ISO/IEC 109181 : 1993(E)
The uniform quantizer is defined by the following equation. Rounding is to the nearest integer:
Sq
round
S
Q
vu
vu
vu
=
F
H
G IKJ
Sq
vu
is the quantized DCT coefficient, normalized by the quantizer step size.
NOTE This equation contains a term which may not be represented with perfect accuracy by any real implementation. The
accuracy requirements for the combined FDCT and quantization procedures are specified in Part 2 of this Specification.
At the decoder, this normalization is removed by the following equation, which defines dequantization:
R
Sq
Q
vu
vu
vu
=
×
NOTE Depending on the rounding used in quantization, it is possible that the dequantized coefficient may be outside the
expected range.
The relationship among samples, DCT coefficients, and quantization is illustrated in Figure A.5.
A.3.5
Differential DC encoding
After quantization, and in preparation for entropy encoding, the quantized DC coefficient Sq
00
is treated separately from
the 63 quantized AC coefficients. The value that shall be encoded is the difference (DIFF) between the quantized DC
coefficient of the current block (DC
i
which is also designated as Sq
00
) and that of the previous block of the same
component (PRED):
DIFF
DC
PRED
i
=

A.3.6
Zigzag sequence
After quantization, and in preparation for entropy encoding, the quantized AC coefficients are converted to the zigzag
sequence. The quantized DC coefficient (coefficient zero in the array) is treated separately, as defined in A.3.5. The zig
zag sequence is specified in Figure A.6.
A.4
Point transform
For various procedures data may be optionally divided by a power of 2 by a point transform prior to coding. There are
three processes which require a point transform: lossless coding, lossless differential frame coding in the hierarchical
mode, and successive approximation coding in the progressive DCT mode.
In the lossless mode of operation the point transform is applied to the input samples. In the difference coding of the
hierarchical mode of operation the point transform is applied to the difference between the input component samples and
the reference component samples. In both cases the point transform is an integer divide by 2
Pt
, where Pt is the value of the
point transform parameter (see B.2.3).
In successive approximation coding the point transform for the AC coefficients is an integer divide by 2
Al
, where Al is the
successive approximation bit position, low (see B.2.3). The point transform for the DC coefficients is an arithmeticshift
right by Al bits. This is equivalent to dividing by 2
Pt
before the level shift (see A.3.1).
The output of the decoder is rescaled by multiplying by 2
Pt
. An example of the point transform is given in K.10.
28
CCITT Rec. T.81 (1992 E)