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Instantaneous Frequency Extraction for Nonstationary Signals via a Squeezing Operator with a fixed-point Iteration Method

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REMOTE SENSING 2024年第8期16卷 1412页

作者： Li, Zhen Gao, Zhaoqi Sun, Fengyuan Gao, Jinghuai Zhang, Wei Xi An Jiao Tong Univ Natl Engn Res Ctr Offshore Oil & Gas Explorat Sch Informat & Commun Engn Xian 710049 Peoples R China Guilin Univ Elect Technol Sch Informat & Commun Guangxi Wireless Broadband Commun & Signal Proc Ke Guilin 541004 Peoples R China

The instantaneous frequency (IF) is an important feature for the analysis of nonstationary signals. For IF estimation, the time-frequency representation (TFR)-based algorithm is used in a common class of methods. TFR-based methods always need the representation concentrated around the "true" IFs and the number of components within the signal. In this paper, we propose a novel method to adaptively estimate the IFs of nonstationary signals, even for weak components of the signals. The proposed technique is not based on the TFR: it is based on the frequency estimation operator (FEO), and the short-time Fourier transform (STFT) is used as its basis. As we know, the FRO is an exact estimation of the IF for weak frequency-modulated (FM) signals, but is not appropriate for strong FM modes. Through theoretical derivation, we determine that the fixed points of the FEOwith respect to the frequency are equivalent to the ridge of the STFT spectrum. Furthermore, the IF of the linear chirp signals is just the fixed points of the FEO. Therefore, we apply the fixed-point algorithm to the FEO to realize the precise and reliable estimation of the IF, even for highly FM signals. Finally, the results using synthetic and real signals show the utility of the proposed method for IF estimation and that it is more robust than the compared method. It should be noted that the proposed method employing the FEO only computes the first-order differential of the STFT for the chirp-like signals, while it can provide a result derived using the second-order estimation operator. Moreover, this new method is effective for the IF estimation of weak components within a signal.

关键词： instantaneous frequency frequency estimation operator linear chirp signals fixed-point algorithm weak component detection

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Learning without loss

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fixed point THEORY AND algorithmS FOR SCIENCES AND ENGINEERING 2021年第1期2021卷 1-51页

作者： Elser, Veit Cornell Univ Dept Phys Ithaca NY 14853 USA

We explore a new approach for training neural networks where all loss functions are replaced by hard constraints. The same approach is very successful in phase retrieval, where signals are reconstructed from magnitude constraints and general characteristics (sparsity, support, etc.). Instead of taking gradient steps, the optimizer in the constraint based approach, called relaxed-reflect-reflect (RRR), derives its steps from projections to local constraints. In neural networks one such projection makes the minimal modification to the inputs x, the associated weights w, and the pre-activation value y at each neuron, to satisfy the equation x & sdot;w=y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$x\cdot w=y$\end{document}. These projections, along with a host of other local projections (constraining pre- and post-activations, etc.) can be partitioned into two sets such that all the projections in each set can be applied concurrently-across the network and across all data in the training batch. This partitioning into two sets is analogous to the situation in phase retrieval and the setting for which the general purpose RRR optimizer was designed. Owing to the novelty of the method, this paper also serves as a self-contained tutorial. Starting with a single-layer network that performs nonnegative matrix factorization, and concluding with a generative model comprising an autoencoder and classifier, all applications and their implementations by projections are described in complete detail. Although the new approach has the potential to extend the scope of neural networks (e.g. by defining activation not through functions but constraint sets), most of the featured models are standard to allow comparison with stochastic gradient descent.

关键词： fixed-point algorithm Projection method Douglas-Rachford Divide and concur Machine learning Artificial neural network Nonnegative matrix factorization

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Energy-Efficient Multi-Carrier Link Adaptation with Sum Rate-Dependent Circuit Power

Energy-Efficient Multi-Carrier Link Adaptation with Sum Rate...

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IEEE Global Telecommunications Conference (GLOBECOM 2010)

作者： Isheden, Christian Fettweis, Gerhard P. Tech Univ Dresden Vodafone Chair Mobile Commun Syst D-01069 Dresden Germany

ISBN: (纸本)9781424456383

Energy-efficient link adaptation is studied for transmission on a frequency-selective parallel AWGN channel. The total power dissipation model includes a circuit power that varies with the sum rate and a power amplifier efficiency that varies with the bandwidth used. The mathematical analysis provides insight into how the subcarrier rates should be chosen for optimal energy efficiency and suggests a simple fixed-point algorithm that finds the solution in few iterations. Moreover, ways of improving the energy efficiency are discussed based on the dependence on bandwidth and distance between transmitter and receiver.

关键词： AWGN channels energy-efficient multicarrier link adaptation fixed-point algorithm frequency-selective parallel AWGN channel mathematical analysis mathematical analysis mobile communication mobile communication devices power amplifier efficiency power ampl

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New Approaches for Solving Permutation Indeterminacy and Scaling Ambiguity in Frequency Domain Separation of Convolved Mixtures

New Approaches for Solving Permutation Indeterminacy and Sca...

