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Volumn 88, Issue 6, 2008, Pages 1553-1564

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

Author keywords

Arithmetic complexity; Discrete cosine transform; Fast Fourier transform

Indexed keywords

ALGORITHMS; FAST FOURIER TRANSFORMS;

EID: 39749108683     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2008.01.004     Document Type: Article
Times cited : (51)

References (53)
  • 1
    • 33947416576 scopus 로고    scopus 로고
    • A modified split-radix FFT with fewer arithmetic operations
    • Johnson S.G., and Frigo M. A modified split-radix FFT with fewer arithmetic operations. IEEE Trans. Signal Process. 55 1 (2007) 111-119
    • (2007) IEEE Trans. Signal Process. , vol.55 , Issue.1 , pp. 111-119
    • Johnson, S.G.1    Frigo, M.2
  • 2
    • 0024959506 scopus 로고
    • Conjugate pair fast Fourier transform
    • Kamar I., and Elcherif Y. Conjugate pair fast Fourier transform. Electron. Lett. 25 5 (1989) 324-325
    • (1989) Electron. Lett. , vol.25 , Issue.5 , pp. 324-325
    • Kamar, I.1    Elcherif, Y.2
  • 3
    • 33947409376 scopus 로고
    • Comment: conjugate pair fast Fourier transform
    • Gopinath R.A. Comment: conjugate pair fast Fourier transform. Electron. Lett. 25 16 (1989) 1084
    • (1989) Electron. Lett. , vol.25 , Issue.16 , pp. 1084
    • Gopinath, R.A.1
  • 4
    • 33947433841 scopus 로고
    • Comment: conjugate pair fast Fourier transform
    • Qian H.-S., and Zhao Z.-J. Comment: conjugate pair fast Fourier transform. Electron. Lett. 26 8 (1990) 541-542
    • (1990) Electron. Lett. , vol.26 , Issue.8 , pp. 541-542
    • Qian, H.-S.1    Zhao, Z.-J.2
  • 5
    • 0000492985 scopus 로고
    • Comment: conjugate pair fast Fourier transform
    • Krot A.M., and Minervina H.B. Comment: conjugate pair fast Fourier transform. Electron. Lett. 28 12 (1992) 1143-1144
    • (1992) Electron. Lett. , vol.28 , Issue.12 , pp. 1143-1144
    • Krot, A.M.1    Minervina, H.B.2
  • 6
    • 0021481259 scopus 로고
    • Simple FFT and DCT algorithms with reduced number of operations
    • Vetterli M., and Nussbaumer H.J. Simple FFT and DCT algorithms with reduced number of operations. Signal Processing 6 4 (1984) 267-278
    • (1984) Signal Processing , vol.6 , Issue.4 , pp. 267-278
    • Vetterli, M.1    Nussbaumer, H.J.2
  • 7
    • 0022700957 scopus 로고
    • Implementation of "split-radix" FFT algorithms for complex, real, and real-symmetric data
    • Duhamel P. Implementation of "split-radix" FFT algorithms for complex, real, and real-symmetric data. IEEE Trans. Acoust. Speech Signal Process. 34 2 (1986) 285-295
    • (1986) IEEE Trans. Acoust. Speech Signal Process. , vol.34 , Issue.2 , pp. 285-295
    • Duhamel, P.1
  • 8
    • 0025418849 scopus 로고
    • Fast Fourier transforms: a tutorial review and a state of the art
    • Duhamel P., and Vetterli M. Fast Fourier transforms: a tutorial review and a state of the art. Signal Processing 19 (April 1990) 259-299
    • (1990) Signal Processing , vol.19 , pp. 259-299
    • Duhamel, P.1    Vetterli, M.2
  • 9
    • 39749086576 scopus 로고    scopus 로고
    • R. Vuduc, J. Demmel, Code generators for automatic tuning of numerical kernels: experiences with FFTW, in: Proceedings of the Semantics, Application, and Implementation of Code Generators Workshop, Montreal, September 2000.
    • R. Vuduc, J. Demmel, Code generators for automatic tuning of numerical kernels: experiences with FFTW, in: Proceedings of the Semantics, Application, and Implementation of Code Generators Workshop, Montreal, September 2000.
  • 10
    • 20744449792 scopus 로고    scopus 로고
    • The design and implementation of FFTW3
    • Frigo M., and Johnson S.G. The design and implementation of FFTW3. Proc. IEEE 93 2 (2005) 216-231
