Fast Fourier transforms: a tutorial review and a state of the art
暂无分享,去创建一个
[1] Ken'iti Kido,et al. A new FFT algorithm of radix 3, 6, and 12 , 1986, IEEE Trans. Acoust. Speech Signal Process..
[2] J. Martens. Recursive cyclotomic factorization--A new algorithm for calculating the discrete Fourier transform , 1984 .
[3] H. Nussbaumer,et al. Fast computation of discrete Fourier transforms using polynomial transforms , 1979 .
[4] R. Mersereau,et al. A unified treatment of Cooley-Tukey algorithms for the evaluation of the multidimensional DFT , 1981 .
[5] Martin Vetterli. Running FIR and IIR filtering using multirate filter banks , 1988, IEEE Trans. Acoust. Speech Signal Process..
[6] R. Yavne,et al. An economical method for calculating the discrete Fourier transform , 1899, AFIPS Fall Joint Computing Conference.
[7] L. Morris. Automatic generation of time efficient digital signal processing software , 1977 .
[8] S. Winograd. Arithmetic complexity of computations , 1980 .
[9] E. Brigham,et al. The fast Fourier transform , 2016, IEEE Spectrum.
[10] C. Rader,et al. A new principle for fast Fourier transformation , 1976 .
[11] H. W. Schüssler,et al. Signal processing II : theories and applications : proceedings of EUSIPCO-83, Second European Signal Processing Conference, Erlangen, W.-Germany, September 12-16, 1983 , 1983 .
[12] H. V. Sorensen,et al. A new efficient algorithm for computing a few DFT points , 1988, 1988., IEEE International Symposium on Circuits and Systems.
[13] Harvey F. Silverman. Further corrections to "An introduction to programming the winograd Fourier transform algorithm (WFTA)" , 1978 .
[14] G. Rivard. Direct fast Fourier transform of bivariate functions , 1977 .
[15] C. Burrus,et al. An in-place, in-order prime factor FFT algorithm , 1981 .
[16] C. Burrus. Index mappings for multidimensional formulation of the DFT and convolution , 1977 .
[17] C. Temperton. Self-sorting mixed-radix fast Fourier transforms , 1983 .
[18] C. Burrus,et al. Fast one-dimensional digital convolution by multidimensional techniques , 1974 .
[19] Wen-Hsiung Chen,et al. A Fast Computational Algorithm for the Discrete Cosine Transform , 1977, IEEE Trans. Commun..
[20] R. Bracewell. Discrete Hartley transform , 1983 .
[21] R. W. Johnson,et al. A methodology for designing, modifying, and implementing Fourier transform algorithms on various architectures , 1990 .
[22] Pierre Duhamel,et al. Algorithms meeting the lower bounds on the multiplicative complexity of length-2n DFTs and their connection with practical algorithms , 1990, IEEE Trans. Acoust. Speech Signal Process..
[23] C. Sidney Burrus,et al. On computing the split-radix FFT , 1986, IEEE Trans. Acoust. Speech Signal Process..
[24] Marshall C. Pease,et al. An Adaptation of the Fast Fourier Transform for Parallel Processing , 1968, JACM.
[25] H. Nawab,et al. Bounds on the minimum number of data transfers in WFTA and FFT programs. [Winograd Fourier Transform Algorithms and Fast Fourier Transform] , 1979 .
[26] Z. Mou,et al. Fast FIR filtering: algorithms and implementations , 1987 .
[27] C. K. Yuen,et al. Theory and Application of Digital Signal Processing , 1978, IEEE Transactions on Systems, Man, and Cybernetics.
[28] C. Burrus,et al. The design of optimal DFT algorithms using dynamic programming , 1982, ICASSP.
[29] M. Vetterli,et al. Simple FFT and DCT algorithms with reduced number of operations , 1984 .
[30] G. Goertzel. An Algorithm for the Evaluation of Finite Trigonometric Series , 1958 .
[31] Pierre Duhamel,et al. Un algorithme de transformation de Fourier rapide à double base , 1985 .
[32] Jean Vuillemin,et al. A combinatorial limit to the computing power of V.L.S.I. circuits , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).
