MPEG-2 Video Coding - Digital Video and Audio Broadcasting Technology - page 139

become orthonormal, implementation of the transform and its inverse is
quite simple.

The transform and its inverse can now be represented as follows:

F = f • M ab • M ab T ;

f = F • M ab T • M ab ;

During the quantization, the results of the transform and its inverse were
additionally influenced by a scalar multiplication

F = f • M ab • M ab T • Q;

f = F • M ab T • M ab • Q ` ;

If only ones are entered in Q and Q', nothing changes. However, the
quantization of the DCT coefficients is reduced towards higher frequencies
via Q.
In various transformation methods, only other matrices M ab are used, in
principle, i.e. "basic functions" from which it is attempted to represent the
original functions are others. In the case of the DCT, these are cosine pat-
terns.
In MPEG-4, these basic patterns, or the coefficients of the matrix M ab,
respectively, are replaced by others. In the case of MPEG-4, this is called
an integer matrix multiplication or also Hadamard transformation. The
transformation matrices used in MPEG-4 AVC are the following:

1 1 1 1
2 1 1 2
1 1 1 1
1 2 2 1

1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1

1 1
1 1

H= C=

T=

T = integer transform for luma and chroma samples
H = Hadamard transform for luma DC coefficients
C = Hadamard transform for chroma DC coeffients

Fig. 7.36. Transformation matrices in MPEG-4 AVC