  In this paper, fast and efficient discrete sine transformation (DST)
algorithms are presented based on the factorization of sparse, scaled
orthogonal, rotation, rotation-reflection, and butterfly matrices. These
algorithms are completely recursive and solely based on DST I-IV. The presented
algorithms have low arithmetic cost compared to the known fast DST algorithms.
Furthermore, the language of signal flow graph representation of digital
structures is used to describe these efficient and recursive DST algorithms
having $(n-1)$ points signal flow graph for DST-I and $n$ points signal flow
graphs for DST II-IV.