    • (2005) Proc. IEEE , vol.93 , Issue.2 , pp. 216-231
    • Frigo, M.1    Johnson, S.G.2
  • 11
    • 0020194418 scopus 로고
    • A fast algorithm for the discrete sine transform implemented by the fast cosine transform
    • Wang Z. A fast algorithm for the discrete sine transform implemented by the fast cosine transform. IEEE Trans. Acoust. Speech Signal Process. 30 5 (1982) 814-815
    • (1982) IEEE Trans. Acoust. Speech Signal Process. , vol.30 , Issue.5 , pp. 814-815
    • Wang, Z.1
  • 12
    • 0025530239 scopus 로고
    • Direct methods for computing discrete sinusoidal transforms
    • Chan S.C., and Ho K.L. Direct methods for computing discrete sinusoidal transforms. IEE Proc. F 137 6 (1990) 433-442
    • (1990) IEE Proc. F , vol.137 , Issue.6 , pp. 433-442
    • Chan, S.C.1    Ho, K.L.2
  • 13
    • 0028468177 scopus 로고
    • Restructured recursive DCT and DST algorithms
    • Lee P., and Huang F.-Y. Restructured recursive DCT and DST algorithms. IEEE Trans. Signal Process. 42 7 (1994) 1600-1609
    • (1994) IEEE Trans. Signal Process. , vol.42 , Issue.7 , pp. 1600-1609
    • Lee, P.1    Huang, F.-Y.2
  • 14
    • 0014363340 scopus 로고
    • An economical method for calculating the discrete Fourier transform
    • Yavne R. An economical method for calculating the discrete Fourier transform. Proceedings of the AFIPS Fall Joint Computer Conference vol. 33 (1968) 115-125
    • (1968) Proceedings of the AFIPS Fall Joint Computer Conference , vol.33 , pp. 115-125
    • Yavne, R.1
  • 15
    • 0021755317 scopus 로고
    • Split-radix FFT algorithm
    • Duhamel P., and Hollmann H. Split-radix FFT algorithm. Electron. Lett. 20 1 (1984) 14-16
    • (1984) Electron. Lett. , vol.20 , Issue.1 , pp. 14-16
    • Duhamel, P.1    Hollmann, H.2
  • 16
    • 0021470438 scopus 로고
    • Recursive cyclotomic factorization-a new algorithm for calculating the discrete Fourier transform
    • Martens J.B. Recursive cyclotomic factorization-a new algorithm for calculating the discrete Fourier transform. IEEE Trans. Acoust. Speech Signal Process. 32 4 (1984) 750-761
    • (1984) IEEE Trans. Acoust. Speech Signal Process. , vol.32 , Issue.4 , pp. 750-761
    • Martens, J.B.1
  • 18
    • 0021619710 scopus 로고
    • A new algorithm to compute the discrete cosine transform
    • Lee B.G. A new algorithm to compute the discrete cosine transform. IEEE Trans. Acoust. Speech Signal Process. 32 6 (1984) 1243-1245
    • (1984) IEEE Trans. Acoust. Speech Signal Process. , vol.32 , Issue.6 , pp. 1243-1245
    • Lee, B.G.1
  • 19
    • 0022137352 scopus 로고
    • On computing the discrete Fourier and cosine transforms
    • Wang Z. On computing the discrete Fourier and cosine transforms. IEEE Trans. Acoust. Speech Signal Process. 33 4 (1985) 1341-1344
    • (1985) IEEE Trans. Acoust. Speech Signal Process. , vol.33 , Issue.4 , pp. 1341-1344
    • Wang, Z.1
  • 20
    • 0000079625 scopus 로고
    • Fast algorithms for the DFT and other sinusoidal transforms
    • Suehiro N., and Hatori M. Fast algorithms for the DFT and other sinusoidal transforms. IEEE Trans. Acoust. Speech Signal Process. 34 3 (1986) 642-644
    • (1986) IEEE Trans. Acoust. Speech Signal Process. , vol.34 , Issue.3 , pp. 642-644
    • Suehiro, N.1    Hatori, M.2
  • 21
    • 84943728327 scopus 로고
    • A fast algorithm for computing the discrete cosine transform
    • Hou H.S. A fast algorithm for computing the discrete cosine transform. IEEE Trans. Acoust. Speech Signal Process. 35 10 (1987) 1455-1461
    • (1987) IEEE Trans. Acoust. Speech Signal Process. , vol.35 , Issue.10 , pp. 1455-1461
    • Hou, H.S.1
  • 22
    • 0025493183 scopus 로고
    • Fast cosine transform based on the successive doubling method
