Intrinsic Fourier Mode Functions

2017 ◽  
Vol 09 (02) ◽  
pp. 1750003
Author(s):  
Vesselin Vatchev
Keyword(s):  
Instantaneous Frequency ◽  
Sufficient Condition ◽  
Fourier Mode ◽  
Intrinsic Mode Functions ◽  
Numerical Examples ◽  
Class Of Functions

In this paper, we study a class of functions that exhibit properties expected from intrinsic mode functions. A type of an empirical instantaneous frequency, depending on the extrema scale, is introduced and its proximity to the classical analytic instantaneous frequency is discussed. We also obtain a sufficient condition for positiveness of the instantaneous frequency and introduce a method similar in nature to EMD but with an empirical frequency as guide in lieu of empirical envelopes. The method is illustrated in several numerical examples.

scholarly journals Certain subclasses of analytic functions involving complex order

Filomat ◽  
2008 ◽  
Vol 22 (2) ◽  
pp. 115-122 ◽  
Author(s):  
T.N. Shanmugam ◽  
S. Sivasubramanian ◽  
B.A. Frasin
Keyword(s):  
Analytic Functions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Complex Order ◽  
Necessary And Sufficient ◽  
Class Of Functions

In the present investigation, we consider an unified class of functions of complex order. Necessary and sufficient condition for functions to be in this class is obtained. The results obtained in this paper generalizes the results obtained by Srivastava and Lashin [10], and Ravichandran et al. [4]. .

scholarly journals On the asymptotic boundary behavior of functions analytic in the unit disk

1977 ◽  
Vol 67 ◽  
pp. 1-13
Author(s):  
James R. Choike
Keyword(s):  
Riemann Surface ◽  
Analytic Function ◽  
Unit Disk ◽  
Boundary Behavior ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Asymptotic Boundary ◽  
Necessary And Sufficient ◽  
Class Of Functions

In [8] a necessary and sufficient condition was given for determining the equivalence of two asymptotic boundary paths for an analytic function w = f(p) on a Riemann surface F. In this paper we give a necessary and sufficient condition for determining the nonequivalence of two asymptotic boundary paths for f(z) analytic in |z| < R, 0 < R ≤ + ∞. We shall, also, illustrate some applications of the main result and examine a class of functions introduced by Valiron.

A note on the age-dependent branching process with immigration

1975 ◽  
Vol 12 (01) ◽  
pp. 130-134 ◽  
Author(s):  
Norman Kaplan
Keyword(s):  
General Class ◽  
Branching Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Direct Generalization ◽  
Age Dependent ◽  
General Class Of Functions ◽  
Branching Process With Immigration ◽  
Necessary And Sufficient ◽  
Class Of Functions

Let {Z(t)}t0be an age-dependent branching process with immigration. For a general class of functions Φ(x), a necessary and sufficient condition is given for whenE{Φ (Z(t))} &lt;∞. This result is a direct generalization of a theorem proven for the branching process without immigration.

scholarly journals A Connection between Basic Univalence Criteria

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Horiana Tudor
Keyword(s):  
Integral Operator ◽  
Sufficient Condition ◽  
Univalence Criteria ◽  
Class Of Functions

We obtain a sufficient condition for the analyticity and the univalence of a class of functions defined by an integral operator. The well-known univalence criteria of Alexander, Noshiro-Warschawski, Nehari, Goluzin, Ozaki-Nunokawa, Becker, and Lewandowski would follow upon specializing the functions and the parameters involved in the main result. The results obtained not only reduce to those earlier works, but they also extend the previous results.

Research on an Algorithm and System for Estimation of Instantaneous Frequency of Rotating Machinery

2012 ◽  
Vol 452-453 ◽  
pp. 153-159
Author(s):  
Rong Qing Yao
Keyword(s):  
Embedded System ◽  
Instantaneous Frequency ◽  
Vibration Signal ◽  
Average Frequency ◽  
Rotating Machinery ◽  
Intrinsic Mode Functions ◽  
System Technology ◽  
Mode Decomposition ◽  
Phase Signal ◽  
The Embedded System

Instantaneous frequency is an import parameter to diagnose faults of rotating machinery. This paper puts forward an algorithm based Hilbert-Huang Transformation (HHT) to estimate the instantaneous frequency of rotating machinery and develops an instantaneous cymometer based embedded system technology. In order to estimate instantaneous frequency of rotating machinery, the vibration signal is decomposed into a series of intrinsic mode functions (IMF) first by the method of empirical mode decomposition (EMD), then one of the intrinsic mode functions is analyzed with the Hilbert transformation to acquire an estimate value of instantaneous frequency. An instantaneous cymometer is also described in this paper, which is designed to measure the average frequency and instantaneous frequency of rotating machinery in real time. The average frequency is acquired from measuring the cycle of key-phase signal, and the instantaneous frequency is from the above-mentioned method based HHT. The instantaneous cymometer is consisted of an embedded system, which is connected to a PC with an Ethernet. The embedded system is based on an ARM chip (Samsung S3C4510) A/D conversion, EMD and Hilbert transform are completed on the embedded system, and then the results are compressed and sent to the PC by TCP/IP.

scholarly journals ANALYSIS OF TEMPORAL VARIATIONS IN TURBIDITY FOR A COASTAL AREA USING THE HILBERT-HUANG-TRANSFORM

2011 ◽  
Vol 1 (32) ◽  
pp. 25
Author(s):  
Shigeru Kato ◽  
Magnus Larson ◽  
Takumi Okabe ◽  
Shin-ichi Aoki
Keyword(s):  
Instantaneous Frequency ◽  
River Mouth ◽  
Original Data ◽  
Temporal Variations ◽  
Intrinsic Mode Functions ◽  
Hilbert Spectrum ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Mode Decomposition ◽  
The Hilbert Transform

