\(em3
\d\fId
\dml
\u\fR (\fIk\fR )
\fIa
\dp\u\fR (\fIk\fR ) = 
\ (1 \(em
2
\u\(em4
\d)\fIa
\dp\u\fR (\fIk\fR \(em 1) + 2
\u\(em3
\d, \ if \fIy\fR (\fIk\fR ) < 3
\fIa
\dp\u\fR (\fIk\fR ) = 
\ (1 \(em
2
\u\(em4
\d)\fIa
\dp\u\fR (\fIk\fR \(em 1) + 2
\u\(em3
\d,
\ if \fIt\fR \fI\d\fId\fR\u(\fIk\fR ) = 1
(2\(hy7)
\fIa
\dp\u\fR (\fIk\fR ) =
\ 1,
if \fIt\fR \fI\d\fIr\fR\u(\fIk\fR ) = 1
\fIa
\dp\u\fR (\fIk\fR ) = 
\ (1 \(em
2
\u\(em4
\d)\fIa
\dp\u\fR (\fIk\fR \(em 1),
+ 2
\u\(em3
\d \ 
otherwise
.PP
Thus, \fIa\fR\d\fIp\fR\u(\fIk\fR ) tends towards the value 2 if the difference 
between \fId\fR\d\fIm\fR\\d\fIs\fR\u(\fIk\fR ) and \fId\fR\d\fIm\fR\\d\fIl\fR\u(\fIk\fR 
) is large (average 
magnitude of
\fII\fR (\fIk\fR ) changing) and \fIa\fR\d\fIp\fR\u(\fIk\fR ) tends towards 
the value\ 0 if 
the difference
is small (average magnitude of \fII\fR (\fIk\fR ) relatively constant).
\fIa\fR\d\fIp\fR\u(\fIk\fR )
also tends towards\ 2 for an idle channel (indicated by
\fIy\fR (\fIk\fR )\ <\ 3) or partial band signals (indicated by
\fIt\fR\d\fId\fR\u(\fIk\fR )\ =\ 1 as described in \(sc\ 2.8). Note that 
\fIa\fR\d\fIp\fR\u(\fIk\fR ) is set to\ 1 upon detection of a 
partial band signal transition
(indicated  by \fIt\fR\d\fIr\fR\u(\fIk\fR )\ =\ 1, see \(sc\ 2.8).
.LP
\fIa
\dp\u\fR (\fIk\fR \(em 1) is then limited to yield \fIa
\dl\u\fR (\fIk\fR )
used in Equation (2\(hy4) above:
\v'6p'
.ce 1000
\fIa
[Formula Deleted]