Why use the discrete cosine transform

[DUET]

The N real numbers x₀, ..., x_N-1 are transformed into the N real numbers X₀, ..., X_N-1 according to one of the formula by DCT.

I would ask what is the benefit and why should we do that?

 

[mathman]

http://en.wikipedia.org/wiki/Discrete_cosine_transform

Try the above for an explanation.