Search results for: periodic signals

Authors: Smita Sonker

Abstract:

Various investigators have determined the degree of approximation of conjugate signals (functions) of functions belonging to different classes Lipα, Lip(α,p), Lip(ξ(t),p), W(Lr,ξ(t), (β ≥ 0)) by matrix summability means, lower triangular matrix operator, product means (i.e. (C,1)(E,1), (C,1)(E,q), (E,q)(C,1) (N,p,q)(E,1), and (E,q)(N,pn) of their conjugate trigonometric Fourier series. In this paper, we shall determine the degree of approximation of 2π-periodic function conjugate functions of f belonging to the function classes Lipα and W(Lr; ξ(t); (β ≥ 0)) by (C1.T) -means of their conjugate trigonometric Fourier series. On the other hand, we shall review above-mentioned work in the light of Lenski.

Keywords: signals, trigonometric fourier approximation, class W(L^r, \xi(t), conjugate fourier series

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Authors: Zi-Gui Huang, Shen-Hsien Hu

Abstract:

This study proposes a fabrication of phononic-crystal acoustic wave device. A graphene-like atomic structure was adopted as the main research subject, and a graphene-like structure was designed using piezoelectric material zinc oxide and its periodic boundary conditions were defined using the finite element method. The effects of a hexagonal honeycomb structure were investigated regarding the band gap phenomenon. The use of micro-electromechanical systems process technology to make the film etched micron graphics, designed to produce four kinds of different piezoelectric structure (plat, periodic, single defect and double defects). Frequency response signals and phase change were also measured in this paper.

Keywords: MEMS, phononic crystal, piezoelectric material, Zinc oxide

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Authors: Takashi Mitsuishi, Koji Saigusa

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This paper presents circular polar coordinates transformation of periodic fuzzy membership function. The purpose is identification of domain of periodic membership functions in consequent part of IF-THEN rules. The proposed methods are applied to the simple color construct system.

Keywords: periodic membership function, polar coordinates transformation, defuzzification, circular coordinates

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Authors: Seyed Sadegh Naseralavi

Abstract:

This paper presents a Kernel parallelization equation for damage identification in structures under unknown periodic excitations. Herein, the dynamic differential equation of the motion of structure is viewed as a mapping from displacements to external forces. Utilizing this viewpoint, a new method for damage detection in structures under periodic loads is presented. The developed method requires only two periods of load. The method detects the damages without finding the input loads. The method is based on the fact that structural displacements under free and forced vibrations are associated with two parallel subspaces in the displacement space. Considering the concept, kernel parallelization equation (KPE) is derived for damage detection under unknown periodic loads. The method is verified for a case study under periodic loads.

Keywords: Kernel, unknown periodic load, damage detection, Kernel parallelization equation

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Authors: Yanpei Zhen

Abstract:

The nonlinear Schrödinger (NLS) equation models wave dynamics in many physical problems related to fluids, plasmas, and optics. The standing periodic waves are known to be modulationally unstable, and rogue waves (localized perturbations in space and time) have been observed on their backgrounds in numerical experiments. The exact solutions for rogue waves arising on the periodic standing waves have been obtained analytically. It is natural to ask if the rogue waves persist on the standing periodic waves in the integrable discretizations of the integrable NLS equation. We study the standing periodic waves in the semidiscrete integrable system modeled by the high-order Ablowitz-Ladik (AL) equation. The standing periodic wave of the high-order AL equation is expressed by the Jacobi cnoidal elliptic function. The exact solutions are obtained by using the separation of variables and one-fold Darboux transformation. Since the cnoidal wave is modulationally unstable, the rogue waves are generated on the periodic background.

