The Area-Time Complexity of Binary Multiplication
Journal of the ACM (JACM)
Introduction to VLSI Systems
New layouts for the shuffle-exchange graph(Extended Abstract)
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Multi-dimensional systolic networks, for discrete fourier transform
ISCA '84 Proceedings of the 11th annual international symposium on Computer architecture
On routing two-point nets across a channel
DAC '82 Proceedings of the 19th Design Automation Conference
A complexity theory for VLSI
Computational Aspects of VLSI
Parallel Processing with the Perfect Shuffle
IEEE Transactions on Computers
A Combinatorial Limit to the Computing Power of VLSI Circuits
IEEE Transactions on Computers
IEEE Transactions on Computers
The VLSI Complexity of Sorting
IEEE Transactions on Computers
The cube-connected-cycles: A versatile network for parallel computation
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Optimal VLSI architectures for multidimensional DFT
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
Optimal VLSI architectures for multidimensional DFT (preliminary version)
ACM SIGARCH Computer Architecture News - Symposium on parallel algorithms and architectures
VLSI Architectures for Multidimensional Transforms
IEEE Transactions on Computers
Parallel Implementation of Multidimensional Transforms without Interprocessor Communication
IEEE Transactions on Computers
An Efficient Algorithm for the Computation of the MultidimensionalDiscrete Fourier Transform
Multidimensional Systems and Signal Processing
Journal of VLSI Signal Processing Systems - Parallel VLSI architectures for image and video processing
A Parallel Algorithm for 2-D DFT Computation with No Interprocessor Communication
IEEE Transactions on Parallel and Distributed Systems
Optimal VLSI Networks for Multidimensional Transforms
IEEE Transactions on Parallel and Distributed Systems
Architectural design of array processors for multi-dimensional discrete Fourier transform
Highly parallel computaions
A systolic VLSI architecture for multi-dimensional transforms
ICASSP'93 Proceedings of the 1993 IEEE international conference on Acoustics, speech, and signal processing: plenary, special, audio, underwater acoustics, VLSI, neural networks - Volume I
An efficient radix-two algorithm to compute the 2D Fourier transform
ICECS'05 Proceedings of the 4th WSEAS international conference on Electronics, control and signal processing
New area-time lower bounds for the multidimensional DFT
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
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It is often desirable in modern signal processing applications to perform two-dimensional or three-dimensional Fourier transforms. Until the advent of VLSI it was not possible to think about one chip implementation of such processes. In this paper several methods for implementing the multidimensional Fourier transform together with the VLSI computational model are reviewed and discussed. We show that the lower bound for the computation of the multidimensional transform is O(n2 log2 n). Existing nonoptimal architectures suitable for implementing the 2-D transform, the RAM array transposer, mesh connected systolic array, and the linear systolic matrix vector multiplier are discussed for area time tradeoff. For achieving a higher degree of concurrency we suggest the use of rotators for permutation of data. With ``hybrid designs'' comprised of a rotator and one-dimensional arrays which compute the one-dimensional Fourier transform we propose two methods for implementation of multidimensional Fourier transform. One design uses the perfect shuffle for rotations and achieves an AT2p of O(n2 log2 n路 log2 N). An optimal architecture for calculation of multidimensional Fourier transform is proposed in this paper. It is based on arrays of processors computing one-dimensional Fourier transforms and a rotation network or rotation array. This architecture realizes the AT2p lower bound for the multidimensional FT processing.