    • Arguello F., and Zapata E.L. Fast cosine transform based on the successive doubling method. Electronic Lett. 26 19 (1990) 1616-1618
    • (1990) Electronic Lett. , vol.26 , Issue.19 , pp. 1616-1618
    • Arguello, F.1    Zapata, E.L.2
  • 23
    • 0031098885 scopus 로고    scopus 로고
    • Fast algorithm for computing discrete cosine transform
    • Kok C.W. Fast algorithm for computing discrete cosine transform. IEEE Trans. Signal Process. 45 3 (1997) 757-760
    • (1997) IEEE Trans. Signal Process. , vol.45 , Issue.3 , pp. 757-760
    • Kok, C.W.1
  • 25
    • 0141473171 scopus 로고    scopus 로고
    • The algebraic approach to the discrete cosine and sine transforms and their fast algorithms
    • Püschel M., and Moura J.M.F. The algebraic approach to the discrete cosine and sine transforms and their fast algorithms. SIAM J.Comput. 32 5 (2003) 1280-1316
    • (2003) SIAM J.Comput. , vol.32 , Issue.5 , pp. 1280-1316
    • Püschel, M.1    Moura, J.M.F.2
  • 26
    • 85143189941 scopus 로고    scopus 로고
    • M. Püschel, Cooley-Tukey FFT like algorithms for the DCT, in: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 2, Hong Kong, April 2003, pp. 501-504.
    • M. Püschel, Cooley-Tukey FFT like algorithms for the DCT, in: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 2, Hong Kong, April 2003, pp. 501-504.
  • 28
    • 0016974761 scopus 로고
    • A storage efficient way to implement the discrete cosine transform
    • Haralick R.M. A storage efficient way to implement the discrete cosine transform. IEEE Trans. Comput. 25 (1976) 764-765
    • (1976) IEEE Trans. Comput. , vol.25 , pp. 764-765
    • Haralick, R.M.1
  • 29
    • 0017538003 scopus 로고
    • A fast computational algorithm for the discrete cosine transform
    • Chen W.-H., Smith C.H., and Fralick S.C. A fast computational algorithm for the discrete cosine transform. IEEE Trans. Comm. 25 9 (1977) 1004-1009
    • (1977) IEEE Trans. Comm. , vol.25 , Issue.9 , pp. 1004-1009
    • Chen, W.-H.1    Smith, C.H.2    Fralick, S.C.3
  • 30
    • 0017981049 scopus 로고
    • On the computation of the discrete cosine transform
    • Narasimha M.J., and Peterson A.M. On the computation of the discrete cosine transform. IEEE Trans. Comm. 26 6 (1978) 934-936
    • (1978) IEEE Trans. Comm. , vol.26 , Issue.6 , pp. 934-936
    • Narasimha, M.J.1    Peterson, A.M.2
  • 31
    • 0018019573 scopus 로고
    • On computing the discrete cosine transform
    • Tseng B.D., and Miller W.C. On computing the discrete cosine transform. IEEE Trans. Comput. 27 10 (1978) 966-968
    • (1978) IEEE Trans. Comput. , vol.27 , Issue.10 , pp. 966-968
    • Tseng, B.D.1    Miller, W.C.2
  • 33
    • 0018983824 scopus 로고
    • A fast cosine transform in one and two dimensions
    • Makhoul J. A fast cosine transform in one and two dimensions. IEEE Trans. Acoust. Speech Signal Process. 28 1 (1980) 27-34
    • (1980) IEEE Trans. Acoust. Speech Signal Process. , vol.28 , Issue.1 , pp. 27-34
    • Makhoul, J.1
  • 34
    • 0003169474 scopus 로고
    • Fast computation of the discrete cosine transform and the discrete Hartley transform
    • Malvar H.S. Fast computation of the discrete cosine transform and the discrete Hartley transform. IEEE Trans. Acoust. Speech Signal Process. 35 10 (1987) 1484-1485
    • (1987) IEEE Trans. Acoust. Speech Signal Process. , vol.35 , Issue.10 , pp. 1484-1485
    • Malvar, H.S.1
  • 35
    • 0026173787 scopus 로고
    • A new algorithm to compute the DCT and its inverse
    • Li W. A new algorithm to compute the DCT and its inverse. IEEE Trans. Signal Process. 39 6 (1991) 1305-1313
    • (1991) IEEE Trans. Signal Process. , vol.39 , Issue.6 , pp. 1305-1313
    • Li, W.1
  • 36
    • 84966222128 scopus 로고
