The LGTs can then be derived by the eigen-decomposition of the GGL Lc. Lc=UΦUT??(2)
where columns of orthogonal matrix U are the basis vectors of the LGT, and Φ is the diagonal eigenvalue matrix. In fact, DCTs and DSTs, including DCT-2, DCT-8 and DST7, are LGTs derived from certain forms of GGLs. DCT-2 is derived by setting Vc1=0; DST-7 is derived by setting Vc=Wc; DCT-8 is derived by setting Vc2=Wc; DST-4 is derived by setting Vc1=2wc; and DCT-4 is derived by setting Vc2=2wc.