Fast and Stable Algorithms for Discrete Sine Transformations having Orthogonal Factors

Sirani K M. Perera

doi:10.1007/978-3-319-12307-3_50

Fast and Stable Algorithms for Discrete Sine Transformations having Orthogonal Factors

Sirani K M. Perera

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

   In this chapter we derive fast, recursive, and numerically stable radix-2 algorithms for discrete sine transformations (DST) having sparse and orthogonal factors. These real radix-2 stable algorithms are completely recursive, fast, and based on the simple orthogonal factors. Comparing to the known bulky and mostly unstable DST algorithms, our algorithms are easy to implement and use only permutations, scaling by constants,butterfly operations, and plane rotations/rotation-reflections. 
 
   For a given vector     x    , we also analyze error bounds of computing for the     y    =     S       x    for the     presented DST algorithms:       S      . Finally a classification of these real radix-2 DST algorithms       enables us to establish the excellent forward and backward stability based on the sparse and orthogonal factors.      

Original language	American English
Title of host publication	Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science
DOIs	https://doi.org/10.1007/978-3-319-12307-3_50
State	Published - 2015

Keywords

Discrete Fourier Transform
Error Bound
Recursive Algorithm

Disciplines

Electrical and Computer Engineering
Applied Mathematics
Numerical Analysis and Scientific Computing
Theory and Algorithms

Access to Document

10.1007/978-3-319-12307-3_50License: Unspecified

StableDST_Paper_Abstract_Springer.pdfFinal published version, 132 KBLicense: Unspecified

Cite this

@inbook{348481bee54b42b88ca74cd675d166af,

title = "Fast and Stable Algorithms for Discrete Sine Transformations having Orthogonal Factors",

abstract = " In this chapter we derive fast, recursive, and numerically stable radix-2 algorithms for discrete sine transformations (DST) having sparse and orthogonal factors. These real radix-2 stable algorithms are completely recursive, fast, and based on the simple orthogonal factors. Comparing to the known bulky and mostly unstable DST algorithms, our algorithms are easy to implement and use only permutations, scaling by constants,butterfly operations, and plane rotations/rotation-reflections. For a given vector x , we also analyze error bounds of computing for the y = S x for the presented DST algorithms: S . Finally a classification of these real radix-2 DST algorithms enables us to establish the excellent forward and backward stability based on the sparse and orthogonal factors. ",

keywords = "Discrete Fourier Transform, Error Bound, Recursive Algorithm",

author = "{M. Perera}, {Sirani K}",

note = "Sirani M. Perera and Vadim Olshevsky, Fast and Stable Algorithms for Discrete Sine Transformations having Orthogonal Factors, In: M. Cojocaru, I. S. Kotsireas, R. Makarov, R. Melnik, and H. Shodiev (Eds.): Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science, vol. 117: 347-354, Springer, (2015)-DOI 10.1007/978-3-319-12307-3_50",

year = "2015",

doi = "10.1007/978-3-319-12307-3_50",

language = "American English",

booktitle = "Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science",

}

TY - CHAP

T1 - Fast and Stable Algorithms for Discrete Sine Transformations having Orthogonal Factors

AU - M. Perera, Sirani K

N1 - Sirani M. Perera and Vadim Olshevsky, Fast and Stable Algorithms for Discrete Sine Transformations having Orthogonal Factors, In: M. Cojocaru, I. S. Kotsireas, R. Makarov, R. Melnik, and H. Shodiev (Eds.): Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science, vol. 117: 347-354, Springer, (2015)-DOI 10.1007/978-3-319-12307-3_50

PY - 2015

Y1 - 2015

N2 - In this chapter we derive fast, recursive, and numerically stable radix-2 algorithms for discrete sine transformations (DST) having sparse and orthogonal factors. These real radix-2 stable algorithms are completely recursive, fast, and based on the simple orthogonal factors. Comparing to the known bulky and mostly unstable DST algorithms, our algorithms are easy to implement and use only permutations, scaling by constants,butterfly operations, and plane rotations/rotation-reflections. For a given vector x , we also analyze error bounds of computing for the y = S x for the presented DST algorithms: S . Finally a classification of these real radix-2 DST algorithms enables us to establish the excellent forward and backward stability based on the sparse and orthogonal factors.

AB - In this chapter we derive fast, recursive, and numerically stable radix-2 algorithms for discrete sine transformations (DST) having sparse and orthogonal factors. These real radix-2 stable algorithms are completely recursive, fast, and based on the simple orthogonal factors. Comparing to the known bulky and mostly unstable DST algorithms, our algorithms are easy to implement and use only permutations, scaling by constants,butterfly operations, and plane rotations/rotation-reflections. For a given vector x , we also analyze error bounds of computing for the y = S x for the presented DST algorithms: S . Finally a classification of these real radix-2 DST algorithms enables us to establish the excellent forward and backward stability based on the sparse and orthogonal factors.

KW - Discrete Fourier Transform

KW - Error Bound

KW - Recursive Algorithm

U2 - 10.1007/978-3-319-12307-3_50

DO - 10.1007/978-3-319-12307-3_50

M3 - Chapter

BT - Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science

ER -