Search results for: stochastic decomposition.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 588

Search results for: stochastic decomposition.

588 Network-Constrained AC Unit Commitment under Uncertainty Using a Bender’s Decomposition Approach

Authors: B. Janani, S. Thiruvenkadam

Abstract:

In this work, the system evaluates the impact of considering a stochastic approach on the day ahead basis Unit Commitment. Comparisons between stochastic and deterministic Unit Commitment solutions are provided. The Unit Commitment model consists in the minimization of the total operation costs considering unit’s technical constraints like ramping rates, minimum up and down time. Load shedding and wind power spilling is acceptable, but at inflated operational costs. The evaluation process consists in the calculation of the optimal unit commitment and in verifying the fulfillment of the considered constraints. For the calculation of the optimal unit commitment, an algorithm based on the Benders Decomposition, namely on the Dual Dynamic Programming, was developed. Two approaches were considered on the construction of stochastic solutions. Data related to wind power outputs from two different operational days are considered on the analysis. Stochastic and deterministic solutions are compared based on the actual measured wind power output at the operational day. Through a technique capability of finding representative wind power scenarios and its probabilities, the system can analyze a more detailed process about the expected final operational cost.

Keywords: Benders’ decomposition, network constrained AC unit commitment, stochastic programming, wind power uncertainty.

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587 Decomposition of Graphs into Induced Paths and Cycles

Authors: I. Sahul Hamid, Abraham V. M.

Abstract:

A decomposition of a graph G is a collection ψ of subgraphs H1,H2, . . . , Hr of G such that every edge of G belongs to exactly one Hi. If each Hi is either an induced path or an induced cycle in G, then ψ is called an induced path decomposition of G. The minimum cardinality of an induced path decomposition of G is called the induced path decomposition number of G and is denoted by πi(G). In this paper we initiate a study of this parameter.

Keywords: Path decomposition, Induced path decomposition, Induced path decomposition number.

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586 Induced Acyclic Path Decomposition in Graphs

Authors: Abraham V. M., I. Sahul Hamid

Abstract:

A decomposition of a graph G is a collection ψ of graphs H1,H2, . . . , Hr of G such that every edge of G belongs to exactly one Hi. If each Hi is either an induced path in G, then ψ is called an induced acyclic path decomposition of G and if each Hi is a (induced) cycle in G then ψ is called a (induced) cycle decomposition of G. The minimum cardinality of an induced acyclic path decomposition of G is called the induced acyclic path decomposition number of G and is denoted by ¤Çia(G). Similarly the cyclic decomposition number ¤Çc(G) is defined. In this paper we begin an investigation of these parameters.

Keywords: Cycle decomposition, Induced acyclic path decomposition, Induced acyclic path decomposition number.

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585 Solving Stochastic Eigenvalue Problem of Wick Type

Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

Abstract:

In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Itô chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition method using the Wiener-Itô chaos expansion. Once the approximation of the solution is performed using the finite element method for example, the statistics of the numerical solution can be easily evaluated.

Keywords: Eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Itô chaos expansion.

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584 Performance Analysis of a Discrete-time GeoX/G/1 Queue with Single Working Vacation

Authors: Shan Gao, Zaiming Liu

Abstract:

This paper treats a discrete-time batch arrival queue with single working vacation. The main purpose of this paper is to present a performance analysis of this system by using the supplementary variable technique. For this purpose, we first analyze the Markov chain underlying the queueing system and obtain its ergodicity condition. Next, we present the stationary distributions of the system length as well as some performance measures at random epochs by using the supplementary variable method. Thirdly, still based on the supplementary variable method we give the probability generating function (PGF) of the number of customers at the beginning of a busy period and give a stochastic decomposition formulae for the PGF of the stationary system length at the departure epochs. Additionally, we investigate the relation between our discretetime system and its continuous counterpart. Finally, some numerical examples show the influence of the parameters on some crucial performance characteristics of the system.

Keywords: Discrete-time queue, batch arrival, working vacation, supplementary variable technique, stochastic decomposition.

