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Parallel implementation of multidimensional transforms without interprocessor communication

IEEE TRANSACTIONS ON COMPUTERS 1999年第9期48卷 951-961页

作者： Marino, F Swartzlander, EE Politecn Bari Dipartimento Ingn Elettrotecn & Elettron I-70125 Bari Italy Univ Texas Dept Elect & Comp Engn Austin TX 78712 USA

This paper presents a modular algorithm which is suitable for computing a large class of multidimensional transforms in a general purpose parallel environment without interprocessor communication. Since it is based on matrix-vector multiplication, it does not impose restrictions on the size of the input data as many existing algorithms do. The method is fully general since it does not depend on the specific nature of the transform kernel and, therefore, it may be used for a wide variety of transforms. Moreover, since some one-dimensional Fast Fourier Transform algorithms map the input sequence onto two or more dimensions, the new method also may be employed to efficiently compute the 1D FFT in parallel. In addition, the proposed algorithm is exploited to derive a fully systolic VLSI architecture performing multidimensional transforms, which does not need the transposer required by classical architectures.

关键词： parallel processing multidimensional transforms 2D DFT 1D FFT systolic VLSI architectures

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OPTIMAL VLSI NETWORKS FOR multidimensional transforms

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 1994年第7期5卷 763-769页

作者： ALNUWEIRI, HM Department of Electrical Engineering University of British Columbia Vancouver BC Canada

This short note presents a new class of AT2-optimal networks for computing the multidimensional Discrete Fourier Transform. Although optimal networks have been proposed previously, the networks proposed in this short note are based on a new methodology for mapping large K-shuffle networks, K greater-than-or-equal-to 2, onto smaller area networks that maintain the optimality of the DFT network. Such networks are used to perform the index-rotation operations needed by the multidimensional computation. The resulting networks have simple regular layouts, and can be easily partitioned among several chips in order to reduce the number of input-output pins per chip.

关键词： PARALLEL PROCESSING VLSI COMPUTATIONS DISCRETE FOURIER TRANSFORM multidimensional transforms AREA-TIME TRADEOFFS FOLDED INDEX-ROTATION NETWORKS SHUFFLE PERMUTATIONS

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EQUIVALENCE OF multidimensional transforms AND REVERSION METHODS OF SOLVING NONLINEAR EQUATIONS

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PROCEEDINGS OF THE INSTITUTION OF ELECTRICAL ENGINEERS-LONDON 1973年第1期120卷 144-145页

作者： ANJAIAH, B REDDY, DC OSMANIA UNIV COLL ENGNDEPT ELECTR & COMMUN ENGNHYDERABAD 7INDIA

The multidimensional-transform method and the reversion method of obtaining the respone of nonlinear control systems are compared. It is proved that, for a fairly general class of systems, the reversion method and the transform method not only yield the same solution, but also that the linear approximation and the higher-order approximations to the solution by both the methods are identical. This identification makes it possible to predict the stability of nonlinear systems in the transformed domain under rather restricted conditions.

关键词： nonlinear equations transforms reversion methods Stability in control theory transformed domain stability differential equations equivalence multidimensional transforms Nonlinear control systems nonlinear control systems

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VLSI ARCHITECTURES FOR multidimensional transforms

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IEEE TRANSACTIONS ON COMPUTERS 1991年第9期40卷 1053-1057页

作者： CHAKRABARTI, C JAJA, J UNIV MARYLAND INST ADV COMP STUDIESDEPT ELECT ENGNSYST RES CTRCOLLEGE PKMD 20742

In this paper we propose a family of VLSI architectures with area-time tradeoffs for computing (N x N x ... x N) d-dimensional linear separable transforms. For fixed-precision arithmetic with b bits, the architectures have an area A = O(N(d) + 2a), computation time T = O(d N(d/2-a)b) and achieve the AT2 bound of AT2 = O(n2b2) for constant d, where n = N(d) and 0 < a less-than-or-equal-to d/2.