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International Joint Conference on Neural Networks (IJCNN)

作者： Chen, Zhitang Chan, Laiwan Chinese Univ Hong Kong Dept Comp Sci & Engn Shatin Hong Kong Peoples R China

ISBN: (纸本)9781424496365

Permutation indeterminacy and scaling ambiguity occur in ICA and they are particularly problematic in time-frequency domain separation of convolutive mixtures. The quality of separation is severely degraded if these two problems are not well addressed. In this paper, we propose new approaches to solve the permutation indeterminacy and scaling ambiguity in the separation of convolutive mixture in frequency domain. We first apply Short Time Fourier Transform to the observed signals in order to transform the convolutive mixing in time domain to instantaneous mixing in time-frequency domain. A fixed-point algorithm with test of saddle point is adopted to derive the separated components in each frequency bin. To solve the permutation problem, we propose a new matching algorithm for this purpose. First we use discrete Haar Wavelet Transform to extract the feature vectors from the magnitude waveforms of the separated components and use Singular Value Decomposition to achieve dimension reduction. The permutation problem is solved by clustering the feature vectors using the new matching algorithm which is a combination of basic K-means and Hungarian algorithm. To solve the scaling ambiguity problem, we treat it as an overcomplete problem and realize it by maximizing the posterior of the scaling factor. Finally, experiments are conducted using benchmark data to present the effectiveness and performance of our proposed algorithms.

关键词： Clustering algorithms Feature extraction Fourier transforms Haar transforms Hungarian algorithm K-means algorithm Time domain analysis Time frequency analysis Wavelet transforms blind source separation blind source separation convolution convolutive mixtures dimension reduction discrete Haar wavelet transform feature extraction feature vector extraction fixed-point algorithm independent component analysis independent component analysis matching algorithm pattern matching permutation indeterminacy scaling ambiguity problem short time Fourier transform singular value decomposition singular value decomposition time-frequency analysis time-frequency domain separation wavelet transforms

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Gas Network Hierarchical Optimisation-An Illustrative Example 14th

Gas Network Hierarchical Optimisation-An Illustrative Exampl...

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14th APCA International Conference on Automatic Control and Soft Computing (CONTROLO)

作者： Perdicoulis, T. -P. Azevedo dos Santos, P. Lopes Univ Coimbra Engn Dept ECT UTAD ISR Coimbra Portugal Univ Porto INESC TEC Porto Portugal Univ Porto EE Dept FEUP Porto Portugal

ISBN: (纸本)9783030586553;9783030586539;9783030586522

In this work, we describe the application of hierarchical coordination to gas networks optimisation, required by the problem decomposition. The problem is decomposed geographically and then special attention is given to the coordination of an iterative algorithm where every agent finds its best settings based on the decisions of its nearest-neighbours. The result is a decentralised fixed-point algorithm whose structure is described in an example network and using an algebraic setting of the kind of the transient optimisation problem, owing to the case study complexity. The method performance is assessed on the example-network.

关键词： Coordination fixed-point algorithm Gas network optimisation Graph theory Hierachical theory

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Regularized CT reconstruction on unstructured grid

Regularized CT reconstruction on unstructured grid

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Conference on Medical Imaging - Physics of Medical Imaging

作者： Chen, Yun Lu, Yao Ma, Xiangyuan Xu, Yuesheng Sun Yat Sen Univ Sch Data & Comp Sci Guangzhou 510275 Guangdong Peoples R China Sun Yat Sen Univ Sch Math & Computat Sci Guangzhou 510275 Guangdong Peoples R China Guangdong Prov Key Lab Computat Sci Guangzhou Guangdong Peoples R China

ISBN: (纸本)9781510600188

D Computed tomography (CT) is an ill-posed problem. Reconstruction on unstructured grid reduces the computational cost and alleviates the ill-posedness by decreasing the dimension of the solution space. However, there was no systematic study on edge-preserving regularization methods for CT reconstruction on unstructured grid. In this work, we propose a novel regularization method for CT reconstruction on unstructured grid, such as triangular or tetrahedral meshes generated from the initial images reconstructed via analysis reconstruction method (e.g., filtered back-projection). The proposed regularization method is modeled as a three-term optimization problem, containing a weighted least square fidelity term motivated by the simultaneous algebraic reconstruction technique (SART). The related cost function contains two non-differentiable terms, which bring difficulty to the development of the fast solver. A fixed-point proximity algorithm with SART is developed for solving the related optimization problem, and accelerating the convergence. Finally, we compare the regularized CT reconstruction method to SART with different regularization methods. Numerical experiments demonstrated that the proposed regularization method on unstructured grid is effective to suppress noise and preserve edge features.

关键词： CT reconstruction regularization unstructured grid proximity operator fixed-point algorithm

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Control of Nonlinear Systems with Reach-Avoid-Stay Specifications: A Lyapunov-Barrier Approach with an Application to the Moore-Greizer Model

Control of Nonlinear Systems with Reach-Avoid-Stay Specifica...