    • A polynomial approach to fast algorithms for discrete Fourier-cosine and Fourier-sine transforms
    • Steidl G., and Tasche M. A polynomial approach to fast algorithms for discrete Fourier-cosine and Fourier-sine transforms. Math. Comput. 56 193 (1991) 281-296
    • (1991) Math. Comput. , vol.56 , Issue.193 , pp. 281-296
    • Steidl, G.1    Tasche, M.2
  • 37
    • 0001616254 scopus 로고
    • On the multiplicative complexity of discrete cosine transforms
    • Feig E., and Winograd S. On the multiplicative complexity of discrete cosine transforms. IEEE Trans. Inform. Theory 38 4 (1992) 1387-1391
    • (1992) IEEE Trans. Inform. Theory , vol.38 , Issue.4 , pp. 1387-1391
    • Feig, E.1    Winograd, S.2
  • 38
    • 0033116740 scopus 로고    scopus 로고
    • Architecture-oriented regular algorithms for discrete sine and cosine transforms
    • Astola J., and Akopian D. Architecture-oriented regular algorithms for discrete sine and cosine transforms. IEEE Trans. Signal Process. 47 4 (1999) 1109-1124
    • (1999) IEEE Trans. Signal Process. , vol.47 , Issue.4 , pp. 1109-1124
    • Astola, J.1    Akopian, D.2
  • 39
    • 0035452271 scopus 로고    scopus 로고
    • Two new algorithms based on product system for discrete cosine transform
    • Guo Z., Shi B., and Wang N. Two new algorithms based on product system for discrete cosine transform. Signal Processing 81 (2001) 1899-1908
    • (2001) Signal Processing , vol.81 , pp. 1899-1908
    • Guo, Z.1    Shi, B.2    Wang, N.3
  • 40
    • 7544224483 scopus 로고    scopus 로고
    • Fast and numerically stable algorithms for discrete cosine transforms
    • Plonka G., and Tasche M. Fast and numerically stable algorithms for discrete cosine transforms. Linear Algebra Appl. 394 (2005) 309-345
    • (2005) Linear Algebra Appl. , vol.394 , pp. 309-345
    • Plonka, G.1    Tasche, M.2
  • 42
    • 0000276706 scopus 로고
    • A fast DCT-SQ scheme for images
    • Arai Y., Agui T., and Nakajima M. A fast DCT-SQ scheme for images. Trans. IEICE 71 11 (1988) 1095-1097
    • (1988) Trans. IEICE , vol.71 , Issue.11 , pp. 1095-1097
    • Arai, Y.1    Agui, T.2    Nakajima, M.3
  • 44
    • 0002004984 scopus 로고
    • Vectorizing the FFTs
    • Rodrigue G. (Ed)
    • Swarztrauber P.N. Vectorizing the FFTs. In: Rodrigue G. (Ed). Parallel Computations (1982) 51-83
    • (1982) Parallel Computations , pp. 51-83
    • Swarztrauber, P.N.1
  • 49
    • 85060734922 scopus 로고
    • Fast Fourier transforms-for fun and profit
    • Gentleman W.M., and Sande G. Fast Fourier transforms-for fun and profit. Proc. AFIPS 29 (1966) 563-578
    • (1966) Proc. AFIPS , vol.29 , pp. 563-578
    • Gentleman, W.M.1    Sande, G.2
  • 50
    • 0012032535 scopus 로고    scopus 로고
    • Accuracy of the discrete Fourier transform and the fast Fourier transform
    • Schatzman J.C. Accuracy of the discrete Fourier transform and the fast Fourier transform. SIAM J. Sci. Comput. 17 5 (1996) 1150-1166
    • (1996) SIAM J. Sci. Comput. , vol.17 , Issue.5 , pp. 1150-1166
    • Schatzman, J.C.1
  • 52
    • 0016495267 scopus 로고
    • Analysis of linear digital networks
    • Crochiere R.E., and Oppenheim A.V. Analysis of linear digital networks. Proc. IEEE 63 4 (1975) 581-595
    • (1975) Proc. IEEE , vol.63 , Issue.4 , pp. 581-595
    • Crochiere, R.E.1    Oppenheim, A.V.2
  • 53
    • 39749202318 scopus 로고    scopus 로고
    • X. Shao, S.G. Johnson, Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations, Signal Processing (2008), in press. doi: 10.1016/j.sigpro.2007.11.024.
    • X. Shao, S.G. Johnson, Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations, Signal Processing (2008), in press. doi: 10.1016/j.sigpro.2007.11.024.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.