Two-Dimensional Transforms Using Number Theoretic Techniques

[1]  L. Marton,et al.  Advances in Electronics and Electron Physics , 1958 .

[2]  I. Niven,et al.  An introduction to the theory of numbers , 1961 .

[3]  Christopher S. Wallace,et al.  A Suggestion for a Fast Multiplier , 1964, IEEE Trans. Electron. Comput..

[4]  J. Tukey,et al.  An algorithm for the machine calculation of complex Fourier series , 1965 .

[5]  Richard I. Tanaka,et al.  Residue arithmetic and its applications to computer technology , 1967 .

[6]  Michael J. Corinthios,et al.  The Design of a Class of Fast Fourier Transform Computers , 1971, IEEE Transactions on Computers.

[7]  Peter J. Nicholson,et al.  Algebraic Theory of Finite Fourier Transforms , 1971, Journal of computer and system sciences (Print).

[8]  J. Pollard,et al.  The fast Fourier transform in a finite field , 1971 .

[9]  Charles M. Rader,et al.  Discrete Convolutions via Mersenne Transrorms , 1972, IEEE Transactions on Computers.

[10]  C. Burrus,et al.  Fast Convolution using fermat number transforms with applications to digital filtering , 1974 .

[11]  N. Ahmed,et al.  Discrete Cosine Transform , 1996 .

[12]  Trieu-Kien Truong,et al.  The use of finite fields to compute convolutions , 1975, IEEE Trans. Inf. Theory.

[13]  L. Leibowitz.  A simplified binary arithmetic for the Fermat number transform , 1976 .

[14]  Ernest L. Hall,et al.  Image Processing by Transforms Over a Finite Field , 1977, IEEE Transactions on Computers.

[15]  I. S. Reed,et al.  X-Ray Reconstruction by Finite Field Transforms , 1977, IEEE Transactions on Nuclear Science.

[16]  Anastasios N. Venetsanopoulos,et al.  The Discrete Fourier Transform Over Finite Rings with Application to Fast Convolution , 1978, IEEE Transactions on Computers.

[17]  C. K. Yuen,et al.  Theory and Application of Digital Signal Processing , 1978, IEEE Transactions on Systems, Man, and Cybernetics.

[18]  Underwood Dudley.  Elementary Number Theory , 1978 .

[19]  Charles M. Rader,et al.  Number theory in digital signal processing , 1979 .

[20]  K. R. Rao,et al.  Unified Matrix Treatment of Discrete Transforms , 1979, IEEE Transactions on Computers.

[21]  Graham A. Jullien,et al.  Implementation of Multiplication, Modulo a Prime Number, with Applications to Number Theoretic Transforms , 1980, IEEE Transactions on Computers.

[22]  Anna Z. Baraniecka.  DIGITAL FILTERING USING NUMBER-THEORETIC TECHNIQUES. , 1980 .

[23]  G A Jullien,et al.  Residue number system implementations of number theoretic transforms in complex residue rings , 1980 .

[24]  Hari K. Nagpal.  Processor architectures for fast computation of multi-dimensional unitary transforms , 1981 .

[25]  Graham A. Jullien,et al.  Processor Architectures for Two-Dimensional Convolvers Using a Single Multiplexed Computational Element with Finite Field Arithmetic , 1983, IEEE Transactions on Computers.

[26]  Charles M. Rader,et al.  Digital processing of signals , 1983 .

[27]  M. Schroeder.  Number Theory in Science and Communication , 1984 .

[28]  Michael A. Soderstrand,et al.  Residue number system arithmetic: modern applications in digital signal processing , 1986 .

[29]  C. W. Slayman,et al.  A high-speed high-density silicon 8/spl times/8-bit parallel multiplier , 1987 .

[30]  James V. Krogmeier,et al.  The design of dual-mode complex signal processors based on quadratic modular number codes , 1987 .

[31]  Graham A. Jullien,et al.  Complex digital signal processing over finite rings , 1987 .

[32]  R. Tolimieri,et al.  Algorithms for Discrete Fourier Transform and Convolution , 1989 .

[33]  Graham A. Jullien,et al.  On Modulus Replication for Residue Arithmetic Computations of Complex Inner Products , 1990, IEEE Trans. Computers.

[34]  Graham A. Jullien,et al.  Array processing on finite polynomial rings , 1990, [1990] Proceedings of the International Conference on Application Specific Array Processors.

[35]  Graham A. Jullien,et al.  Algorithms for length 15 and 30 discrete cosine transform , 1991, [1991] Conference Record of the Twenty-Fifth Asilomar Conference on Signals, Systems & Computers.

[36]  Graham A. Jullien,et al.  Number Theoretic Techniques in Digital Signal Processing , 1991 .

[37]  F. J. Taylor,et al.  A reduced-complexity finite field ALU , 1991 .

[38]  Graham A. Jullien,et al.  VLSI implementations of number theoretic concepts with applications in signal processing , 1992, Optics & Photonics.

[39]  A. Holt,et al.  New number theoretic transform , 1992 .

[40]  Said Boussakta,et al.  New two dimensional transform , 1993 .

[41]  Martin Vetterli,et al.  Hartley transforms over finite fields , 1993, IEEE Trans. Inf. Theory.

[42]  Graham A. Jullien,et al.  Large Dynamic Range Computations over Small Finite Rings , 1994, IEEE Trans. Computers.

[43]  Graham A. Jullien,et al.  An array processor for inner product computations using a Fermat number ALU , 1995, Proceedings The International Conference on Application Specific Array Processors.

[44]  G. Jullien,et al.  An algorithm for multiplication modulo (2/spl and/N-1) , 1996, Proceedings of the 39th Midwest Symposium on Circuits and Systems.