[33] T. Kailath,et al. VLSI and Modern Signal Processing , 1984 .
[34] David C. Munson,et al. Floating point roundoff error in the prime factor FFT , 1981 .
[35] J. O. Eklundh,et al. A Fast Computer Method for Matrix Transposing , 1972, IEEE Transactions on Computers.
[36] R. Bracewell. The fast Hartley transform , 1984, Proceedings of the IEEE.
[37] Henri J. Nussbaumer,et al. Computation of Convolutions and Discrete Fourier Transforms by Polynomial Transforms , 1978, IBM J. Res. Dev..
[38] Victor Y. Pan. The Additive and Logical Complexities of Linear and Bilinear Arithmetic Algorithms , 1983, J. Algorithms.
[39] Martin Vetterli,et al. Improved Fourier and Hartley transform algorithms: Application to cyclic convolution of real data , 1987, IEEE Trans. Acoust. Speech Signal Process..
[40] Richard E. Blahut,et al. Fast Algorithms for Digital Signal Processing , 1985 .
[41] S. Winograd,et al. Abelian semi-simple algebras and algorithms for the Discrete Fourier Transform , 1984 .
[42] W. Stammler,et al. Error analysis and resulting structural improvements for fixed point FFTs , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.
[43] S. Winograd,et al. New algorithms for the multidimensional discrete Fourier transform , 1983 .
[44] Pierre Duhamel,et al. A connection between bit-reverse and matrix transpose, hardware and software consequences , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.
[45] Jacques Morgenstern,et al. The Linear Complexity of Computation , 1975, JACM.
[46] Jr. Earl E. Swartzlander,et al. VLSI Signal Processing Systems , 1985 .
[47] S. Winograd. On the multiplicative complexity of the Discrete Fourier Transform , 1979 .
[48] G. Bergland,et al. A radix-eight fast Fourier transform subroutine for real-valued series , 1969 .
[49] Charles M. Rader,et al. Number theory in digital signal processing , 1979 .
[50] Michael A. Soderstrand,et al. Residue number system arithmetic: modern applications in digital signal processing , 1986 .
[51] David M. W. Evans. An improved digit-reversal permutation algorithm for the fast Fourier and Hartley transforms , 1987, IEEE Trans. Acoust. Speech Signal Process..
[52] L. Morris,et al. A comparative study of time efficient FFT and WFTA programs for general purpose computers , 1978 .
[53] P. Duhamel,et al. New 2nDCT algorithms suitable for VLSI implementation , 1987, ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing.
[54] G. Bruun. z-transform DFT filters and FFT's , 1978 .
[55] Pierre Duhamel,et al. Existence of a 2n FFT algorithm with a number of multiplications lower than 2n+1 , 1984 .
[56] K. R. Rao,et al. Orthogonal Transforms for Digital Signal Processing , 1979, IEEE Transactions on Systems, Man, and Cybernetics.
[57] B. Lee. A new algorithm to compute the discrete cosine Transform , 1984 .
[58] S. Winograd. On computing the Discrete Fourier Transform. , 1976, Proceedings of the National Academy of Sciences of the United States of America.
[59] Pierre Duhamel,et al. Implementation of "Split-radix" FFT algorithms for complex, real, and real-symmetric data , 1986, IEEE Trans. Acoust. Speech Signal Process..
[60] P. Welch. The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms , 1967 .
[61] P. Duhamel,et al. `Split radix' FFT algorithm , 1984 .
[62] Alvin M. Despain,et al. Very Fast Fourier Transform Algorithms Hardware for Implementation , 1979, IEEE Transactions on Computers.
[63] Soo-Chang Pei,et al. Split-vector radix 2-D fast Fourier transform , 1987 .
[64] Pierre Duhamel,et al. In-place butterfly-style FFT of 2-D real sequences , 1988, IEEE Trans. Acoust. Speech Signal Process..
[65] Howard C. Card,et al. VLSI computations: from physics to algorithms , 1987, Integr..
[66] R. Singleton. An algorithm for computing the mixed radix fast Fourier transform , 1969 .
[67] Michael T. Heideman,et al. Computation of an odd-length DCT from a real-valued DFT of the same length , 1992, IEEE Trans. Signal Process..
