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A Structured fast Algorithm for the VLSI Pipeline Implementation of Inverse Discrete Cosine Transform

CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2021年第11期40卷 5351-5366页

作者： Chiper, Doru Florin Tech Univ Gheorghe Asachi Iasi Appl Elect Dept Iasi Romania

The forward and inverse DCT has many applications in digital signal processing area, but, due to its high arithmetic complexity, it is necessary to find efficient software implementations or even to find VLSI implementations for them. Existing fast algorithms for IDCT or DCT have a SFG graph that is not very regular and modular and, even more importantly, the topology of the interconnection network is not easy to implement in VLSI due to the so-called retrograde indexing. Due to this problem, there are few pipeline implementations for IDCT and DCT, although pipelining is an efficient engineering solution that allows high speed performance with a reduced hardware complexity and power consumption. In this paper, we present an efficient solution to successfully reformulate the IDCT algorithm with a focus on developing a modular and regular computation structure that can be easily implemented using a pipelined VLSI architecture. Using new restructuring input sequences that can be computed in parallel with the new SFG graph in a pipeline manner, a novel efficient fast algorithm for the computation of inverse discrete cosine transform is presented. The obtained SFG graph has the best structure that can be obtained for IDCT, avoiding the so-called retrograde indexing and being highly regular and modular. Moreover, the obtained SFG graph is scalable, being easy to extend to larger values of N that is a power of 2. It can also be used to obtain a generalization of a radix-2 algorithm for length N = p center dot 2(m), where "p" is a prime number. This algorithm is based on a recursive decomposition of the computation of the inverse DCT that requires a reduced number of arithmetic operations and has a regular and simple computational structure that can be easily implemented in VLSI in a pipeline manner. Its main advantages are its simple, regular and modular computational structure and its high potential to be pipelined so that it can be used to obtain an efficient pipeline VL

关键词： Inverse discrete cosine transform fast algorithms VLSI implementation

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Image Compression Via a fast DCT Approximation

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IEEE LATIN AMERICA TRANSACTIONS 2010年第6期8卷 708-713页

作者： Bayer, F. M. Cintra, R. J. Univ Fed Fronteira Sul Erechim RS Brazil Univ Fed Pernambuco Programa Posgrad Estat Recife PE Brazil

Discrete transforms play an important role in digital signal processing. In particular, due to its transform domain energy compaction properties, the discrete cosine transform (DCT) is pivotal in many image processing problems. This paper introduces a numerical approximation method for the DCT based on round-off techniques. The proposed method is a multiplierless technique with low arithmetic complexity. Emphasis was given to approximating the 8-point DCT. A fast algorithm for the introduced 8-point approximate transform was derived. An application in image compression was examined. In several scenarios, the utilization of the proposed method for image compression resulted in comparable or better performances, when compared to the usual DCT-based methodology.

关键词： discrete cosine transforms fast algorithms image coding complexity theory

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fast implementation of two-dimensional APES and CAPON spectral estimators

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MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING 2002年第1期13卷 35-53页

作者： Larsson, EG Stoica, P Univ Florida Dept Elect & Comp Engn Gainesville FL 32611 USA Uppsala Univ Dept Syst & Control S-75103 Uppsala Sweden

The matched-filterbank spectral estimators APES and CAPON have recently received considerable attention in a number of applications. Unfortunately, their computational complexity tends to limit their usage in several cases - a problem that has previously been addressed by different authors. In this paper, we introduce a novel approach to the computation of the APES and CAPON spectra, which leads to a computational method that is considerably faster than all existing techniques. The new implementations of APES and CAPON are called fast APES and fast CAPON, respectively, and are developed for the two-dimensional case, with the one-dimensional case as a special case. Numerical examples are provided to demonstrate the application of APES to synthetic aperture radar (SAR) imaging, and to illustrate the reduction in computational complexity provided by our method.

关键词： two-dimensional spectral estimation APES CAPON fast algorithms displacement rank

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fast algorithm for the three-dimensional Poisson equation in infinite domains

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IMA JOURNAL OF NUMERICAL ANALYSIS 2021年第4期41卷 3024-3045页

作者： Zheng, Chunxiong Ma, Xiang Xinjiang Univ Coll Math & Syst Sci Urumqi 830046 Peoples R China Tsinghua Univ Dept Math Sci Beijing 100084 Peoples R China

This paper is concerned with a fast finite element method for the three-dimensional Poisson equation in infinite domains. Both the exterior problem and the strip-tail problem are considered. Exact Dirichletto-Neumann (DtN)-type artificial boundary conditions (ABCs) are derived to reduce the original infinite-domain problems to suitable truncated-domain problems. Based on the best relative Chebyshev approximation for the square-root function, a fast algorithm is developed to approximate exact ABCs. One remarkable advantage is that one need not compute the full eigensystem associated with the surface Laplacian operator on artificial boundaries. In addition, compared with the modal expansion method and the method based on Pade approximation for the square-root function, the computational cost of the DtN mapping is further reduced. An error analysis is performed and numerical examples are presented to demonstrate the efficiency of the proposed method.

