Signal Flow Graph Approach to Efficient DST I-IV Algorithms

TL;DR

This paper introduces new recursive and efficient algorithms for discrete sine transforms (DST I-IV) based on matrix factorizations, utilizing signal flow graphs to clearly illustrate their digital structures and reduce computational cost.

Contribution

It presents novel recursive DST algorithms based solely on DST I-IV, with low arithmetic complexity and clear signal flow graph representations, improving efficiency over existing methods.

Findings

Algorithms are fully recursive and based on DST I-IV.

Significant reduction in arithmetic cost compared to known algorithms.

Signal flow graphs effectively illustrate the digital structures.

Abstract

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.