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Volumn 41, Issue 2, 1994, Pages 133-139

Generalized Fermat-Mersenne Number Theoretic Transform

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; DIFFERENTIAL EQUATIONS; DIGITAL ARITHMETIC; INVERSE PROBLEMS; NUMBER THEORY; SIGNAL PROCESSING; THEOREM PROVING;

EID: 0028375151     PISSN: 10577130     EISSN: None     Source Type: Journal    
DOI: 10.1109/82.281844     Document Type: Article
Times cited : (13)

References (33)
  • 1
    • 84968484267 scopus 로고
    • The fast Fourier transform over finite fields
    • J. M. Pollard, “The fast Fourier transform over finite fields,” Math. Comput., vol. 25, pp. 365–374, 1971.
    • (1971) Math. Comput , vol.25 , pp. 365-374
    • Pollard, J.M.1
  • 2
    • 0015482478 scopus 로고
    • Discrete convolutions via Mersenne transform
    • C. M. Rader, “Discrete convolutions via Mersenne transform,” IEEE Trans. Computers, vol. C-21, 1269–1273, 1972.
    • (1972) IEEE Trans. Computers , vol.C-21 , pp. 1269-1273
    • Rader, C.M.1
  • 3
    • 0015965118 scopus 로고
    • Fast convolution using Fermat number transform with application to digital filtering
    • R. C. Agarwal and C. S. Burrus, “Fast convolution using Fermat number transform with application to digital filtering,” IEEE Trans. Acoust. Speech, Signal Proc., vol. 22, 87–97. 1974.
    • (1974) IEEE Trans. Acoust. Speech, Signal Proc. , vol.22 , pp. 87-97
    • Agarwal, R.C.1    Burrus, C.S.2
  • 4
    • 0025494229 scopus 로고
    • FIR filtering by the modified Fermat number transform
    • W. Li and A. M. Peterson, “FIR filtering by the modified Fermat number transform,” IEEE Trans. Acoust. Speech, Signal Proc., vol. 38, pp. 1641–1645, 1990.
    • (1990) IEEE Trans. Acoust. Speech, Signal Proc. , vol.38 , pp. 1641-1645
    • Li, W.1    Peterson, A.M.2
  • 5
    • 0022103089 scopus 로고
    • Realization of adaptive digital filtering using the Fermat number transform
    • Y. C. Lee, B. K. Min, and M. Suk, “Realization of adaptive digital filtering using the Fermat number transform,” IEEE Trans. Acoust. Speech, Signal Proc., vol. ASSP-33, pp. 1036–1039, 1985.
    • (1985) IEEE Trans. Acoust. Speech, Signal Proc. , vol.ASSP-33 , pp. 1036-1039
    • Lee, Y.C.1    Min, B.K.2    Suk, M.3
  • 6
    • 0020834243 scopus 로고
    • Convolution of long integer sequences by means of number-theoretic transform over residue class polynomial ring
    • J. B. Martens and M. C. Vanwormhondt, “Convolution of long integer sequences by means of number-theoretic transform over residue class polynomial ring.” IEEE Trans. Acoust. Speech, Signal Proc. vol. 31, pp. 1125–1134, 1983.
    • (1983) IEEE Trans. Acoust. Speech, Signal Proc. , vol.31 , pp. 1125-1134
    • Martens, J.B.1    Vanwormhondt, M.C.2
  • 7
    • 0020834682 scopus 로고
    • Convolution using a conjugate symmetry property for number theoretic transform over rings of regular integers
    • J. B. Martens and M. C. Vanwormhondt, “Convolution using a conjugate symmetry property for number theoretic transform over rings of regular integers.” IEEE Trans. Acoust. Speech, Signal Proc., vol. ASSP-31, 1121–1125, 1983.
    • (1983) IEEE Trans. Acoust. Speech, Signal Proc. , vol.ASSP-31 , pp. 1121-1125
    • Martens, J.B.1    Vanwormhondt, M.C.2
  • 8
    • 0021473510 scopus 로고
    • Two-dimensoinal convolutions by means of number theoretic transform over residue class polynomial ring
    • J. B. Martens, “Two-dimensoinal convolutions by means of number theoretic transform over residue class polynomial ring.” IEEE Trans. Acoust. Speech, Signal Proc., vol. ASSP-32, 862–871, 1984.
    • (1984) IEEE Trans. Acoust. Speech, Signal Proc. , vol.ASSP-32 , pp. 862-871
    • Martens, J.B.1
  • 9
    • 0020798334 scopus 로고
    • Number-theoretic transforms for the calculations of convolutions
    • J. B. Martens, “Number-theoretic transforms for the calculations of convolutions.” IEEE Trans. Acoust. Speech, Signal Proc., vol. ASSP-31, pp. 969–978, 1983.
