Discrete Cosine Transformation formula disparity

Well, I was programming something 开发者_开发知识库that required the use of DCT. I found 2 resources for the DCT formula:

Mathworks

Wikipedia

Initially I used the wikipedia version of DCT-II. In the DCT-II section of wiki page, it is written that some authors further multiply the X0 term by 1/√2 and multiply the resulting matrix by an overall scale factor, which makes the DCT-II matrix orthogonal, but breaks the direct correspondence with a real-even DFT of half-shifted input. And the mathworks site does this only.

What is this property being talked about?

I beleive that they are trying to say that that are concerned about making the DCT-II transform matrix a unitary matrix. It is nice from a signal processing standpoint to have a unitary matrix because when we transform the signal back to its original domain, we are not adding any more power into the signal.

However, the 1-D DFT:

can be rewritten in terms of sines and consies (using Euler's Identity). If the input is a real-even signal, the even terms of the DFT will correspond to the terms of the DCT. Some people like to simplify their algorithms by simply taking the DFT of a signal, and only concentrating on the even terms.