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fast fundamental frequency estimation: Making a statistically efficient estimator computationally efficient

SIGNAL PROCESSING 2017年 135卷 188-197页

作者： Nielsen, Jesper Kjaer Jensen, Tobias Lindstrom Jensen, Jesper Rindom Christensen, Mads Graesboll Jensen, Soren Holdt Aalborg Univ Audio Anal Lab AD MT Rendsburggade 14 DK-9000 Aalborg Denmark Bang & Olufsen AS Acoust Res Peter Bangs Vej 15 DK-7600 Struer Denmark Aalborg Univ Dept Elect Syst Fredrik Bajers Vej 7B DK-9220 Aalborg Denmark

Modelling signals as being periodic is common in many applications. Such periodic signals can be represented by a weighted sum of sinusoids with frequencies being an integer multiple of the fundamental frequency. Due to its widespread use, numerous methods have been proposed to estimate the fundamental frequency, and the maximum likelihood (ML) estimator is the most accurate estimator in statistical terms. When the noise is assumed to be white and Gaussian, the ML estimator is identical to the non-linear least squares (NLS) estimator. Despite being optimal in a statistical sense, the NLS estimator has a high computational complexity. In this paper, we propose an algorithm for lowering this complexity significantly by showing that the NLS estimator can be computed efficiently by solving two Toeplitz-plus-Hankel systems of equations and by exploiting the recursive-in-order matrix structures of these systems. Specifically, the proposed algorithm reduces the time complexity to the same order as that of the popular harmonic summation method which is an approximate NLS estimator. The performance of the proposed algorithm is assessed via Monte Carlo and timing studies. These show that the proposed algorithm speeds up the evaluation of the NLS estimator by a factor of 50-100 for typical scenarios.

关键词： Fundamental frequency estimation Toeplitz Hankel fast algorithms Pitch

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Simulation of two-dimensional steady-state heat conduction problems by a fast singular boundary method

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2019年 108卷 149-157页

作者： Li, Weiwei Xu, Shaoqiang Shao, Mingyu Shandong Univ Technol Sch Transportat & Vehicle Engn Zibo 255049 Peoples R China

The study presents a fast direct algorithm for solutions of systems arising from singular boundary method (SBM) in two-dimensional (2D) steady-state heat conduction problems. As a strong-form boundary discretization collocation technique, the SBM is mathematically simple, easy-to-implement, and free of mesh. Similar to boundary element method (BEM), the SBM generates a dense coefficient matrix, which requires O(N-3) operations and O(N-2) memory to solve the system with direct solvers. In this study, a fast direct solver based on recursive skeletonization factorization (RSF) is applied to solve the linear systems in the SBM. Due to the fact that the coefficient matrix is hierarchically block separable, we can construct a multilevel generalized LU decomposition that allows fast application of the inverse of the coefficient matrix. Combing the RSF and the SBM can dramatically reduce the operations and the memory to O(N). The accuracy and effectiveness of the RSF-SBM are tested through some 2D heat conduction problems including isotropic and anisotropic cases.

关键词： Singular boundary method fast algorithms Heat conduction Interpolative decomposition fast factorization

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fast and Accurate Amplitude Demodulation of Wideband Signals

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2021年 69卷 4039-4054页

作者： Gabrielaitis, Mantas IST Austria A-3400 Klosterneuburg Austria

Amplitude demodulation is a classical operation used in signal processing. For a long time, its effective applications in practice have been limited to narrowband signals. In this work, we generalize amplitude demodulation to wideband signals. We pose demodulation as a recovery problem of an oversampled corrupted signal and introduce special iterative schemes belonging to the family of alternating projection algorithms to solve it. Sensibly chosen structural assumptions on the demodulation outputs allow us to reveal the high inferential accuracy of the method over a rich set of relevant signals. This new approach surpasses current state-of-the-art demodulation techniques apt to wideband signals in computational efficiency by up to many orders of magnitude with no sacrifice in quality. Such performance opens the door for applications of the amplitude demodulation procedure in new contexts. In particular, the new method makes online and large-scale offline data processing feasible, including the calculation of modulator-carrier pairs in higher dimensions and poor sampling conditions, independent of the signal bandwidth. We illustrate the utility and specifics of applications of the new method in practice by using natural speech and synthetic signals.