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American Control Conference (ACC)

作者： Meng, Yiming Li, Yinan Liu, Jun Univ Waterloo Dept Appl Math Waterloo ON Canada

ISBN: (纸本)9781665441971

The study of control synthesis for reach-avoid-stay objectives for nonlinear systems has received considerable interest in recent years. Such objectives can be naturally treated as a formal specification and effectively handled by formal methods. While formal methods often rely on constructing a finite-state approximation and developing algorithms to capture the winning set (a set of initial states from which a controller exists to realize the given task), Lyapunov methods can characterize stability and safety properties without having to discretize the state space. Inspired by recent work on converse Lyapunov-barrier theorems, we propose control Lyapunov-barrier functions to provide sufficient conditions for control synthesis with reach-avoid-stay specifications. A comparison between the proposed Lyapunov method and formal methods based on a fixed-point algorithm is illustrated by an application to enhancing the performance of jet engine compressors, which is based on a reduced Moore-Greitzer nonlinear ODE model. We apply a quadratic programming (QP) framework to reactively synthesize controllers in the case study.

关键词： Reach-avoid-stay specifications control Lyapunov-barrier functions formal methods fixed-point algorithm Moore-Greitzer nonlinear ODE model quadratic programming

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Quantitative Analyses on the Finite Precision Effect of Computerized Logistic Map

Quantitative Analyses on the Finite Precision Effect of Comp...

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International Conference on Wireless Communications and Signal Processing

作者： Zhang, Bo Wang, Guangyi Han, Chunyan Hangzhou Dianzi Univ Sch Elect Informat Hangzhou Zhejiang Peoples R China Binzhou Univ Dept Phys & Elect Sci Binzhou Shandong Peoples R China

ISBN: (纸本)9781424448562

The aperiodic chaotic signals turn out to be periodic signals in the computerizing realization due to the finite precision effect. Currently there doesn't exist quantitative analyses in this field. Inspired by the AD/DA method this paper simulates the fixed-point algorithm in floating-point environment, and then employs curve-fitting method to get the quantitative relation between the maximum cycle of the chaotic orbit and the digital precision in computerizing chaotic logistic map.

关键词： chaos Logistic map finite precision effect fixed-point algorithm

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Reconfigurable control allocation against aircraft control effector failures

Reconfigurable control allocation against aircraft control e...

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IEEE Conference on Control Applications

作者： Zhang, Youmin Suresh, V. Sivasubramaniam Jiang, Bin Theilliol, Didier Concordia Univ Dept Mech & Ind Engn Montreal PQ H3G 1M8 Canada Sauer Danfoss Aps DK-6430 Nordborg Denmark Nanjing Univ Aeronaut & Astronaut Coll Automat Engn Nanjing 210016 Peoples R China Ctr Rech Informat Nancy CNRS UMR 7039 F-54506 Vandoeuvre Les Nancy France

ISBN: (纸本)9781424404421

Due to increased requirements on the reliability, maneuverability and survivability of modern and future manned and unmanned aerial vehicles, more control effectors/surfaces are being introduced. This introduces redundant or overactuated control effectors and requires the control allocation function, together with baseline flight control law, to be implemented in the overall flight control systems. In particular, in the case of control effector (actuator) failures or control surface damages, an effective re-distribution (or reallocation) of the control surface deflections with the remaining healthy control effectors is needed in order to achieve acceptable performance even in the presence of control effector failures. In this paper, as a preliminary study of reconfigurable control allocation (control re-allocation) applied to a realistic and nonlinear aircraft model, a pseudo-inverse method and a fixed-point algorithm are implemented and tested in an ADMIRE (Aero-Data Model In Research Environment) benchmark aircraft model. Partial loss of control effectiveness faults have been implemented in the ADMIRE,benchmark and used for evaluating the control re-allocation schemes. Simulation results show satisfactory results for accommodating the control effector failures.

关键词： reconfigurable control allocation pseudo-inverse method fixed-point algorithm nonlinear aircarft model control effector failures

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EWMA-Triggered Waterfilling for Reduced-Complexity Resource Management in ad-hoc Connections

EWMA-Triggered Waterfilling for Reduced-Complexity Resource ...

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IEEE 24th International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)

作者： Gonter, Johannes Goertz, Norbert Rupp, Markus Gartner, Wolfgang Vienna Univ Technol Inst Telecommun A-1040 Vienna Austria

ISBN: (纸本)9781467362337

This paper introduces a highly efficient waterfilling-based strategy for optimal use of the channel in vehicular or personal ad-hoc communications. The approach provides near optimum allocation of resources and enables small communications devices to establish connections when the energy efficiency is at its best. Instead of calculating the transmit power through conventional waterfilling, the proposed algorithm calculates the waterlevel, thus providing a decision threshold and a strategy for optimum use of the time-variant channel at the same time. The algorithm adapts to the changing average channel quality by applying an exponentially-weighted moving-average (EWMA) trigger to re-calculate the waterlevel. The new algorithm is compared to an efficient non-iterative algorithm that directly calculates the transmit powers in every time-slot. It is shown that the new strategy reduces computation time by approximately 90% compared to the classic approach without compromising performance measures such as transmitted information or energy. Practical implementation is briefly discussed to demonstrate suitability of the algorithm for integration into tomorrow's communication devices.

关键词： Efficient Waterfilling fixed-point algorithm

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