article

Type-II/III DCT/DST algorithms with reduced number of arithmetic operations

Authors:

Xuancheng Shao,

Steven G. JohnsonAuthors Info & Claims

Signal Processing, Volume 88, Issue 6

Pages 1553 - 1564

https://doi.org/10.1016/j.sigpro.2008.01.004

Published: 01 June 2008 Publication History

Abstract

We present algorithms for the discrete cosine transform (DCT) and discrete sine transform (DST), of types II and III, that achieve a lower count of real multiplications and additions than previously published algorithms, without sacrificing numerical accuracy. Asymptotically, the operation count is reduced from 2Nlog"2N+O(N) to 179Nlog"2N+O(N) for a power-of-two transform size N. Furthermore, we show that an additional N multiplications may be saved by a certain rescaling of the inputs or outputs, generalizing a well-known technique for N=8 by Arai et al. These results are derived by considering the DCT to be a special case of a DFT of length 4N, with certain symmetries, and then pruning redundant operations from a recent improved fast Fourier transform algorithm (based on a recursive rescaling of the conjugate-pair split-radix algorithm). The improved algorithms for the DCT-III, DST-II, and DST-III follow immediately from the improved count for the DCT-II.

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Cited By

Zhong SMueen A(2024)MASS: distance profile of a query over a time seriesData Mining and Knowledge Discovery10.1007/s10618-024-01005-238:3(1466-1492)Online publication date: 1-May-2024
https://dl.acm.org/doi/10.1007/s10618-024-01005-2
Scribano CFranchini GPrato MBertogna M(2023)DCT-Former: Efficient Self-Attention with Discrete Cosine TransformJournal of Scientific Computing10.1007/s10915-023-02125-594:3Online publication date: 7-Feb-2023
https://dl.acm.org/doi/10.1007/s10915-023-02125-5
Khatua PRay K(2022)An Efficient DCT-II Based Harmonic Wavelet Transform for Time-Frequency AnalysisJournal of Signal Processing Systems10.1007/s11265-022-01805-z94:12(1381-1394)Online publication date: 1-Dec-2022
https://dl.acm.org/doi/10.1007/s11265-022-01805-z
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Index Terms

Type-II/III DCT/DST algorithms with reduced number of arithmetic operations
1. Mathematics of computing
  1. Mathematical analysis
    1. Functional analysis
      1. Approximation
    2. Numerical analysis
      1. Computation of transforms
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis

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Published In

cover image Signal Processing

Signal Processing Volume 88, Issue 6

June, 2008

314 pages

ISSN:0165-1684

Issue’s Table of Contents

Copyright © Elsevier B.V. © 2008.

Publisher

Elsevier North-Holland, Inc.

United States

Publication History

Published: 01 June 2008

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Cited By

Zhong SMueen A(2024)MASS: distance profile of a query over a time seriesData Mining and Knowledge Discovery10.1007/s10618-024-01005-238:3(1466-1492)Online publication date: 1-May-2024
https://dl.acm.org/doi/10.1007/s10618-024-01005-2
Scribano CFranchini GPrato MBertogna M(2023)DCT-Former: Efficient Self-Attention with Discrete Cosine TransformJournal of Scientific Computing10.1007/s10915-023-02125-594:3Online publication date: 7-Feb-2023
https://dl.acm.org/doi/10.1007/s10915-023-02125-5
Khatua PRay K(2022)An Efficient DCT-II Based Harmonic Wavelet Transform for Time-Frequency AnalysisJournal of Signal Processing Systems10.1007/s11265-022-01805-z94:12(1381-1394)Online publication date: 1-Dec-2022
https://dl.acm.org/doi/10.1007/s11265-022-01805-z
Boccuto AGerace IGiorgetti V(2022)A Fast Discrete Transform for a Class of Simultaneously Diagonalizable MatricesComputational Science and Its Applications – ICCSA 202210.1007/978-3-031-10522-7_16(214-231)Online publication date: 4-Jul-2022
https://dl.acm.org/doi/10.1007/978-3-031-10522-7_16
Dahiya PJain P(2019)Realization of Second-Order Structure of Recursive Algorithm for Discrete Cosine TransformCircuits, Systems, and Signal Processing10.1007/s00034-018-0885-638:2(791-804)Online publication date: 1-Feb-2019
https://dl.acm.org/doi/10.1007/s00034-018-0885-6
Dutta TSatija URamkumar BManikandan M(2018)Blind Impulse Estimation and Removal Using Sparse Signal Decomposition Framework for OFDM SystemsCircuits, Systems, and Signal Processing10.1007/s00034-017-0573-y37:2(847-861)Online publication date: 1-Feb-2018
https://dl.acm.org/doi/10.1007/s00034-017-0573-y
Chiper DUngureanu P(2011)Novel VLSI algorithm and architecture with good quantization properties for a high-throughput area efficient systolic array implementation of DCTEURASIP Journal on Advances in Signal Processing10.1155/2011/6390432011(1-14)Online publication date: 1-Jan-2011
https://dl.acm.org/doi/10.1155/2011/639043
Long BReinhard EHaines EMcGuire MAliaga DOliveira M(2009)Real-time fluid simulation using discrete sine/cosine transformsProceedings of the 2009 symposium on Interactive 3D graphics and games10.1145/1507149.1507165(99-106)Online publication date: 27-Feb-2009
https://dl.acm.org/doi/10.1145/1507149.1507165

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