关键词： AREA-TIME TRADEOFFS AT2 OPTIMAL multidimensional transforms ROTATOR UNIT SUBBLOCK ROTATOR UNIT SUBBLOCK TRANSPOSE UNIT VLSI ARCHITECTURE

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A unified framework for mapping multidimensional separable DSP transforms onto parallel VLSI structures

A unified framework for mapping multidimensional separable D...

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7th IEEE International Symposium on Signal Processing and Information Technology

作者： Elnaggar, Ayman Aboelaze, Mokhtar Sultan Qaboos Univ Dept Comp Engn POB 33 Muscat Oman York Univ Dept Comp Sci Toronto ON M3J 1PE Canada

ISBN: (纸本)9781424418343

This paper presents a general approach for separable DSP transforms that allows the generation of higher order (longer size) multidimensional (m-d) architectures from 2 m lower order (shorter sizes) architectures. The objective of our work is to derive a unified framework and a design methodology that allows direct mapping of the proposed algorithms into modular VLSI architectures. Our methodology is based on manipulating tensor product forms so that they can be mapped directly into modular parallel architectures. The resulting circuits have very simple modular structure and regular topology.

关键词： recursive algorithms multidimensional transforms tensor products permutation matrices

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Control system analysis using Mathematica and a graphical user interface

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COMPUTING & CONTROL ENGINEERING JOURNAL 1997年第2期8卷 64-69页

作者： Barker, HA Zhuang, M Dept. of Electr. & Electron. Eng. Univ. Coll. of Swansea UK

An environment has been developed in which the computer algebra software Mathematica is used for the analysis of dynamic systems with models constructed through the graphical user interface of the simulation software SIMULINK. The SIMULINK models are passed to Mathematica through MATLAB and MathLink programs under the control of a simple graphical user interface. An application is described in which block-oriented nonlinear systems for analysis by multidimensional transforms. Mathematica procedures are used to determine the multidimensional transfer functions that relate the system outputs to the system inputs and these are used to obtain the time responses and the harmonic responses of the system. The method is illustrated for a feedback control system with a saturation characteristic in the forward path.

关键词： computer algebra software SIMULINK Nonlinear control systems graphical user interface dynamic systems analysis block-oriented nonlinear systems Engineering mathematics and numerical techniques MATLAB programs control system analysis computing time responses transforms nonlinear dynamical systems transfer functions harmonic responses MathLink programs control system analysis feedback Mathematica nonlinear control systems system input-output relations symbol manipulation Graphical user interfaces forward-path saturation characteristic simulation software Control system analysis and synthesis methods multidimensional transforms feedback control system graphical user interfaces multidimensional transfer functions Control system design and analysis Integral transforms software packages digital simulation

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A pipelined architecture for the multidimensional DFT

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2001年第9期49卷 2096-2102页

作者： Yu, SW Swartzlander, EE Intel Corp Austin TX 78746 USA Univ Texas Dept Elect & Comp Engn Austin TX 78712 USA

This paper presents an efficient pipelined architecture for the N-m-point m-dimensional discrete Fourier transform (DFT). By using a two-level index mapping scheme that is different from the conventional decimation-in-time (DIT) or decimation-infrequency (DIF) algorithms, the conventional pipelined architecture for the one-dimensional (1-D) fast Fourier transform (FFT) can be efficiently used for the computation of higher dimensional DFTs. Compared with systolic architectures, the proposed scheme is area-efficient since the computational elements (CEs) use the minimum number of multipliers, and the number of CEs increases only linearly with respect to the dimension m. It can be easily extended to the N-m-point m-dimensional DFT with large m and/or N, and it is more flexible since the throughput can be easily varied to accommodate various area/throughput requirements.