关键词： infinite domain problems exact artificial boundary conditions fast algorithms Chebyshev approximation

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Some nonlinear/adaptive methods for fast recovery of the missing samples of signals

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SIGNAL PROCESSING 2008年第3期88卷 624-638页

作者： Ghandi, Mahmoud Yekta, Mohammad Mahdi Jahani Marvasti, Farokh Sharif Univ Technol Dept Elect Engn Adv Commun Res Inst Tehran Iran

In this paper an iterative method for recovery of the missing samples of signals is investigated in detail, and some novel linear, nonlinear, and adaptive extrapolation techniques are proposed to be used along with it to increase the convergence rate of the recovery system. The proposed methods would remarkably speed up the convergence rate, save processing power, and reduce the delay of the system compared to some well known accelerated versions of the aforementioned iterative algorithm. (C) 2007 Elsevier B.V. All rights reserved.

关键词： signal recovery non-uniform sampling iterative methods extrapolation adaptive processing fast algorithms

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A fast boundary cloud method for 3D exterior electrostatic analysis

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2004年第15期59卷 2019-2046页

作者： Shrivastava, V Aluru, NR Univ Illinois Dept Mech & Ind Engn Beckman Inst Adv Sci & Technol Urbana IL 61801 USA

An accelerated boundary cloud method (BCM) for boundary-only analysis of 3D electrostatic problems is presented here. BCM uses scattered points unlike the classical boundary element method (BEM) which uses boundary elements to discretize the surface of the conductors. BCM combines the weighted least-squares approach for the construction of approximation functions with a boundary integral formulation for the governing equations. A linear base interpolating polynomial that can vary from cloud to cloud is employed. The boundary integrals are computed by using a cell structure and different schemes have been used to evaluate the weakly singular and non-singular integrals. A singular value decomposition (SVD) based acceleration technique is employed to solve the dense linear system of equations arising in BCM. The performance of BCM is compared with BEM for several 3D examples. Copyright (C) 2004 John Wiley Sons, Ltd.

关键词： meshless methods boundary cloud method (BCM) fast algorithms SVD BEM exterior electrostatics

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fast data-independent KLT approximations based on integer functions

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MULTIMEDIA TOOLS AND APPLICATIONS 2024年第26期83卷 67303-67325页

作者： Radunz, A. P. Coelho, D. F. G. Bayer, F. M. Cintra, R. J. Madanayake, A. Univ Fed Pernambuco Dept Estat BR-50670901 Recife Brazil Univ Fed Pernambuco Dept Tecnol Signal Proc Grp BR-55014900 Caruaru Brazil Univ Fed Santa Maria Dept Estat LACESM BR-97105900 Santa Maria Brazil Florida Int Univ Dept Elect & Comp Engn Miami FL 33174 USA

The Karhunen-Loeve transform (KLT) stands as a well-established discrete transform, demonstrating optimal characteristics in data decorrelation and dimensionality reduction. Its ability to condense energy compression into a select few main components has rendered it instrumental in various applications within image compression frameworks. However, computing the KLT depends on the covariance matrix of the input data, which makes it difficult to develop fast algorithms for its implementation. Approximations for the KLT, utilizing specific rounding functions, have been introduced to reduce its computational complexity. Therefore, our paper introduces a category of low-complexity, data-independent KLT approximations, employing a range of round-off functions. The design methodology of the approximate transform is defined for any block-length N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{N}$$\end{document}, but emphasis is given to transforms of N=8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{N} = 8$$\end{document} due to its wide use in image and video compression. The proposed transforms perform well when compared to the exact KLT and approximations considering classical performance measures. For particular scenarios, our proposed transforms demonstrated superior performance when compared to KLT approximations documented in the literature. We also developed fast algorithms for the proposed transforms, further reducing the arithmetic cost associated with their implementation. Evaluation of field programmable gate array (FPGA) hardware implementation metrics was conducted. Practical applicatio