关键词： Demodulation Modulation Wideband Task analysis Minimization Projection algorithms Optimization Alternating projections amplitude demodulation convex programming fast algorithms multidimensional signals nonuniform sampling speech processing wideband signals

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fast Matrix-Vector Multiplication in the Sparse-Grid Galerkin Method

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JOURNAL OF SCIENTIFIC COMPUTING 2011年第3期47卷 328-346页

作者： Zeiser, Andreas TU Berlin Inst Math D-10623 Berlin Germany

Sparse grid discretization of higher dimensional partial differential equations is a means to break the curse of dimensionality. For classical sparse grids based on the one-dimensional hierarchical basis, a sophisticated algorithm has been devised to calculate the application of a vector to the Galerkin matrix in linear complexity, despite the fact that the matrix is not sparse. However more general sparse grid constructions have been recently introduced, e.g. based on multilevel finite elements, where the specified algorithms only have a log-linear scaling. This article extends the idea of the linear scaling algorithm to more general sparse grid spaces. This is achieved by abstracting the algorithm given in (Balder and Zenger, SIAM J. Sci. Comput. 17:631, 1996) from specific bases, thereby identifying the prerequisites for performing the algorithm. In this way one can easily adapt the algorithm to specific discretizations, leading for example to an optimal linear scaling algorithm in the case of multilevel finite element frames.

关键词： Sparse grid Unidirectional principle fast algorithms Linear scaling Multilevel methods

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fast computation of the discrete Walsh and Hadamard transforms

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IEEE TRANSACTIONS ON IMAGE PROCESSING 1998年第6期7卷 898-904页

作者： Sundararajan, D Ahmad, MO Concordia Univ Dept Elect & Comp Engn Ctr Commun & Signal Proc Montreal PQ H3G 1M8 Canada

The discrete Walsh and Hadamard transforms are often used in image processing tasks such as image coding, pattern recognition, and sequency filtering. In this correspondence, a new discrete Walsh transform (DWT) algorithm is derived in which a modified form of the DWT relation is decomposed into smaller-sized transforms using vectorized quantities. A new sequency-ordered discrete Hadamard transform (DHAT) algorithm is also presented. The proposed approach results in more regular algorithms requiring no independent data swapping and fewer array-index updating and bit-reversal operations. An analysis of the computational complexity and the execution time performance are provided. The results are compared with those of the existing algorithms.

关键词： fast algorithms fast Fourier transform Walsh and Hadamard transforms

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ON THE fast SOLUTION OF A LINEAR-SYSTEM ARISING IN NUMERICAL CONFORMAL MAPPING

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 1986年第3期16卷 381-386页

作者： HUBNER, O UNIV GIESSEN INST MATHD-6300 GIESSENFED REP GER

One step of the Newton method for the discretized Theodorsen equation in conformal mapping requires the solution of a certain 2 N ×2 N system. Application of the Gaussian algorithm costs O( N 3 ) arithmetic operations (a.o.). We present an algorithm which reduces the problem to the solution of three N × N linear Toeplitz systems. These systems can be solved in O( N log 2 N ) a.o. This is also the amount of work required by the whole algorithm.

关键词： Conformal mapping Theodorsen integral equation Newton method linear systems FFT Toeplitz matrices fast algorithms

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fast tomographic reconstruction via rotation-based hierarchical backprojection

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SIAM JOURNAL ON APPLIED MATHEMATICS 2007年第2期68卷 574-597页

作者： George, Ashvin Bresler, Yoram Univ Illinois Urbana IL 61801 USA

We introduce a family of fast algorithms for tomographic backprojection in the parallel-beam geometry. The algorithms reduce the computational cost of backprojecting P projections onto an N x N pixel image from the conventional O((NP)-P-2) to O(N-2 log P). The new algorithms aggregate the projections in a hierarchical structure, with images in the hierarchy formed by the rotation and addition of other images made up of fewer projections. While these algorithms are related to existing fast algorithms, this work places them within the signal processing framework, providing a systematic means to optimize and adjust the trade-off between computational cost and accuracy. Rotations are performed separably in order that higher-order interpolators may be used with low computational cost. The same ideas are applied to create a tomographic projection algorithm, which computes projections of an N x N pixel image onto P view-angles at a cost of O( N2 log P).

