Double Preconditioning for Gabor Frames

Projective modules over noncommutative tori are multi-window Gabor frames for modulation spaces

In this paper, from the point of view reducing the system calculation cost, a digital channelized receiver is proposed. The decimation factor of the proposed digital channelized receiver with low calculation cost is equal to the number of signal channels, which is acquired by changing the input signal of the embedded instantaneous frequency measurement receiver. Due to the increase of the system decimation factor, the data to be processed are decreased and the system processing speed is improved indirectly. In this paper, the architecture and working principle of the proposed digital channelized receiver with low calculation cost is firstly given; secondly, the overlapping channel division method used in the digital channelized receiver with low calculation cost is put forward. Meanwhile, the channel arbitration method of the unmodulated or modulated signal in the case of overlapping channel division is analyzed. Then, the frequency measurement principle of the embedded instantaneous frequency measurement receiver is deduced in detail. Through the use of the overlapping channel division method, the proposed digital channelized receiver with low calculation cost is able to avoid the existence of blind spots between channels and increases the interception probabilities of the input signals. And, the proposed digital channelized receiver can distinguish two signals coming simultaneously to the same channel by using the overlapping channel division method. In addition, the channel of the input signal truly residing can be simply determined by using the channel arbitration in the case of overlapping channel division and according to the output frequency of the embedded instantaneous frequency measurement receiver. Finally, the related simulation results verify the correctness and feasibility of the theories and method involved in this paper.

Disentangled convolution for optimizing receptive field

We introduce the Banach space S 0 ⊑ L 2 which has a variety of properties making it a useful tool in Gabor analysis. S 0 can be characterized as the smallest time-frequency homogeneous Banach space of (continuous) functions. We also present other characterizations of S 0 turning it into a very flexible tool for Gabor analysis and allowing for simplifications of various proofs. A careful analysis of both the coefficient and the synthesis mapping in Gabor theory shows that an arbitrary window in S 0 not only is a Bessel atom with respect to arbitrary time-frequency lattices, but also yields boundedness between S 0 and e 1. On the other hand, we can study properties of general L 2-atoms since they induce mappings from S 0 to S′0. This enables us to introduce a new, very natural concept of weak duality of Gabor atoms, applying also to the classical pair of the Gauss-function and its dual function determined by Bastiaans. Using the established results, we show a variety of properties that are desirable in applications, like the continuous dependence of the canonical dual window on the given Gabor window and on the lattice; continuity of thresholding and masking operators from signal processing; and an algorithm for the reconstruction of bandlimited functions from samples of the Gabor transform in a corresponding horizontal strip in the time-frequency plane. We also present an approximate Balian-Low Theorem stating that for close-to-critical lattices, the dual Gabor atoms progressively lose their time-frequency localization.

Real polynomial root-finding by means of matrix and polynomial iterations

MIMO system identification is a fundamental concern in a variety of applications. Various iterative and recursive MIMO system identification algorithms exist in the literature. The iterative algorithms suffer from high computational cost due to large matrix computations and recursive algorithms suffer from slow convergence speed. This paper proposes a fast recursive exact least squares algorithm for MIMO system identification with fast convergence speed and low computational cost. The recursions of the algorithm give rise to a lattice structure. The lattice structure is less sensitive to round-off errors, coefficients variations and can also be used for model order reduction. Although in this work we estimate an FIR (finite impulse response) model of the MIMO system, the framework can also be used for IIR (infinite impulse response) models, and for estimating linear periodically time varying (LPTV) and multivariable systems. The theory proposed is validated using simulation results.

Parametric matched filter based on interference iteration

In this paper, FLANN(functional link ANN) filter is presented for Gaussian noise. FLANN is a singer layer with expanded input vectors and has lower computational cost than MLP(multilayer perceptron). Three types of functional expansion are discussed. BP(back propagation algorithm) for nonlinear activation function and matrix calculation for identical activation function are exploited for training FLANN. Simulation shows that convergence is not guaranteed in BP and related to the initial weight matrix and training images, and that linear FLANN trained by matrix calculation performs better than both nonlinear FLANN trained by BP and Wiener filter in detail region in environment of Gaussian noise

Recently target detection is widely regarded as a typical hot spot in research of sensor networks. A fast target detection algorithm is proposed by using the hypothesis testing (HT) method in the paper. The objective is to determine whether a target is present in a sensor network for decision-makers. Due to the nature of sensor networks, it is desirable to have a fast algorithm to accomplish the detection and judgment process with low computation cost on a distributed network end node. In the paper mobile target detection is formulated as a statistical inference problem according to the mathematical statistics theory. Moreover, a data fusion process with several sensors is also designed to optimize the final decision result for detection synthesis. It has the advantage of low computational complexity, good performance of real time, and yields high target detection correctness. Numerical experiments are used to demonstrate the efficiency of the HT detection algorithm, where magnetic sensors are applied to collect the output signal from an undetermined target.

Meta-heuristic algorithms are widely viewed as feasible techniques to solve continuous large-scale numerical optimization problems. Grey wolf optimizer (GWO) is a relatively new stochastic algorithm with only a few parameters to adjust that can be easily used for global optimization. This paper presents an efficient and robust GWO (ERGWO) variant to solve large-scale numerical optimization problems. Inspired by particle swarm optimization, a nonlinearly adjustment strategy for parameter control is designed to balance exploration and exploitation. Additionally, a modified position-updating equation is presented to improve convergence speed. The performance of ERGWO is verified on 18 benchmark large-scale numerical optimization problems with dimensions ranging from 30 to 10,000, 30 benchmarks from CEC 2014, 30 functions in CEC 2017, respectively. Numerical experiments are performed to compare ERGWO to the basic GWO algorithm, other GWO variants, and other well-known meta-heuristic search techniques. Simulations demonstrate that the proposed ERGWO algorithm can find high quality solutions with low computational cost and very fast convergence.

