ABSTRACT
Similar to the Discrete Cosine Transform (DCT), the discrete sine transform (DST) is mathematically related to the discrete Fourier transform. Both, the DCTs and the DSTs are members of the class of sinusoidal unitary transforms Unitary transform over a set of cosine and sine basis functions. Like the DCT, the DST belongs to the class of sinusoidal unitary transforms with a kernel defined by a set of complete, orthogonal or orthonormal discrete cosine or sine basis functions. Similar to the DCT matrix and the Symmetric cosine transform matrix, the DST matrix and Symmetric sine transform mstrix matrices follow certain symmetries whose center depends on the order of the row vector. The symmetry of the basis vectors and antisymmetry Antisymmetric basis vectors of the basis vectors of the DST and also the DCT matrices are key features to factorize the matrices into sparse matrices sparse matrices.
