B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

306 SAMPLING AND ANALOG-TO-DIGITAL CONVERSION
Figure 6.36
(a) Frame 1.
(b) Frame 2.
(c) Information
transferred
between
frames 1 and 2.
(a)
(b)
(c)
1. Motion estimation and compensation. Here a motion estimator identifies the areas or groups
of blocks from a preceding frame that match corresponding areas in the current frame and
sends the magnitude and direction of the displacement to a predictor in the decoder. The
frame difference information is called the residual.
2. Transforming the residual on a block-by-block basis into more compact form.
The encoded residual signal is transformed into a more compact form by means of a discrete
cosine transform (DCT) (see Sec. 6.5.2 in Haskel et al., 28 ), which uses a numerical value to
represent each pixel and normalizes that value for more efficient transmission. The DCT is of
the form
N-I N-1
F(j, k) = L Lf (n, m) cos
n=O m=O
(2n + l)jn (2m + l)kn
2 N cos
2 N ]
[ ] [
wheref (n, m) is the value assigned to the block in the (n, m) position. The inverse transform is
1 N- I N -l [ (2n + l)jn ] [ (2m +l)kn ]
f(n, m) = N 2 E F(j, k) cos 2 N cos
2 N
The DCT is typically multiplied, for an 8 x 8 block, by the expression C(j)C(k)/4, where
C(x) -{
f2 for X = 0
otherwise
Tables 6.2 and 6.3 depict the pixel block values before and after the DCT. One can
notice from Table 6.3 that there are relatively few meaningful elements, that is, elements
with significant values relative to the values centered about the 0, 0 position. Because of this,
most of the matrix values may be assumed to be zero, and, upon inverse transformation, the
original values are quite accurately reproduced. This process reduces the amount of data that
must be transmitted greatly, perhaps by a factor of 8 to 10 on the average. Note that the size
of the transmitted residual may be that of an individual block or, at the other extreme, that of
the entire picture.
The transformed matrix values of a block (Table 6.4) are normalized so that most of the
values in the block matrix are less than 1. Then the resulting normalized matrix is quantized to