关键词： radon transform fast algorithms backprojection projection tomography separable rotation spline interpolation

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Parameter-free and fast nonlinear piecewise filtering: application to experimental physics

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ANNALS OF TELECOMMUNICATIONS 2020年第11-12期75卷 655-671页

作者： Pascal, Barbara Pustelnik, Nelly Abry, Patrice Geminard, Jean-Christophe Vidal, Valerie Univ Lyon Univ Claude Bernard Lab Phys CNRSENS Lyon Lyon France

Numerous fields of nonlinear physics, very different in nature, produce signals and images that share the common feature of being essentially constituted of piecewise homogeneous phases. Analyzing signals and images from corresponding experiments to construct relevant physical interpretations thus often requires detecting such phases and estimating accurately their characteristics (borders, feature differences, horizontal ellipsis ). However, situations of physical relevance often comes with low to very low signal-to-noise ratio precluding the standard use of classical linear filtering for analysis and denoising and thus calling for the design of advanced nonlinear signal/image filtering techniques. Additionally, when dealing with experimental physics signals/images, a second limitation is the large amount of data that need to be analyzed to yield accurate and relevant conclusions requiring the design of fast algorithms. The present work proposes a unified signal/image nonlinear filtering procedure, with fast algorithms and a data-driven automated hyperparameter tuning, based on proximal algorithms and Stein unbiased estimator principles. The interest and potential of these tools are illustrated at work on low-confinement solid friction signals and porous media multiphase flows.

关键词： Nonlinear physics Solid friction Porous media multiphase flow Nonlinear filtering Proximal operators fast algorithms Automated hyperameter tuning Large size dataset

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AN ADAPTIVE fast TRANSFORM ALGORITHM FOR MULTIDIMENSIONAL DATA-COMPRESSION

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SIGNAL PROCESSING 1995年第1期43卷 29-37页

作者： MORHAC, M MATOUSEK, V Institute of Physics Slovak Academy of Sciences Dúbravská cesta 9 842 28 Bratislava Slovakia

In the paper an original method of construction special orthogonal transform for data compression has been proposed. This method is based on a direct modification of multiplication coefficients of the signal flow graph of the fast Cooley-Tukey's algorithm. The transform matrix is constructed according to the reference vector calculated from the processed data. Using this transform the compression method for multi-dimensional data has been proposed, The method has been proved effective for nuclear physics data. The results obtained using the derived transform and the classical transforms have been compared.

关键词： ORTHOGONAL TRANSFORMS DATA COMPRESSION fast algorithms MULTIDIMENSIONAL SIGNALS

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A COARSE-TO-FINE ALGORITHM FOR fast MEDIAN FILTERING OF IMAGE DATA WITH A HUGE NUMBER OF LEVELS

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SIGNAL PROCESSING 1994年第1-2期39卷 33-41页

作者： ALPARONE, L CAPPELLINI, V GARZELLI, A [a]Dipartimento di Ingegneria Electronica University of Florence via S. Marta 3 50139 Florence Italy

A two-step algorithm exploiting a reduced local grey-level histogram is proposed for efficient running-median calculation in digital monochrome images whose number of levels is considerably large, such as medical images, SAR images, or 2-D data maps. The first step borrows the concept of sliding window for fast update of the local histogram, as well as the strategy of percentile upgrade for fast median retrieval, and provides a coarse estimate of the actual median which is refined in the second stage, involving only a limited portion of the histogram. Comparisons in terms of theoretical number of operations evidence a computing time O(L2) instead of O(L), where L = L1.L2 is the number of levels, and L1 is the size of the reduced histogram. Also computer tests validate the ideal relationship and suggest a practical factorization criterion of the local histogram, when dealing with natural correlated images. Experimental results substantially prove the validity of the novel algorithm as a feasible alternative, for calculation of any rank-order value, to level-sorting techniques, whenever both classic histogram-based schemes and sorting algorithms are prohibitively time-consuming, as it happens in some practical image processing applications.

关键词： IMAGE PROCESSING MEDIAN FILTER RUNNING MEDIAN fast algorithms LOCAL HISTOGRAM

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