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583 Urban Growth Analysis Using Multi-Temporal Satellite Images, Non-stationary Decomposition Methods and Stochastic Modeling

Authors: Ali Ben Abbes, ImedRiadh Farah, Vincent Barra

Abstract:

Remotely sensed data are a significant source for monitoring and updating databases for land use/cover. Nowadays, changes detection of urban area has been a subject of intensive researches. Timely and accurate data on spatio-temporal changes of urban areas are therefore required. The data extracted from multi-temporal satellite images are usually non-stationary. In fact, the changes evolve in time and space. This paper is an attempt to propose a methodology for changes detection in urban area by combining a non-stationary decomposition method and stochastic modeling. We consider as input of our methodology a sequence of satellite images I1, I2, … In at different periods (t = 1, 2, ..., n). Firstly, a preprocessing of multi-temporal satellite images is applied. (e.g. radiometric, atmospheric and geometric). The systematic study of global urban expansion in our methodology can be approached in two ways: The first considers the urban area as one same object as opposed to non-urban areas (e.g. vegetation, bare soil and water). The objective is to extract the urban mask. The second one aims to obtain a more knowledge of urban area, distinguishing different types of tissue within the urban area. In order to validate our approach, we used a database of Tres Cantos-Madrid in Spain, which is derived from Landsat for a period (from January 2004 to July 2013) by collecting two frames per year at a spatial resolution of 25 meters. The obtained results show the effectiveness of our method.

Keywords: Multi-temporal satellite image, urban growth, Non-stationarity, stochastic modeling.

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582 Blind Channel Estimation Based on URV Decomposition Technique for Uplink of MC-CDMA

Authors: Pradya Pornnimitkul, Suwich Kunaruttanapruk, Bamrung Tau Sieskul, Somchai Jitapunkul

Abstract:

In this paper, we investigate a blind channel estimation method for Multi-carrier CDMA systems that use a subspace decomposition technique. This technique exploits the orthogonality property between the noise subspace and the received user codes to obtain channel of each user. In the past we used Singular Value Decomposition (SVD) technique but SVD have most computational complexity so in this paper use a new algorithm called URV Decomposition, which serve as an intermediary between the QR decomposition and SVD, replaced in SVD technique to track the noise space of the received data. Because of the URV decomposition has almost the same estimation performance as the SVD, but has less computational complexity.

Keywords: Channel estimation, MC-CDMA, SVD, URV.

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581 Solving SPDEs by a Least Squares Method

Authors: Hassan Manouzi

Abstract:

We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: Least squares, Wick product, SPDEs, finite element, Wiener chaos expansion, gradient method.

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580 Calculation of Reorder Point Level under Stochastic Parameters: A Case Study in Healthcare Area

Authors: Serap Akcan, Ali Kokangul

Abstract:

We consider a single-echelon, single-item inventory system where both demand and lead-time are stochastic. Continuous review policy is used to control the inventory system. The objective is to calculate the reorder point level under stochastic parameters. A case study is presented in Neonatal Intensive Care Unit.

Keywords: Inventory control system, reorder point level, stochastic demand, stochastic lead time

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579 Generalized Morphological 3D Shape Decomposition Grayscale Interframe Interpolation Method

Authors: Dragos Nicolae VIZIREANU

Abstract:

One of the main image representations in Mathematical Morphology is the 3D Shape Decomposition Representation, useful for Image Compression and Representation,and Pattern Recognition. The 3D Morphological Shape Decomposition representation can be generalized a number of times,to extend the scope of its algebraic characteristics as much as possible. With these generalizations, the Morphological Shape Decomposition 's role to serve as an efficient image decomposition tool is extended to grayscale images.This work follows the above line, and further develops it. Anew evolutionary branch is added to the 3D Morphological Shape Decomposition's development, by the introduction of a 3D Multi Structuring Element Morphological Shape Decomposition, which permits 3D Morphological Shape Decomposition of 3D binary images (grayscale images) into "multiparameter" families of elements. At the beginning, 3D Morphological Shape Decomposition representations are based only on "1 parameter" families of elements for image decomposition.This paper addresses the gray scale inter frame interpolation by means of mathematical morphology. The new interframe interpolation method is based on generalized morphological 3D Shape Decomposition. This article will present the theoretical background of the morphological interframe interpolation, deduce the new representation and show some application examples.Computer simulations could illustrate results.