[68] Joseph H. Rothweiler. Implementation of the in-order prime factor transform for variable sizes , 1982 .
[69] R. Preuss,et al. Very fast computation of the radix-2 discrete Fourier transform , 1982 .
[70] Thompson. Fourier Transforms in VLSI , 1983, IEEE Transactions on Computers.
[71] Martin Vetterli,et al. Fast 2-D discrete cosine transform , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.
[72] Gabor C. Temes,et al. Real-factor FFT algorithms , 1978, ICASSP.
[73] Douglas L. Jones,et al. Real-valued fast Fourier transform algorithms , 1987, IEEE Trans. Acoust. Speech Signal Process..
[74] Harvey F. Silverman,et al. Corrections and an addendum to "An introduction to programming the winograd Fourier transform algorithm (WFTA)" , 1978 .
[75] Alan V. Oppenheim. Papers on digital signal processing , 1969 .
[76] C. Rader. Discrete Fourier transforms when the number of data samples is prime , 1968 .
[77] Martin Vetterli,et al. Split-radix algorithms for length-pm DFT's , 1989, IEEE Trans. Acoust. Speech Signal Process..
[78] G. D. Bergland,et al. A fast Fourier transform algorithm using base 8 iterations , 1968 .
[79] Pierre Duhamel,et al. On computing the inverse DFT , 1988, IEEE Trans. Acoust. Speech Signal Process..
[80] Martin Vetterli,et al. A Discrete Fourier-Cosine Transform Chip , 1986, IEEE J. Sel. Areas Commun..
[81] R. Stasinski. Easy generation of small-Ndiscrete Fourier transform algorithms , 1986 .
[82] R. Mersereau,et al. The representation of two-dimensional sequences as one-dimensional sequences , 1974 .
[83] H. Nussbaumer. Fast Fourier transform and convolution algorithms , 1981 .
[84] Alvin M. Despain,et al. Fourier Transform Computers Using CORDIC Iterations , 1974, IEEE Transactions on Computers.
[85] Ramesh C. Agarwal,et al. Fourier Transform and Convolution Subroutines for the IBM 3090 Vector Facility , 1986, IBM J. Res. Dev..
[86] E. Dubois,et al. A new algorithm for the radix-3 FFT , 1978 .
[87] J. Tukey,et al. An algorithm for the machine calculation of complex Fourier series , 1965 .
[88] Michael T. Heideman. Multiplicative complexity, convolution, and the DFT , 1988 .
[89] Jean Vuillemin,et al. A Combinatorial Limit to the Computing Power of VLSI Circuits , 1983, IEEE Transactions on Computers.
[90] H. J. Nussbaumer,et al. Digital filtering using polynomial transforms , 1977 .
[91] N. Ahmed,et al. Discrete Cosine Transform , 1996 .
[92] C S. Burrus. Efficient Fourier transform and convolution algorithms , 1987 .
[93] Irving John Good,et al. The Interaction Algorithm and Practical Fourier Analysis , 1958 .
[94] Anil K. Jain,et al. A Sinusoidal Family of Unitary Transforms , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.
[95] P. Welch. A fixed-point fast Fourier transform error analysis , 1969 .
[96] T. Parks,et al. A prime factor FFT algorithm using high-speed convolution , 1977 .
[97] Harvey F. Silverman,et al. An introduction to programming the Winograd Fourier transform algorithm (WFTA) , 1977 .
[98] Martin Vetterli. Analysis, synthesis and computational complexity of digital filter banks , 1986 .
[99] C. Sidney Burrus,et al. On the number of multiplications necessary to compute a length-2nDFT , 1986, IEEE Trans. Acoust. Speech Signal Process..
[100] B. K. Bhagavan,et al. Fast Computational Algorithms for Bit Reversal , 1974, IEEE Transactions on Computers.
[101] C. Sidney Burrus. Unscrambling for fast DFT algorithms , 1988, IEEE Trans. Acoust. Speech Signal Process..
[102] Jean-Marc Delosme,et al. Highly concurrent computing structures for matrix arithmetic and signal processing , 1982, Computer.