Keywords: Darboux transformation, periodic wave, Rogue wave, separating the variables

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Authors: Ammara Mehmood, Aneela Zameer, Muhammad Asif Zahoor Raja, Muhammad Faisal Fateh

Abstract:

In this work, the strength of bio-inspired computational intelligence based technique is exploited for parameter estimation for the periodic signals using Continuous Differential Evolution (CDE) by defining an error function in the mean square sense. Multidimensional and nonlinear nature of the problem emerging in sinusoidal signal models along with noise makes it a challenging optimization task, which is dealt with robustness and effectiveness of CDE to ensure convergence and avoid trapping in local minima. In the proposed scheme of Continuous Differential Evolution based Signal Parameter Estimation (CDESPE), unknown adjustable weights of the signal system identification model are optimized utilizing CDE algorithm. The performance of CDESPE model is validated through statistics based various performance indices on a sufficiently large number of runs in terms of estimation error, mean squared error and Thiel’s inequality coefficient. Efficacy of CDESPE is examined by comparison with the actual parameters of the system, Genetic Algorithm based outcomes and from various deterministic approaches at different signal-to-noise ratio (SNR) levels.

Keywords: parameter estimation, bio-inspired computing, continuous differential evolution (CDE), periodic signals

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Authors: E. Benga, T. Tengen, A. Alugongo

Abstract:

Periodic and continuous inventory models are the two classical management tools used to handle inventories. These models have advantages and disadvantages. The implementation of both continuous (r,Q) inventory and periodic (R, S) inventory models in most manufacturing plants comes with higher cost. Such high inventory costs are due to the fact that most manufacturing plants are not flexible enough. Since demand and lead-time are two important variables of every inventory models, their effect on the flexibility of the manufacturing plant matter most. Unfortunately, these effects are not clearly understood by managers. The reason is that the decision parameters of the continuous (r, Q) inventory and periodic (R, S) inventory models are not designed to effectively deal with the issues of uncertainties such as poor manufacturing performances, delivery performance supplies performances. There is, therefore, a need to come up with a predictive and hybrid inventory model that can combine in some sense the feature of the aforementioned inventory models. A linear combination technique is used to hybridize both continuous (r, Q) inventory and periodic (R, S) inventory models. The behavior of such hybrid inventory model is described by a differential equation and then optimized. From the results obtained after simulation, the continuous (r, Q) inventory model is more effective than the periodic (R, S) inventory models in the short run, but this difference changes as time goes by. Because the hybrid inventory model is more cost effective than the continuous (r,Q) inventory and periodic (R, S) inventory models in long run, it should be implemented for strategic decisions.

Keywords: periodic inventory, continuous inventory, hybrid inventory, optimization, manufacturing plant

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Authors: Smita Sonker, Uaday Singh

Abstract:

Various investigators have determined the degree of approximation of functions belonging to the classes W(L r , ξ(t)), Lip(ξ(t), r), Lip(α, r), and Lipα using different summability methods with monotonocity conditions. Recently, Lal has determined the degree of approximation of the functions belonging to Lipα and W(L r , ξ(t)) classes by using Ces`aro-N¨orlund (C 1 .Np)- summability with non-increasing weights {pn}. In this paper, we shall determine the degree of approximation of 2π - periodic functions f belonging to the function classes Lipα and W(L r , ξ(t)) by C 1 .T - means of Fourier series of f. Our theorems generalize the results of Lal and we also improve these results in the light off. From our results, we also derive some corollaries.

Keywords: Lipschitz classes, product matrix operator, signals, trigonometric Fourier approximation

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Authors: Song Ni, Junxiang Xu

Abstract:

This paper concerns quasi-periodic perturbations with parameters of 2-dimensional degenerate systems. If the equilibrium point of the unperturbed system is elliptic-type degenerate. Assume that the perturbation is real analytic quasi-periodic with diophantine frequency. Without imposing any assumption on the perturbation, we can use a path of equilibrium points to tackle with the Melnikov non-resonance condition, then by the Leray-Schauder Continuation Theorem and the Kolmogorov-Arnold-Moser technique, it is proved that the equation has a small response solution for many sufficiently small parameters.