Keywords: 3D shape decomposition representation, mathematical morphology, gray scale interframe interpolation

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578 Non-Stationary Stochastic Optimization of an Oscillating Water Column

Authors: María L. Jalón, Feargal Brennan

Abstract:

A non-stationary stochastic optimization methodology is applied to an OWC (oscillating water column) to find the design that maximizes the wave energy extraction. Different temporal cycles are considered to represent the long-term variability of the wave climate at the site in the optimization problem. The results of the non-stationary stochastic optimization problem are compared against those obtained by a stationary stochastic optimization problem. The comparative analysis reveals that the proposed non-stationary optimization provides designs with a better fit to reality. However, the stationarity assumption can be adequate when looking at averaged system response.

Keywords: Non-stationary stochastic optimization, oscillating water column, temporal variability, wave energy.

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577 Dynamic Slope Scaling Procedure for Stochastic Integer Programming Problem

Authors: Takayuki Shiina

Abstract:

Mathematical programming has been applied to various problems. For many actual problems, the assumption that the parameters involved are deterministic known data is often unjustified. In such cases, these data contain uncertainty and are thus represented as random variables, since they represent information about the future. Decision-making under uncertainty involves potential risk. Stochastic programming is a commonly used method for optimization under uncertainty. A stochastic programming problem with recourse is referred to as a two-stage stochastic problem. In this study, we consider a stochastic programming problem with simple integer recourse in which the value of the recourse variable is restricted to a multiple of a nonnegative integer. The algorithm of a dynamic slope scaling procedure for solving this problem is developed by using a property of the expected recourse function. Numerical experiments demonstrate that the proposed algorithm is quite efficient. The stochastic programming model defined in this paper is quite useful for a variety of design and operational problems.

Keywords: stochastic programming problem with recourse, simple integer recourse, dynamic slope scaling procedure

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576 Stochastic Estimation of Cavity Flowfield

Authors: Yin Yin Pey, Leok Poh Chua, Wei Long Siauw

Abstract:

Linear stochastic estimation and quadratic stochastic estimation techniques were applied to estimate the entire velocity flow-field of an open cavity with a length to depth ratio of 2. The estimations were done through the use of instantaneous velocity magnitude as estimators. These measurements were obtained by Particle Image Velocimetry. The predicted flow was compared against the original flow-field in terms of the Reynolds stresses and turbulent kinetic energy. Quadratic stochastic estimation proved to be more superior than linear stochastic estimation in resolving the shear layer flow. When the velocity fluctuations were scaled up in the quadratic estimate, both the time-averaged quantities and the instantaneous cavity flow can be predicted to a rather accurate extent.

Keywords: Open cavity, Particle Image Velocimetry, Stochastic estimation, Turbulent kinetic energy.

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575 Stochastic Programming Model for Power Generation

Authors: Takayuki Shiina

Abstract:

We consider power system expansion planning under uncertainty. In our approach, integer programming and stochastic programming provide a basic framework. We develop a multistage stochastic programming model in which some of the variables are restricted to integer values. By utilizing the special property of the problem, called block separable recourse, the problem is transformed into a two-stage stochastic program with recourse. The electric power capacity expansion problem is reformulated as the problem with first stage integer variables and continuous second stage variables. The L-shaped algorithm to solve the problem is proposed.

Keywords: electric power capacity expansion problem, integerprogramming, L-shaped method, stochastic programming

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574 N-Sun Decomposition of Complete Graphs and Complete Bipartite Graphs

Authors: R. Anitha, R. S. Lekshmi

Abstract:

Graph decompositions are vital in the study of combinatorial design theory. Given two graphs G and H, an H-decomposition of G is a partition of the edge set of G into disjoint isomorphic copies of H. An n-sun is a cycle Cn with an edge terminating in a vertex of degree one attached to each vertex. In this paper we have proved that the complete graph of order 2n, K2n can be decomposed into n-2 n-suns, a Hamilton cycle and a perfect matching, when n is even and for odd case, the decomposition is n-1 n-suns and a perfect matching. For an odd order complete graph K2n+1, delete the star subgraph K1, 2n and the resultant graph K2n is decomposed as in the case of even order. The method of building n-suns uses Walecki's construction for the Hamilton decomposition of complete graphs. A spanning tree decomposition of even order complete graphs is also discussed using the labeling scheme of n-sun decomposition. A complete bipartite graph Kn, n can be decomposed into n/2 n-suns when n/2 is even. When n/2 is odd, Kn, n can be decomposed into (n-2)/2 n-suns and a Hamilton cycle.

