Signal flow graph approach to efficient and forward stable DST algorithms

Perera, Sirani M.

doi:10.1016/j.laa.2017.05.050

Cited by 8 publications

(18 citation statements)

References 47 publications

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“…The proposed factorization of the DST-IV matrix is based on the self-enclosed DST-II factorization in Lemma III.4. Before we proceed, let us recall the DST-IV matrix factorization formula in [9], [12] s.t.…”

Section: Sparse Orthogonal Diagonal Bidiagonal and Recursive Factors To Compute Dst-iv Matrixmentioning

confidence: 99%

“…Moreover, [11] has used the same factorization for DST-II and IV as in [7]. The authors in [9], [12], however, produce radix-2, completely recursive, and stable DST I-IV algorithms. Furthermore, [12] established a connection between algebraic operations used in the sparse and scaled orthogonal factorization of DST I-IV matrices and signal flow graphs.…”

Section: Introductionmentioning

confidence: 99%

“…The authors in [9], [12], however, produce radix-2, completely recursive, and stable DST I-IV algorithms. Furthermore, [12] established a connection between algebraic operations used in the sparse and scaled orthogonal factorization of DST I-IV matrices and signal flow graphs. We refer to many more historical remarks on DST factorizations and the corresponding signal flow graphs in [12].…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, [12] established a connection between algebraic operations used in the sparse and scaled orthogonal factorization of DST I-IV matrices and signal flow graphs. We refer to many more historical remarks on DST factorizations and the corresponding signal flow graphs in [12]. We note here that the DCT algorithms in [8], [9], [13] and the relationship between cosine and sine transform matrices in [10] can be used to obtain the DST algorithms in [12].…”

Section: Introductionmentioning

confidence: 99%

“…We refer to many more historical remarks on DST factorizations and the corresponding signal flow graphs in [12]. We note here that the DCT algorithms in [8], [9], [13] and the relationship between cosine and sine transform matrices in [10] can be used to obtain the DST algorithms in [12]. On the other hand, one can use an elegant factorization for Chebyshev-like Vandermonde matrices to factor the DCT and DST matrices as described in [14].…”

Section: Introductionmentioning

confidence: 99%

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Sparse Matrix Based Low-Complexity, Recursive, and Radix-2 Algorithms for Discrete Sine Transforms

Perera

Lingsch

2021

IEEE Access

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This paper presents factorizations of each discrete sine transform (DST) matrices of types I, II, III, and IV into a product of sparse, diagonal, bidiagonal, and scaled orthogonal matrices. Based on the proposed matrix factorization formulas, reduced multiplication complexity, recursive, and radix-2 DST-I/II/III/IV algorithms are presented. We will present the lowest multiplication complexity DST-IV algorithm in the literature. The paper fills a gap in the self-recursive, exact, and radix-2 DST-I/II/III algorithms executed via diagonal, bidiagonal, scaled orthogonal, and simple matrix factors for any input n = 2 t (t ≥ 1). The paper establishes a novel relationship between DST-II and DST-IV matrices using diagonal and bidiagonal matrices. Similarly, a novel relationship between DST-I and DST-III matrices is proposed using sparse and diagonal matrices. These interweaving relationships among DST matrices enable us to bridge the existing factorizations of the DST matrices with the proposed factorization formulas. We present signal flow graphs to provide a layout for realizing the proposed algorithms in DST-based integrated circuit designs. Additionally, we describe an implementation of algorithms based on the proposed DST-II and DST-III factorizations within a double random phase encoding (DRPE) image encryption scheme.INDEX TERMS Discrete sine transforms, self/completely recursive and radix-2 algorithms, complexity and performance of algorithms, sparse and orthogonal matrices, signal flow graphs VOLUME ....

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Section: Sparse Orthogonal Diagonal Bidiagonal and Recursive Factors To Compute Dst-iv Matrixmentioning

confidence: 99%