scholarly journals Frequency-Frequency Interactions in Chaos Communications

2019 ◽  
pp. 1460-1468
Author(s):  
Ibrahim Q. AbdulRahman ◽  
Kais A. M. Al Naimee ◽  
Rashid K. Al-Dhahir
Keyword(s):  
Chaotic System ◽  
Fourier Transformation ◽  
Chaotic Systems ◽  
The Other ◽  
New Method ◽  
Fast Fourier Transformation ◽  
Scanning Frequency

In this research, the frequency-frequency interactions in chaotic systems has been experimentally and numerically studied. We have injected two frequencies on chaotic system where one of these frequencies is modulated with chaotic waveform and the other is untiled as a scanning frequency to find modulating frequency. It is observed that the Fast Fourier Transformation (FFT) peaks amplitude increased when the value of the two frequencies are matched. Thus, the modulating frequency could be observed, this leads to discover a new method to detect the modulating frequency without synchronization.

scholarly journals Normal and Abnormal Human Face Detection Based on DCT and FFT Techniques - A Proposed Method

2021 ◽  
Author(s):  
Samir Bandyopadhyay ◽  
Shawni Dutta ◽  
Vishal Goyal ◽  
Payal Bose
Keyword(s):  
Face Detection ◽  
Fourier Transformation ◽  
Input Image ◽  
The Other ◽  
Fast Fourier Transformation ◽  
Length Variation ◽  
Human Face ◽  
Discrete Cosine Transformation ◽  
Cosine Transformation ◽  
Human Face Detection

In today’s world face detection is the most important task. Due to the chromosomes disorder sometimes a human face suffers from different abnormalities. For example, one eye is bigger than the other, cliff face, different chin-length, variation of nose length, length or width of lips are different, etc. For computer vision currently this is a challenging task to detect normal and abnormal face and facial parts from an input image. In this research paper a method is proposed that can detect normal or abnormal faces from a frontal input image. This method used Fast Fourier Transformation (FFT) and Discrete Cosine Transformation of frequency domain and spatial domain analysis to detect those faces.

NEW METHOD FOR STABILIZATION OF UNSTABLE PERIODIC ORBITS IN CHAOTIC SYSTEMS

1995 ◽  
Vol 05 (01) ◽  
pp. 281-295 ◽  
Author(s):  
ZBIGNIEW GALIAS
Keyword(s):  
Periodic Orbits ◽  
Chaotic System ◽  
System Parameter ◽  
Chaotic Systems ◽  
New Method ◽  
Unstable Periodic Orbits ◽  
Numerical Example ◽  
Element Set

In this paper we present a new method of controlling periodic orbits in chaotic systems. This method can be applied in situations when the chaotic system depends on one system parameter, which can be changed over a continuous interval or over a discrete, two-element set. We compare the new method to other ones, discuss its properties, and illustrate our approach with a numerical example.

Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

2019 ◽  
Vol 29 (14) ◽  
pp. 1950197 ◽  
Author(s):  
P. D. Kamdem Kuate ◽  
Qiang Lai ◽  
Hilaire Fotsin
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
The Novel ◽  
Algebraic Equations ◽  
The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

Chirp waveform control to produce broad harmonic plateau and single attosecond pulse

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Hang Liu ◽  
Cui-Yan Xu ◽  
Xiao-Dan Jing ◽  
Yan Qiao ◽  
Li-Qiang Feng
Keyword(s):  
Instantaneous Frequency ◽  
Free Electron ◽  
Fourier Transformation ◽  
Attosecond Pulse ◽  
The Other ◽  
Laser Parameters ◽  
Waveform Control ◽  
Chirped Pulses ◽  
Attosecond Pulses

Abstract Waveform control of three kinds of chirped pulses (i.e. βt, βt 2 and βt 3) to produce harmonic spectra and attosecond pulses has been investigated. It is found that by properly choosing the chirps, the chirp delays and the other laser parameters, not only the instantaneous frequency of some specific half profiles can be decreased, but also its intensity can be increased. As a result, the free electron can receive more energy when it accelerates in these regions, thus leading to the extension of the harmonic cutoff and harmonic plateau. Finally, through the Fourier transformation of the harmonic spectra and by superposing some harmonics, three single attosecond pulses with the durations of 30 as, 33 as and 39 as can be obtained.

scholarly journals Active Contour Model Using Fast Fourier Transformation for Salient Object Detection

Electronics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 192
Author(s):  
Umer Sadiq Khan ◽  
Xingjun Zhang ◽  
Yuanqi Su
Keyword(s):  
Object Detection ◽  
Fourier Transformation ◽  
Active Contour ◽  
Active Contour Model ◽  
Salient Object Detection ◽  
Fast Fourier Transformation ◽  
Salient Object ◽  
Active Contour Models ◽  
Contour Model ◽  
Contour Models