We propose in this work a simple framework to build a hierarchical family of tumor growth models by selecting a subset of the most important parameters of our base model with respect to the evolution of the tumor volume. The importance of each parameter is identified through a model-free sensitivity analysis technique, the elementary effects (EE), due to its simplicity and low computational cost. This model framework encompasses the essential hypotheses and the limited set of important parameters acquired from the sensitivity analysis. In this way, we are able to create a family of models described by at least the same essential conditions and parameters but with different complexities regarding the number of parameters used. Numerical experiments are conducted to show the reasoning behind the hierarchical developed family of tumor growth modes. The modeling framework in this manner provides a powerful way for studying a model itself or either its simplification or extension. The framework can also be tailored to form the basis for future models, incorporating new processes and phenomena.

Analytical models have been exhaustively used to study simple seawater intrusion problems and the sustainable management of groundwater resources in coastal aquifers because of its simplicity, easy implementation, and low computational cost. Most of these models are based on the sharp‐interface approximation and the Ghyben–Herzberg relation, and their governing equations are expressed in terms of a single potential theory to calculate critical pumping rates in a coastal pumping scenario. The Ghyben–Herzberg approach neglects mixing of fresh water and seawater and implicitly assumes that salt water remains static. Therefore, the results of the analytical solutions may be inaccurate and unacceptable for some real‐complex case studies. This paper provides insight into the validity of sharp‐interface models to deal with seawater intrusion in coastal aquifers, i.e. when they can be applied to obtain accurate enough results. For that purpose, this work compares sharp‐interface solutions, based on the Ghyben–Herzberg approach, with numerical three‐dimensional variable‐density flow simulations for a set of heterogeneous groundwater flow and mass transport parameters, and different scenarios of spatially distributed recharge values and spatial wells placement. The numerical experiment has been carried out in a 3D unconfined synthetic aquifer using the finite difference numerical code SEAWAT for solving the coupled partial differential equations of flow and density‐dependent transport. This paper finds under which situations the sharp‐interface solution gives good predictions in terms of seawater penetration, transition zone width and critical pumping rates. Additionally, the simulation runs indicate to which parameters and scenarios the results are more sensitive. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we first propose and analyze a novel mixed-type DG method for the coupled Stokes--Darcy problem on simplicial meshes. The proposed formulation is locally conservative. A mixed-type DG method in conjunction with the stress-velocity formulation is employed for the Stokes equations, where the symmetry of stress is strongly imposed. The staggered DG method is exploited to discretize the Darcy equations. As such, the discrete formulation can be easily adapted to account for the Beavers--Joseph--Saffman interface conditions without introducing additional variables. Importantly, the continuity of normal velocity is satisfied exactly at the discrete level. A rigorous convergence analysis is performed for all the variables. Then we devise and analyze a domain decomposition method via the use of Robin-type interface boundary conditions, which allows us to solve the Stokes subproblem and the Darcy subproblem sequentially with low computational costs. The convergence of the proposed iterative method is analyzed rigorously. In particular, the proposed iterative method also works for very small viscosity coefficient. Finally, several numerical experiments are carried out to demonstrate the capabilities and accuracy of the novel mixed-type scheme, and the convergence of the domain decomposition method.

In the future, energy storage systems (ESSs) will be widely deployed on the generation side of renewable energy to smooth its power fluctuations. To optimize the revenue of wind farm with ESSs, it is economical to combine the low operating cost of wind turbines with the high regulation accuracy of ESSs to deliver frequency regulation and energy services to the power system. In this paper, a two-stage flexible coordination scheme is proposed for the wind farm with ESSs in a joint energy and frequency regulation market. In the first stage, utilizing the day-ahead prediction results, the strategy space is optimized through dynamic programming. In second stage, taking the short-term prediction results into account, a rolling programming algorithm is proposed to revise the real-time policy and cope with the impact of day-ahead prediction errors. This scheme enables the real-time prediction and optimization with relatively low computational cost. Additionally, the internal power distribution of the wind farm for each wind turbines is also considered. The validity and real-time performance of the proposed two-stage framework is proved through numerical experiments.

Waste heat recovery aims to increase the overall system efficiency and thus, reduce emissions. One technology commonly considered is the Organic Rankine Cycle (ORC) which uses a refrigerant as the working fluid. For an efficient operation of the ORC, the different components, e.g., the turbine, need to be optimised considering the entire system. This paper investigates the capability of meanline modelling for nozzled turbines to model the non-ideal gas effects of different refrigerants. For optimal implementation at a system level, it is important to have sufficient accuracy and low computational cost. The meanline model was compared with CFD for three different working fluids. A 3D parametric model was generated, and a numerical experiment was performed using Latin Hypercube Sampling. Seven meanline design parameters were investigated over a broad design space to show the influence of each respective one on turbine performance. Subsequently, the meanline model was calibrated against a subset of geometries and compared to the entire data sample. The average error stayed below 5%, which is sufficiently accurate for preliminary-stage calculations.