    • (1983) IEEE Trans. Acoust. Speech, Signal Proc. , vol.ASSP-31 , pp. 969-978
    • Martens, J.B.1
  • 10
    • 0025517248 scopus 로고
    • Number-theoretic fast algorithms for bilinear and other generalized transforms
    • A. E. Yagle, “Number-theoretic fast algorithms for bilinear and other generalized transforms,” IEEE Trans. Auto. Cont., vol. 35, pp. 1275–1276, 1990.
    • (1990) IEEE Trans. Auto. Cont , vol.35 , pp. 1275-1276
    • Yagle, A.E.1
  • 11
    • 0024129779 scopus 로고
    • Fast multidimensional discrete Hartley transform using Fermat number transform
    • Pt. E
    • S. Boussakta and A. G. J. Holt, “Fast multidimensional discrete Hartley transform using Fermat number transform,” IEEE Proc., Pt. E, vol. 135, pp. 253–257, 1988.
    • (1988) IEEE Proc. , vol.135 , pp. 253-257
    • Boussakta, S.1    Holt, A.G.J.2
  • 12
    • 2942584350 scopus 로고
    • The fast decoding of Reed-Solomon code using Fermat number theoretic transforms
    • I. S. Reed, T. K. Truong, and L. R. Welch, “The fast decoding of Reed-Solomon code using Fermat number theoretic transforms,” IEEE Trans. Info. Theory, vol. 24, pp. 497–499, 1978.
    • (1978) IEEE Trans. Info. Theory , vol.24 , pp. 497-499
    • Reed, I.S.1    Truong, T.K.2    Welch, L.R.3
  • 13
    • 0017554799 scopus 로고
    • The solution of elliptic partial differential equations using number theoretic transforms with application to narrow of limited computer hardware
    • Y. W. Eastwood and C. R. Jasshope, “The solution of elliptic partial differential equations using number theoretic transforms with application to narrow of limited computer hardware,” Comput. Physics Comm., vol. 13, pp. 233–239, 1977.
    • (1977) Comput. Physics Comm , vol.13 , pp. 233-239
    • Eastwood, Y.W.1    Jasshope, C.R.2
  • 14
    • 85024269132 scopus 로고
    • Implementation of number theoretic transforms
    • J. M. Pollard, “Implementation of number theoretic transforms.” Electronics Letters, vol. 12, pp. 378–379, 1976.
    • (1976) Electronics Letters , vol.12 , pp. 378-379
    • Pollard, J.M.1
  • 15
    • 84939038030 scopus 로고
    • Fast number theoretic transforms for digital filtering
    • K. Y. Liu, I. S. Reed, and T. K. Truong, “Fast number theoretic transforms for digital filtering,” Electronics Letters, vol. 12, pp. 644-646 1976.
    • (1976) Electronics Letters , vol.12 , pp. 644-646
    • Liu, K.Y.1    Reed, I.S.2    Truong, T.K.3
  • 16
  • 17
    • 77956841133 scopus 로고
    • Integer convolutions over the finite fields GF(3 + 2n+ 1)
    • S. W. Golomb, I. S. Reed, and T. K. Truong, “Integer convolutions over the finite fields GF(3 + 2n+ 1),” SIAM J. Applied Math., vol. 32, pp. 356–365, 1977.
    • (1977) SIAM J. Applied Math. , vol.32 , pp. 356-365
    • Golomb, S.W.1    Reed, I.S.2    Truong, T.K.3
  • 18
    • 0039761035 scopus 로고
    • A report on primes of the form k-2n+1 and on factors of Fermat numbers
    • R. M. Robinson, “A report on primes of the form k-2n+1 and on factors of Fermat numbers.” Proc. Amer. Math. Soc., vol. 9, pp. 673–681, 1958.
    • (1958) Proc. Amer. Math. Soc. , vol.9 , pp. 673-681
    • Robinson, R.M.1
  • 19
    • 84966226429 scopus 로고
    • Properties of the sequences 3. 2n +1
    • S. W. Golomb, “Properties of the sequences 3. 2n +1,” Math. Comput., vol. 30, 657–663, 1976.
    • (1976) Math. Comput , vol.30 , pp. 657-663
    • Golomb, S.W.1
  • 20
    • 0017623946 scopus 로고
    • Digital filtering using pseudo-Fermat number transforms
    • N. J. Nussbaumer, “Digital filtering using pseudo-Fermat number transforms,” IEEE Trans. Acoust. Speech, Signal Proc., vol. ASSP-26, pp. 79–83, 1977.
    • (1977) IEEE Trans. Acoust. Speech, Signal Proc. , vol.ASSP-26 , pp. 79-83
    • Nussbaumer, N.J.1
  • 21
    • 0016999709 scopus 로고
    • Digital filtering using complex Mersenne transforms
    • N. J. Nussbaumer, “Digital filtering using complex Mersenne transforms,” IBM J. Research Devel., vol. 20, pp. 498–504, 1976.