The active contour model is a comprehensive research technique used for salient object detection. Most active contour models of saliency detection are developed in the context of natural scenes, and their role with synthetic and medical images is not well investigated. Existing active contour models perform efficiently in many complexities but facing challenges on synthetic and medical images due to the limited time like, precise automatic fitted contour and expensive initialization computational cost. Our intention is detecting automatic boundary of the object without re-initialization which further in evolution drive to extract salient object. For this, we propose a simple novel derivative of a numerical solution scheme, using fast Fourier transformation (FFT) in active contour (Snake) differential equations that has two major enhancements, namely it completely avoids the approximation of expansive spatial derivatives finite differences, and the regularization scheme can be generally extended more. Second, FFT is significantly faster compared to the traditional solution in spatial domain. Finally, this model practiced Fourier-force function to fit curves naturally and extract salient objects from the background. Compared with the state-of-the-art methods, the proposed method achieves at least a 3% increase of accuracy on three diverse set of images. Moreover, it runs very fast, and the average running time of the proposed methods is about one twelfth of the baseline.

Soft Computing Simulations of Chaotic Systems

2019 ◽  
Vol 29 (08) ◽  
pp. 1950112 ◽  
Author(s):  
Erivelton G. Nepomuceno ◽  
Priscila F. S. Guedes ◽  
Alípio M. Barbosa ◽  
Matjaž Perc ◽  
Robert Repnik
Keyword(s):  
Lower Bound ◽  
Soft Computing ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Logistic Map ◽  
Largest Lyapunov Exponent ◽  
Lower And Upper Bounds ◽  
Finite Precision ◽  
Chua Circuit ◽  
Widespread Interest

Soft computing strategies are drawing widespread interest in engineering and science fields, particularly so because of their capacity to reason and learn in a domain of inherent uncertainty, approximation, and unpredictability. However, soft computing research devoted to finite precision effects in chaotic system simulations is still in a nascent stage, and there are ample opportunities for new discoveries. In this paper, we consider the error that is due to finite precision in the simulation of chaotic systems. We present a generalized version of the lower bound error using an arbitrary number of natural interval extensions. The lower bound error has been used to simulate a chaotic system with lower and upper bounds. The width of this interval does not diverge, which is an advantage compared to other techniques. We illustrate our approach on three systems, namely the logistic map, the Singer map and the Chua circuit. Moreover, we validate the method by calculating the largest Lyapunov exponent.

scholarly journals On Newcomb's method of investigating periodicities and its application to Brückner's weather cycle

1914 ◽  
Vol 90 (619) ◽  
pp. 349-355
Keyword(s):  
Thermal Radiation ◽  
The Other ◽  
New Method ◽  
Critical Examination ◽  
Numerical Work ◽  
Average Value ◽  
Other Hand ◽  
Relationship Of ◽  
The Relationship ◽  
Great Simplicity

During the last few years of his life Prof. Simon Newcomb was keenly interested in the problem of periodicities, and devised a new method for their investigation. This method is explained, and to some extent applied, in a paper entitled "A Search for Fluctuations in the Sun's Thermal Radiation through their Influence on Terrestrial Temperature." The importance of the question justifies a critical examination of the relationship of the older methods to that of Newcomb, and though I do not agree with his contention that his process gives us more than can be obtained from Fourier's analysis, it has the advantage of great simplicity in its numerical work, and should prove useful in a certain, though I am afraid, very limited field. Let f ( t ) represent a function of a variable which we may take to be the time, and let the average value of the function be zero. Newcomb examines the sum of the series f ( t 1 ) f ( t 1 + τ) + f ( t 2 ) f ( t 2 + τ) + f ( t 3 ) f ( t 3 + τ) + ..., where t 1 , t 2 , etc., are definite values of the variable which are taken to lie at equal distances from each other. If the function be periodic so as to repeat itself after an interval τ, the products are all squares and each term is positive. If, on the other hand, the periodic time be 2τ, each product will be negative and the sum itself therefore negative. It is easy to see that if τ be varied continuously the sum of the series passes through maxima and minima, and the maxima will indicated the periodic time, or any of its multiples.

Generation of Wave-Field Time Histories by the Modulated Discrete Fourier Transformation

2003 ◽  
Author(s):  
Yousun Li
Keyword(s):  
Wave Field ◽  
Fourier Transformation ◽  
Time Instant ◽  
Discrete Fourier Transformation ◽  
Fast Fourier Transformation ◽  
Structural Members ◽  
Random Waves ◽  
Offshore Structure ◽  
Time Histories ◽  
The Time Domain

In the time domain simulation of the response of an offshore structure under random waves, the time histories of the wave field should be generated as the input to the dynamic equations. Herein the wave field is the wave surface elevation, the water particle velocities and accelerations at structural members. The generated time histories should be able to match the given wave-field spectral descriptions, to trace the structural member motions if it is a compliant offshore structure, and be numerically efficient. Most frequently used generation methods are the direct summation of a limited number of cosine functions, the Fast Fourier Transformation, and the digital filtering model. However, none of them can really satisfy all the above requirements. A novel technique, called the Modulated Discrete Fourier Transformation, has been developed. Under this method, the wave time histories at each time instant is a summation of a few time-varying complex functions. The simulated time histories have continuous spectral density functions, and the motions of the structural members are well included. This method seems to be superior to all the conventional methods in terms of the above mentioned three requirements.

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