  The discrete cosine transform (DCT), introduced by Ahmed, Natarajan and Rao,
has been used in many applications of digital signal processing, data
compression and information hiding. There are four types of the discrete cosine
transform. In simulating the discrete cosine transform, we propose a
generalized discrete cosine transform with three parameters, and prove its
orthogonality for some new cases. A new type of discrete cosine transform is
proposed and its orthogonality is proved. Finally, we propose a generalized
discrete W transform with three parameters, and prove its orthogonality for
some new cases.