Keywords: Hamilton cycle, n-sun decomposition, perfectmatching, spanning tree.

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573 Analysis of Catalytic Properties of Ni3Al Thin Foils for the Methanol and Hexane Decomposition

Authors: M. Michalska-Domańska, P. Jóźwik, Z. Bojar

Abstract:

Intermetallic Ni3Al – based alloys belong to a group of advanced materials characterized by good chemical and physical properties (such as structural stability, corrosion resistance) which offer advenced technological applications. The paper presents the study of catalytic properties of Ni3Al foils (thickness approximately 50 &m) in the methanol and hexane decomposition. The egzamined material posses microcrystalline structure without any additional catalysts on the surface. The better catalytic activity of Ni3Al foils with respect to quartz plates in both methanol and hexane decomposition was confirmed. On thin Ni3Al foils the methanol conversion reaches approximately 100% above 480 oC while the hexane conversion reaches approximately 100% (98,5%) at 500 oC. Deposit formed during the methanol decomposition is built up of carbon nanofibers decorated with metal-like nanoparticles.

Keywords: hexane decomposition, methanol decomposition, Ni3Al thin foils, Ni nanoparticles

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572 Stochastic Scheduling to Minimize Expected Lateness in Multiple Identical Machines

Authors: Ghulam Zakria, Zailin Guan , Yasser Riaz Awan, Wan Lizhi

Abstract:

There are many real world problems in which parameters like the arrival time of new jobs, failure of resources, and completion time of jobs change continuously. This paper tackles the problem of scheduling jobs with random due dates on multiple identical machines in a stochastic environment. First to assign jobs to different machine centers LPT scheduling methods have been used, after that the particular sequence of jobs to be processed on the machine have been found using simple stochastic techniques. The performance parameter under consideration has been the maximum lateness concerning the stochastic due dates which are independent and exponentially distributed. At the end a relevant problem has been solved using the techniques in the paper..

Keywords: Quantity Production Flow Shop, LPT Scheduling, Stochastic Scheduling, Maximum Lateness, Random Due Dates

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571 Optimizing Approach for Sifting Process to Solve a Common Type of Empirical Mode Decomposition Mode Mixing

Authors: Saad Al-Baddai, Karema Al-Subari, Elmar Lang, Bernd Ludwig

Abstract:

Empirical mode decomposition (EMD), a new data-driven of time-series decomposition, has the advantage of supposing that a time series is non-linear or non-stationary, as is implicitly achieved in Fourier decomposition. However, the EMD suffers of mode mixing problem in some cases. The aim of this paper is to present a solution for a common type of signals causing of EMD mode mixing problem, in case a signal suffers of an intermittency. By an artificial example, the solution shows superior performance in terms of cope EMD mode mixing problem comparing with the conventional EMD and Ensemble Empirical Mode decomposition (EEMD). Furthermore, the over-sifting problem is also completely avoided; and computation load is reduced roughly six times compared with EEMD, an ensemble number of 50.

Keywords: Empirical mode decomposition, mode mixing, sifting process, over-sifting.

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570 N-Sun Decomposition of Complete, Complete Bipartite and Some Harary Graphs

Authors: R. Anitha, R. S. Lekshmi

Abstract:

Graph decompositions are vital in the study of combinatorial design theory. A decomposition of a graph G is a partition of its edge set. An n-sun graph is a cycle Cn with an edge terminating in a vertex of degree one attached to each vertex. In this paper, we define n-sun decomposition of some even order graphs with a perfect matching. We have proved that the complete graph K2n, complete bipartite graph K2n, 2n and the Harary graph H4, 2n have n-sun decompositions. A labeling scheme is used to construct the n-suns.

