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3.19 Discrete Cosine Transforms 101
Obviously, the basis functions (rows) are either symmetric or antisymmetric.
The DCT can be viewed as a set of FIR filters where the coefficients in each row
represent the impulse responses. All of the filters except the first one should either
be a highpass or a bandpass filter, i.e., they should have a zero at z = I in order to
suppress the DC component. In this case we do have a zero at z = 1, since the sum
of the coefficients for all rows is zero, except for the first row. We therefore conclude
that the EDCT is suitable for image coding applications.
3.19.2 ODCT (Odd Discrete Cosine Transform)
The ODCT (odd discrete cosine transform) is defined as
The denominator of the cosine term is an odd number. The IODCT (inverse
ODCT) is
where
The forward and inverse transforms are identical, but it can be shown that
the basis functions are neither symmetric nor antisymmetric. Further, the DC
component appears in the other components. Hence, the ODCT is unsuitable for
image coding applications.
3.19.3 SDCT (Symmetric Discrete Cosine Transform)
The SDCT (symmetric discrete cosine transform) is denned as
The ISDCT (Inverse SDCT) is