关键词： discrete Fourier transform multidimensional transforms pipelined architecture

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A mapping-based design for nonsubsampled hourglass filter banks in arbitrary dimensions

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2008年第4期56卷 1466-1478页

作者： Lu, Yue M. Do, Minh N. Univ Illinois Dept Elect & Comp Engn Coordinated Sci Lab Urbana IL 61801 USA Univ Illinois Beckman Inst Urbana IL 61801 USA

multidimensional hourglass filter banks decompose the frequency spectrum of input signals into hourglass-shaped directional subbands, each aligned with one of the frequency axes. The directionality of the spectral partitioning makes these filter banks useful in separating the directional information in multidimensional signals. Despite the existence of various design techniques proposed for the 2-D case, to our best knowledge, the design of hourglass filter banks in 3-D and higher dimensions with finite impulse response (FIR) filters and perfect reconstruction has not been previously reported. In this paper, we propose a novel mapping-based design for the hourglass filter banks in arbitrary dimensions, featuring perfect reconstruction, FIR filters, efficient implementation using lifting/ladder structures, and a near-tight frame construction. The effectiveness of the proposed mapping-based design depends on the study of a set of conditions on the frequency supports of the mapping kernels. These conditions ensure that we can still get good frequency responses when the component filters used are nonideal. Among all feasible choices, we then propose an optimal specification for the mapping kernels, which leads to the simplest passband shapes and involves the fewest number of frequency variables. Finally, we illustrate the proposed techniques by a design example in 3-D, and an application in video denoising.

关键词： directional decomposition directional filter banks filter design hourglass filter banks multidimensional transforms

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Generalized convolution as a tool for the multi-dimensional filtering tasks

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multidimensional SYSTEMS AND SIGNAL PROCESSING 2008年第3-4期19卷 361-377页

作者： Korohoda, Przemyslaw Dabrowski, Adam AGH Univ Sci & Technol Chair Elect PL-30059 Krakow Poland Poznan Univ Tech Chair Control & Syst Engn PL-60965 Poznan Poland

In this paper the so-called generalized convolution, being in fact an adequate adaptation of the well known circular convolution concept to any invertible block-transform, is proposed, developed, and analysed. First the proposed idea is summarized for a one-dimensional case. Then it is extended to multidimensional problems. The presented generalized convolution concept is based on the earlier A-convolution. This idea is recalled at the beginning and a set of techniques for studying the dependence of the respective coefficients on the arbitrary transform, is suggested. The generalized convolution matrix, being an extension of that for the circular convolution, is introduced and adapted to an arbitrary invertible transform. The filtering problem is then defined and presented in the transform domain. The multidimensional analysis starts with two-dimensional problems, then it is continued with formulas for multidimensional filtering tasks. The paper is illustrated with examples computed for twenty carefully selected transforms. Among them are Haar, Hadamard, Hartley, Karhunen-Loeve and a family of 16 discrete trigonometric transforms.

关键词： filtering generalized convolution multidimensional transforms

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multidimensional TRANSFORM INVERSION WITH APPLICATIONS TO THE TRANSIENT M/G/1 QUEUE

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ANNALS OF APPLIED PROBABILITY 1994年第3期4卷 719-740页

作者： Choudhury, Gagan L. Lucantoni, David M. Whitt, Ward AT&T Bell Labs Holmdel NJ 07733 USA AT&T Bell Labs Murray Hill NJ 07974 USA

We develop an algorithm for numerically inverting multidimensional transforms. Our algorithm applies to any number of continuous variables (Laplace transforms) and discrete variables (generating functions). We use the Fourier-series method;that is, the inversion formula is the Fourier series of a periodic function constructed by aliasing. This amounts to an application of the Poisson summation formula. By appropriately exponentially damping the given function, we control the aliasing error. We choose the periods of the multidimensional periodic function so that each infinite series is a finite sum of nearly alternating infinite series. Then we apply the Euler transformation to compute the infinite series from finitely many terms. The multidimensional inversion algorithm enables us, evidently for the first time, to calculate probability distributions quickly and accurately from several classical transforms in queueing theory. For example, we apply our algorithm to invert the two-dimensional transforms of the joint distribution of the duration of a busy period and the number served in that busy period, and the time-dependent transient queue-length and workload distributions in the M/G/1 queue. In other related work, we have applied the inversion algorithms here to calculate time-dependent distributions in the transient BMAP/G/1 queue (with a batch Markovian arrival process) and the piecewise-stationary M-t/G(t)/1 queue.

关键词： Numerical transform inversion Laplace transforms generating functions multidimensional transforms Fourier transforms Fourier-series method Poisson summation formula M/G/1 queue transient distributions

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