Keywords: Decomposition, Hamilton cycle, n-sun graph, perfect matching, spanning tree.

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569 Comparison of Reliability Systems Based Uncertainty

Authors: A. Aissani, H. Benaoudia

Abstract:

Stochastic comparison has been an important direction of research in various area. This can be done by the use of the notion of stochastic ordering which gives qualitatitive rather than purely quantitative estimation of the system under study. In this paper we present applications of comparison based uncertainty related to entropy in Reliability analysis, for example to design better systems. These results can be used as a priori information in simulation studies.

Keywords: Uncertainty, Stochastic comparison, Reliability, serie's system, imperfect repair.

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568 On Diffusion Approximation of Discrete Markov Dynamical Systems

Authors: Jevgenijs Carkovs

Abstract:

The paper is devoted to stochastic analysis of finite dimensional difference equation with dependent on ergodic Markov chain increments, which are proportional to small parameter ". A point-form solution of this difference equation may be represented as vertexes of a time-dependent continuous broken line given on the segment [0,1] with "-dependent scaling of intervals between vertexes. Tending " to zero one may apply stochastic averaging and diffusion approximation procedures and construct continuous approximation of the initial stochastic iterations as an ordinary or stochastic Ito differential equation. The paper proves that for sufficiently small " these equations may be successfully applied not only to approximate finite number of iterations but also for asymptotic analysis of iterations, when number of iterations tends to infinity.

Keywords: Markov dynamical system, diffusion approximation, equilibrium stochastic stability.

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567 The Strict Stability of Impulsive Stochastic Functional Differential Equations with Markovian Switching

Authors: Dezhi Liu Guiyuan Yang Wei Zhang

Abstract:

Strict stability can present the rate of decay of the solution, so more and more investigators are beginning to study the topic and some results have been obtained. However, there are few results about strict stability of stochastic differential equations. In this paper, using Lyapunov functions and Razumikhin technique, we have gotten some criteria for the strict stability of impulsive stochastic functional differential equations with markovian switching.

Keywords: Impulsive; Stochastic functional differential equation; Strict stability; Razumikhin technique.

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566 Mean Square Stability of Impulsive Stochastic Delay Differential Equations with Markovian Switching and Poisson Jumps

Authors: Dezhi Liu

Abstract:

In the paper, based on stochastic analysis theory and Lyapunov functional method, we discuss the mean square stability of impulsive stochastic delay differential equations with markovian switching and poisson jumps, and the sufficient conditions of mean square stability have been obtained. One example illustrates the main results. Furthermore, some well-known results are improved and generalized in the remarks.

Keywords: Impulsive, stochastic, delay, Markovian switching, Poisson jumps, mean square stability.

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565 Segmentation of Noisy Digital Images with Stochastic Gradient Kernel

Authors: Abhishek Neogi, Jayesh Verma, Pinaki Pratim Acharjya

Abstract:

Image segmentation and edge detection is a fundamental section in image processing. In case of noisy images Edge Detection is very less effective if we use conventional Spatial Filters like Sobel, Prewitt, LOG, Laplacian etc. To overcome this problem we have proposed the use of Stochastic Gradient Mask instead of Spatial Filters for generating gradient images. The present study has shown that the resultant images obtained by applying Stochastic Gradient Masks appear to be much clearer and sharper as per Edge detection is considered.

Keywords: Image segmentation, edge Detection, noisy images, spatialfilters, stochastic gradient kernel.

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564 Noise Analysis of Single-Ended Input Differential Amplifier using Stochastic Differential Equation

Authors: Tarun Kumar Rawat, Abhirup Lahiri, Ashish Gupta

Abstract:

In this paper, we analyze the effect of noise in a single- ended input differential amplifier working at high frequencies. Both extrinsic and intrinsic noise are analyzed using time domain method employing techniques from stochastic calculus. Stochastic differential equations are used to obtain autocorrelation functions of the output noise voltage and other solution statistics like mean and variance. The analysis leads to important design implications and suggests changes in the device parameters for improved noise characteristics of the differential amplifier.

Keywords: Single-ended input differential amplifier, Noise, stochastic differential equation, mean and variance.