Turbidity data obtained by field observations off the Tenryu River mouth were analyzed using the Hilbert-Huang Transform (HHT) in order to investigate the characteristic variations in time and in the frequency domain. The Empirical Mode Decomposition (EMD) decomposed the original data into only eight intrinsic mode functions (IMFs) and a residue in the first step of the HHT. In the second step, the Hilbert transform was applied to the IMFs to calculate the Hilbert spectrum, which is the time-frequency distribution of the instantaneous frequency and energy. The changes in instantaneous frequencies showed correspondence to high turbidity events in the Hilbert spectrum. The investigation of instantaneous frequency variations can be used to understand transitions in the state of the turbidity. The comparison between the Fourier spectrum and the Hilbert spectrum integrated in time showed that the Hilbert spectrum makes it possible to detect and quantify the cycle of locally repeated events.

scholarly journals Data Interpretation Technology of GPR Survey Based on Variational Mode Decomposition

2019 ◽  
Vol 9 (10) ◽  
pp. 2017 ◽  
Author(s):  
Juncai Xu ◽  
Bangjun Lei
Keyword(s):  
Instantaneous Frequency ◽  
Data Interpretation ◽  
Variational Mode Decomposition ◽  
Intrinsic Mode Functions ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Synthetic Signal ◽  
Mode Decomposition ◽  
The Media ◽  
Ground Penetrating

Data interpretation is the crucial scientific component that influences the inspection accuracy of ground penetrating radar (GPR). Developing algorithms for interpreting GPR data is a research focus of increasing interest. The problem of algorithms for interpreting GPR data is unresolved. To this end, this study proposes a sophisticated algorithm for interpreting GPR data with the aim of improving the inspection resolution. The algorithm is formulated by integrating variational mode decomposition (VMD) and Hilbert–Huang transform techniques. With this method, the intrinsic mode function of the GPR data is first produced using the VMD of the data, followed by obtaining the instantaneous frequency by using the Hilbert–Huang transform to analyze the intrinsic mode functions. The instantaneous frequency data can be decomposed into three frequency attributes, including frequency division section, time-frequency section, and space frequency section, which constitute a platform to gain insight into the nature of the GPR data, such that the inspected media components can be examined. The effectiveness of the proposed method on a synthetic signal from a GPR forward model was studied, with the multi-resolution performance being tested. Inspecting the media of a highroad by analyzing the GPR data, with the abnormal characteristics being designated, validated the applicability of the proposed method.

scholarly journals MONO-COMPONENTS VS IMFs IN SIGNAL DECOMPOSITION

2008 ◽  
Vol 06 (03) ◽  
pp. 353-374 ◽  
Author(s):  
TAO QIAN ◽  
LIMING ZHANG ◽  
HONG LI
Keyword(s):  
Empirical Mode Decomposition ◽  
Instantaneous Frequency ◽  
Signal Decomposition ◽  
Intrinsic Mode Functions ◽  
Mode Decomposition ◽  
Adaptive Decomposition

The concepts of intrinsic mode functions and mono-components are investigated in relation to the empirical mode decomposition. Mono-components are defined to be the functions for which non-negative analytic instantaneous frequency is well defined. We show that a great variety of functions are mono-components based on which adaptive decomposition of signals are theoretically possible. We justify the role of empirical mode decomposition in signal decomposition in relation to mono-components.

scholarly journals Global Stability Analysis of Neural Networks with Constant Time Delay via Frobenius Norm

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
N. Mohamed Thoiyab ◽  
P. Muruganantham ◽  
Grienggrai Rajchakit ◽  
Nallappan Gunasekaran ◽  
Bundit Unyong ◽  
...  
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Lyapunov Functional ◽  
Constant Time Delay ◽  
Constant Time ◽  
Frobenius Norm ◽  
Sufficient Condition ◽  
Numerical Examples ◽  
Global Stability Analysis ◽  
Bounded Functions

This paper deals with the global asymptotic robust stability (GARS) of neural networks (NNs) with constant time delay via Frobenius norm. The Frobenius norm result has been utilized to find a new sufficient condition for the existence, uniqueness, and GARS of equilibrium point of the NNs. Some suitable Lyapunov functional and the slope bounded functions have been employed to find the new sufficient condition for GARS of NNs. Finally, we give some comparative study of numerical examples for explaining the advantageous of the proposed result along with the existing GARS results in terms of network parameters.

scholarly journals Robust Controllability and Observability of Boolean Control Networks under Different Disturbances

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Yuanhua Wang ◽  
Xiao Zhang ◽  
Yaqi Hao
Keyword(s):  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Reachable State ◽  
Numerical Examples ◽  
Control Networks ◽  
Robust Controllability ◽  
Controllability And Observability ◽  
Control Sequences

This paper investigates robust controllability and observability of Boolean control networks under disturbances. Firstly, under unobservable disturbances, some sufficient conditions are obtained for robust controllability of BCNs. Then an algorithm is proposed to construct the least control sequences which drive the trajectory from a state to a given reachable state. If the disturbances are observable, by defining the order-preserving system, an efficient sufficient condition is obtained for robust controllability of BCNs. Finally, the robust observability problem is converted into an equivalent robust controllability via set controllability and is solved by using the results obtained for set controllability. Some numerical examples are presented to illustrate the obtained results.

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