    • (1976) IBM J. Research Devel , vol.20 , pp. 498-504
    • Nussbaumer, N.J.1
  • 22
    • 0026172116 scopus 로고
    • A new approach to solve the sequence-length constraint problem in circular convolutions using number-theoretic transform
    • H. Lu and S. Lee, “A new approach to solve the sequence-length constraint problem in circular convolutions using number-theoretic transform,” IEEE Transactions on Signal Proc., vol. 39, pp. 1314–1321, 1991.
    • (1991) IEEE Transactions on Signal Proc. , vol.39 , pp. 1314-1321
    • Lu, H.1    Lee, S.2
  • 23
    • 84938023228 scopus 로고
    • Washington, D.C.: Carnegie Institute
    • L. E. Dixon, History of the theory of numbers, vol. I, Washington, D.C.: Carnegie Institute, 1919, p. 376.
    • (1919) History of the theory of numbers , vol.1 , pp. 376
    • Dixon, L.E.1
  • 24
    • 84941607205 scopus 로고
    • Binary paradigm and systolic array implementation for residue arithmetic
    • Department of Computer Science and Engineering, Southern Methodist University Dallas, Texas
    • D. Y. Y. Yun and C. N. Zhang, “Binary paradigm and systolic array implementation for residue arithmetic,” Technical Report 84-CSE-21, Department of Computer Science and Engineering, Southern Methodist University, Dallas, Texas, 1984.
    • (1984) Technical Report 84-CSE-21
    • Yun, D.Y.Y.1    Zhang, C.N.2
  • 25
    • 0001464763 scopus 로고
    • Multiplication of multidigit numbers on automata
    • A. Karatsuba and Yu. Ofman, “Multiplication of multidigit numbers on automata,” Soviet Physics Dokl., vol. 7, pp. 595–596, 1963.
    • (1963) Soviet Physics Dokl , vol.7 , pp. 595-596
    • Karatsuba, A.1    Ofman, Y.2
  • 26
    • 34250459760 scopus 로고
    • Fast multiplication of integers
    • in German
    • A. Schonhage and V. Strassen, “Fast multiplication of integers.” (in German), Computing, vol. 7, pp. 281–292, 1971.
    • (1971) Computing , vol.7 , pp. 281-292
    • Schonhage, A.1    Strassen, V.2
  • 27
    • 0017010342 scopus 로고
    • A simplified binary arithmetic for the Fermat number transform
    • L. M. Leibowitz, “A simplified binary arithmetic for the Fermat number transform,” IEEE Trans. Acoust. Speech, Signal Proc., vol. ASSP-24, pp. 356–359, 1976.
    • (1976) IEEE Trans. Acoust. Speech, Signal Proc. , vol.ASSP-24 , pp. 356-359
    • Leibowitz, L.M.1
  • 29
    • 84966217500 scopus 로고
    • On computing the discrete Fourier transform
    • S. Winograd, “On computing the discrete Fourier transform,” Math. Comput., vol. 32, pp. 175–195, 1978.
    • (1978) Math. Comput , vol.32 , pp. 175-195
    • Winograd, S.1
  • 30
    • 77956849235 scopus 로고
    • Number theoretic transforms in rings of cyclotomic integers
    • R. Creutzburg and G. Steidl, “Number theoretic transforms in rings of cyclotomic integers,” J. Info. Proc. Cybernetics, vol. 11–12, pp. 573–584, 1988.
    • (1988) J. Info. Proc. Cybernetics , vol.11-12 , pp. 573-584
    • Creutzburg, R.1    Steidl, G.2
  • 31
    • 0021470438 scopus 로고
    • Recursive cyclotomic factorization—a new algorithm for calculating the discrete Fourier transform
    • J. B. Martens, “Recursive cyclotomic factorization—a new algorithm for calculating the discrete Fourier transform,” IEEE Trans. Acoust. Speech, Signal Proc., vol. ASSP-32, pp. 750–760, 1984.
    • (1984) IEEE Trans. Acoust. Speech, Signal Proc. , vol.ASSP-32 , pp. 750-760
    • Martens, J.B.1
  • 32
    • 0014520310 scopus 로고
    • An algorithm for computing the mixed radix fast Fourier transform
    • W. Singleton, “An algorithm for computing the mixed radix fast Fourier transform,” IEEE Trans. AU, vol. 17, 1969.
    • (1969) IEEE Trans. AU , vol.17
    • Singleton, W.1
  • 33
    • 84941607206 scopus 로고
    • Generalized Fermat and Mersenne numbers
    • S. Ligh and P. Jones, “Generalized Fermat and Mersenne numbers,” Fibonacci Quarterly, vol. 20, pp. 12–16, 1982.
    • (1982) Fibonacci Quarterly , vol.20 , pp. 12-16
    • Ligh, S.1    Jones, P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.