New generalized conversion method of the MDCT to MDST coefficients in the frequency domain for arbitrary symmetric windowing function

Britaňák, Vladimír

doi:10.1016/j.dsp.2013.03.004

Cited by 8 publications

(6 citation statements)

References 11 publications

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“…In this section, we utilize the relationship among DST matrices established in Section IV to identify a relationship among the proposed DST factorization and the existing factorization of DST matrices. The relationship between DST-II and DST-IV will be utilized to establish a connection between the proposed DST-II factorization with the existing DST-II factorization in [7], [9], [11], [12], [45]- [47]. We will also show the DST-III factorization in [7], [9]- [12], [46] can be seen as the proposed self-contained DST-III factorization.…”

Section: A Connection Between the Proposed Dst Factorization And The Existing Dst Factorizationsmentioning

confidence: 99%

“…The following result shows that the proposed factorization of the DST-II matrix can be converted into the existing DST-II factorization in [7], [9], [11], [12], [45]- [47].…”

Section: A Connection Between the Proposed Dst Factorization And The Existing Dst Factorizationsmentioning

confidence: 99%

“…Moreover, the proposed DST factorizations for the types I/II/III can be seen as a real variant of the self-contained factorization of the DFT matrices in [48], [49]. Also, the proposed DST-I/II/III factorizations are easy to implement and establish a bridge to the existing DST factorizations in [7], [9]- [12], [45]- [47]. We will see in Section V that the proposed algorithms are self-recursive as opposed to completely recursive algorithms in the literature.…”

Section: A Connection Between the Proposed Dst Factorization And The Existing Dst Factorizationsmentioning

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: A Connection Between the Proposed Dst Factorization And The Existing Dst Factorizationsmentioning

confidence: 99%

“…The following result shows that the proposed factorization of the DST-II matrix can be converted into the existing DST-II factorization in [7], [9], [11], [12], [45]- [47].…”

Section: A Connection Between the Proposed Dst Factorization And The Existing Dst Factorizationsmentioning

confidence: 99%

Section: A Connection Between the Proposed Dst Factorization And The Existing Dst Factorizationsmentioning

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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“…The DCT-II computation can be performed by means of the Chen algorithm [45]. Such algorithm is based on a decomposition that expresses C II 2N in terms of C II N and C IV N [9,16,18,20,[46][47][48]. The matrix form of the Chen algorithm is given by [2, p. 96] 1…”

Section: Relationships Between Dct-ii and Dct-ivmentioning

confidence: 99%

Low-complexity Scaling Methods for DCT-II Approximations

Coelho,

Cintra,

Madanayake

et al. 2021

Preprint

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This paper introduces a collection of scaling methods for generating 2N-point DCT-II approximations based on N-point low-complexity transformations. Such scaling is based on the Hou recursive matrix factorization of the exact 2N-point DCT-II matrix. Encompassing the widely employed Jridi-Alfalou-Meher scaling method, the proposed techniques are shown to produce DCT-II approximations that outperform the transforms resulting from the JAM scaling method according to total error energy and mean squared error. Orthogonality conditions are derived and an extensive error analysis based on statistical simulation demonstrates the good performance of the introduced scaling methods. A hardware implementation is also provided demonstrating the competitiveness of the proposed methods when compared to the JAM scaling method.

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“…Among applications of the DFT; sine and cosine waves of the DFT with different frequencies are used to classify the traffic monitoring sites into different seasonal patterns [35], DST has been identified as the method which generates better results for noise estimation as compared with Discrete Cosine Transform (DCT) and the DFT [10], discrete fractional sine transform has identified as the method for generating fingerprint templates with high recognition accuracy [49], DCT, DEST, and DFT can be approximated to the Karhunen Loeve Transformation (KLT) and the connection of KLT to the color image compression [6,22,31,32], DST can be used to analyze image reconstruction via signal transition through a square-optical fiber lenses [47], spectral interference and additive wideband noise on the accuracy of the normalized frequency estimator can be investigated through discrete-time sine-wave [1], to mention a few. Together with the above, the engagement of DCT and DST in image processing, signal processing, finger print enhancement, quick response code (QR code), and multimode interface can also be seen in e.g., [2,7,11,12,16,18,19,20,21,23,24,29,30,39,40,43,44,45].…”

Section: Introductionmentioning

confidence: 99%

Signal flow graph approach to efficient and forward stable DST algorithms

Perera

2018

Linear Algebra and its Applications

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New generalized conversion method of the MDCT to MDST coefficients in the frequency domain for arbitrary symmetric windowing function

Cited by 8 publications

References 11 publications

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

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

Low-complexity Scaling Methods for DCT-II Approximations

Signal flow graph approach to efficient and forward stable DST algorithms

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