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563 A Scenario-Based Approach for the Air Traffic Flow Management Problem with Stochastic Capacities

Authors: Soumia Ichoua

Abstract:

In this paper, we investigate the strategic stochastic air traffic flow management problem which seeks to balance airspace capacity and demand under weather disruptions. The goal is to reduce the need for myopic tactical decisions that do not account for probabilistic knowledge about the NAS near-future states. We present and discuss a scenario-based modeling approach based on a time-space stochastic process to depict weather disruption occurrences in the NAS. A solution framework is also proposed along with a distributed implementation aimed at overcoming scalability problems. Issues related to this implementation are also discussed.

Keywords: Air traffic management, sample average approximation, scenario-based approach, stochastic capacity.

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562 New Subband Adaptive IIR Filter Based On Polyphase Decomposition

Authors: Young-Seok Choi

Abstract:

We present a subband adaptive infinite-impulse response (IIR) filtering method, which is based on a polyphase decomposition of IIR filter. Motivated by the fact that the polyphase structure has benefits in terms of convergence rate and stability, we introduce the polyphase decomposition to subband IIR filtering, i.e., in each subband high order IIR filter is decomposed into polyphase IIR filters with lower order. Computer simulations demonstrate that the proposed method has improved convergence rate over conventional IIR filters.

Keywords: Subband adaptive filter, IIR filtering. Polyphase decomposition.

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561 PTH Moment Exponential Stability of Stochastic Recurrent Neural Networks with Distributed Delays

Authors: Zixin Liu, Jianjun Jiao Wanping Bai

Abstract:

In this paper, the issue of pth moment exponential stability of stochastic recurrent neural network with distributed time delays is investigated. By using the method of variation parameters, inequality techniques, and stochastic analysis, some sufficient conditions ensuring pth moment exponential stability are obtained. The method used in this paper does not resort to any Lyapunov function, and the results derived in this paper generalize some earlier criteria reported in the literature. One numerical example is given to illustrate the main results.

Keywords: Stochastic recurrent neural networks, pth moment exponential stability, distributed time delays.

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560 A Computational Stochastic Modeling Formalism for Biological Networks

Authors: Werner Sandmann, Verena Wolf

Abstract:

Stochastic models of biological networks are well established in systems biology, where the computational treatment of such models is often focused on the solution of the so-called chemical master equation via stochastic simulation algorithms. In contrast to this, the development of storage-efficient model representations that are directly suitable for computer implementation has received significantly less attention. Instead, a model is usually described in terms of a stochastic process or a "higher-level paradigm" with graphical representation such as e.g. a stochastic Petri net. A serious problem then arises due to the exponential growth of the model-s state space which is in fact a main reason for the popularity of stochastic simulation since simulation suffers less from the state space explosion than non-simulative numerical solution techniques. In this paper we present transition class models for the representation of biological network models, a compact mathematical formalism that circumvents state space explosion. Transition class models can also serve as an interface between different higher level modeling paradigms, stochastic processes and the implementation coded in a programming language. Besides, the compact model representation provides the opportunity to apply non-simulative solution techniques thereby preserving the possible use of stochastic simulation. Illustrative examples of transition class representations are given for an enzyme-catalyzed substrate conversion and a part of the bacteriophage λ lysis/lysogeny pathway.

Keywords: Computational Modeling, Biological Networks, Stochastic Models, Markov Chains, Transition Class Models.

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559 A Novel Instantaneous Frequency Computation Approach for Empirical Mode Decomposition

Authors: Liming Zhang

Abstract:

This paper introduces a new instantaneous frequency computation approach  -Counting Instantaneous Frequency for a general class of signals called simple waves. The classsimple wave contains a wide range of continuous signals for which the concept instantaneous frequency has a perfect physical sense. The concept of  -Counting Instantaneous Frequency also applies to all the discrete data. For all the simple wave signals and the discrete data, -Counting instantaneous frequency can be computed directly without signal decomposition process. The intrinsic mode functions obtained through empirical mode decomposition belongs to simple wave. So  -Counting instantaneous frequency can be used together with empirical mode decomposition.

Keywords: Instantaneous frequency, empirical mode decomposition, intrinsic mode function.

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