关键词： Approximate transforms fast algorithms Image compression Karhunen-Loeve transform Low-complexity transforms

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Loop-tree implementation of the adaptive integral method (AIM) for numerically-stable, broadband, fast electromagnetic modeling

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2004年第8期52卷 2130-2140页

作者： Okhmatovski, VI Morsey, JD Cangellaris, AC Cadence Design Syst Inc Tempe AZ 85282 USA Univ Illinois Dept Elect & Comp Engn Ctr Computat Electromagnet Urbana IL 61801 USA

The adaptive integral method (AIM) is implemented in conjunction with the loop-tree (LT) decomposition of the electric current density in the method of moments approximation of the electric field integral equation. The representation of the unknown currents in terms of its solenoidal and irrotational components allows for accurate, broadband electromagnetic (EM) simulation without low-frequency numerical instability problems, while scaling of computational complexity and memory storage with the size of the problem of the are of the same order as in the conventional AIM algorithm. The proposed algorithm is built as an extension to the conventional AIM formulation that utilizes roof-top expansion functions, thus providing direct and easy way for the development of the new stable formulation when the roof-top based AIM is available. A new preconditioning strategy utilizing near interactions in the system which are typically available in the implementation of fast solvers is proposed and tested. The discussed preconditioner can be used with both roof-top and LT formulations of AIM and other fast algorithms. The resulting AIM implementation is validated through its application to the broadband, EM analysis of large microstrip antennas and planar interconnect structures.

关键词： fast algorithms full-wave electromagnetic (EM) CAD loop-tree (LT) decomposition low frequency method of moments (MoM)

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Multilple-incidence and multifrequency for profile reconstruction of random rough surfaces using the 3-D electromagnetic fast multipole model

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 2004年第11期42卷 2499-2510页

作者： El-Shenawee, M Miller, EL Univ Arkansas Dept Elect Engn Fayetteville AR 72701 USA Northeastern Univ Dept Elect & Comp Engn Ctr Subsurface Sensing & Imaging Syst Boston MA 02115 USA

A fast algorithm for reconstructing the profile of random rough surfaces using electromagnetic scattering data is presented. The algorithm is based on merging a fast forward solver and an efficient optimization technique. The steepest de- scent fast multipole method is used as the three-dimensional fast forward solver. A rapidly convergent descent method employing a "marching-on" strategy for processing multifrequency and multi-incidence angle data is introduced to minimize an underlying cost function. The cost function represents the error between true (synthetic) and simulated scattered field data. Several key issues that impact the accuracy in reconstructing the rough profile are examined in this work, e.g., the location and number of receivers, the incident and scattered directions, the surface roughness, and details regarding the manner in which sensitivity information is computed in the inversion scheme. The results show that using the multiple-incidence (one angle at a time) and the multifrequency (onefrequency at a time) strategies lead to improve the profile reconstruction.

关键词： fast algorithms inverse scattering optimization techniques profile reconstruction rough surface scattering

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fast ADAPTATION OF EQUALIZER AND DESIRED RESPONSE FOR DIGITAL DATA RECEIVERS

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IEE JOURNAL ON ELECTRONIC CIRCUITS AND SYSTEMS 1978年第5期2卷 159-166页

作者： DOAN, HB CANTONI, A Department of Electrical Engineering University of Newcastle Newcastle Australia

The paper considers the design of the equaliser and the desired overall system impulse response (d.i.r.) for various types of detection algorithms used to recover digital data which has suffered intersymbol interference. The joint optimisation of the equaliser and desired response is formulated using a mean-square error cost. A constraint on the desired response is introduced which enables simple adaptive algorithms to be derived for determining the optimum equalizer and d.i.r. One of the algorithms considered has been found to converge rapidly and is thus ideally suited for application where fast start-up is required. Simulation results of the probability of error performance of various detection algorithms, using the equaliser and d.i.r. designed according to the approach developed in the paper, are presented. These results show that the performance obtained is comparable to that achieved with systems in which the equaliser and d.i.r. are designed according to other techniques. The disadvantage of these other techniques is that they usually lead to algorithms which are difficult to make adaptive and are slow to converge.

关键词： system impulse response General circuit analysis and synthesis methods detection algorithms Data communication equipment and techniques transient response gradient algorithms equalisers digital communication systems signal detection data communication systems simulation studies equaliser design Signal processing and detection intersymbol interference Other data transmission digital data receivers Filters and other networks fast algorithms

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