Some 1-D DCT Properties

1) Linearity:

2) Energy conservations:

	(4.3.8)

3) Symmetry:

(a) General case:

(b) Real-valued case:

4)  Eigenvectors of unitary DCT: Define the column vector

and define the matrix C with elements:

Then the vector contains the unitary DCT, whose elements are given as

A unitary matrix is one whose inverse is the same as the transpose . For the unitary DCT, we have

and energy balance equation,

which is a slight modification on the DCT Parseval relation (4.3.8). So the unitary DCT preserves the energy of the signal x.

(continued in the next slide)