Page 115 - DSP Integrated Circuits

100 Chapter 3 Digital Signal Processing

Note that the denominator of the cosine term is an even number. This trans-
form is also called DCT-II. The IEDCT (Inverse EDCT) is

where

A careful analysis shows that the forward and inverse transforms differ.
Hence two different algorithms must be implemented. Further, we are, for imple-
mentation reasons that will be evident in Chapter 11, particularly interested in
the symmetry properties of the basis functions of the DCTs. Generally, the DC com-
ponent of an image is very large compared with the other frequency components
and must therefore not appear as an error in the higher-frequency components [30,
37, 38].

EXAMPLE 3.7
Determine if the basis functions of the EDCT are symmetric or antisymmetric and
if the DC component leaks into the higher-order frequency components. For the
sake of simplicity, use a DCT with N = 4.
For the EDCT we get

We get after simplification