Keywords: quasi-periodic systems, KAM-iteration, degenerate equilibrium point, response solution

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Authors: Launcelot McGrath

Abstract:

A comprehensive understanding of physiological data is a vital aid to the anaesthesiologist in monitoring and maintaining the well-being of a patient undergoing surgery. Bio signal analysis is one of the most important topics that researchers have tried to develop over the last century to understand numerous human diseases. Understanding which biological signals are most important during anaesthesia is critically important. It is important that the anaesthesiologist understand both the signals themselves and the limitations introduced by the processes of acquisition. In this article, we provide an overview of different types of biological signals as well as the mechanisms applied to acquire them.

Keywords: biological signals, signal acquisition, anaesthesiology, patient monitoring

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Authors: Farid Nouioua, Abdelouaheb Ardjouni

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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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Authors: Aries Nawel, Bentarzi Mohamed

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This paper deals with the study of some probabilistic and statistical properties of a Periodic Integer-Valued Moving Average Model (PINMA_{S}(q)). The closed forms of the mean, the second moment and the periodic autocovariance function are obtained. Furthermore, the time reversibility of the model is discussed in details. Moreover, the estimation of the underlying parameters are obtained by the Yule-Walker method, the Conditional Least Square method (CLS) and the Weighted Conditional Least Square method (WCLS). A simulation study is carried out to evaluate the performance of the estimation method. Moreover, an application on real data set is provided.

Keywords: periodic integer-valued moving average, periodically correlated process, time reversibility, count data

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Authors: Tomotaka Aoki, Isao Tomita

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We examined the on-off ratio and frequency components of output signals from an electron-interference device made of GaAs/AlₓGa₁₋ₓAs by solving the time-dependent Schrödinger's equation on conducting electrons in the channel waveguide of the device. For electron-wave modulation, a periodic voltage of frequency f was applied to the channel. Furthermore, we examined the voltage-amplitude dependence of the signals in time and frequency domains and found that large applied voltage deformed the output-signal waveform and created additional side modes (frequencies) near the modulation frequency f and that there was a trade-off between on-off ratio and side-mode creation.

Keywords: electrical conduction, electron interference, frequency spectrum, on-off ratio

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Authors: Boukari Nassim

Abstract:

This paper describes the use of odd pair autoregressive coefficients (Yule _Walker and Burg) for the feature extraction of electroencephalogram (EEG) signals. In the classification: the radial basis function neural network neural network (RBFNN) is employed. The RBFNN is described by his architecture and his characteristics: as the RBF is defined by the spread which is modified for improving the results of the classification. Five types of EEG signals are defined for this work: Set A, Set B for normal signals, Set C, Set D for interictal signals, set E for ictal signal (we can found that in Bonn university). In outputs, two classes are given (AC, AD, AE, BC, BD, BE, CE, DE), the best accuracy is calculated at 99% for the combined odd pair autoregressive coefficients. Our method is very effective for the diagnosis of epileptic EEG signals.

Keywords: epilepsy, EEG signals classification, combined odd pair autoregressive coefficients, radial basis function neural network

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Authors: Jing Qing-feng, Liu Danmei

Abstract:

Based on the optimum detection, signal projection and Maximum A Posteriori (MAP) rule, Proakis has deduced the theoretical BER equation of Gray coded MPSK signals. Proakis analyzed the BER theoretical equations mainly based on the projection of signals, which is difficult to be understood. This article solve the same problem based on the signal space, which explains the vectors relations among the sending signals, received signals and noises. The more explicit and easy-deduced process is illustrated in this article based on the signal space, which can illustrated the relations among the signals and noises clearly. This kind of deduction has a univocal geometry meaning. It can explain the correlation between the production and calculation of BER in vector level.

Keywords: MPSK, MAP, signal space, BER

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Authors: Alexander Kelíšek, Denisa Janasová, Veronika Mitašová

Abstract:

Weak signals using is often associated with early warning. It is possible to find a link between early warning, respectively early problems detection and risk management. The idea of early warning is very important in the context of crisis management because of the risk prevention possibility. Weak signals are likened to risk symptoms. Nowadays, their usefulness as a tool of proactive problems solving is emphasized. Based on it, it is possible to use weak signals not only in strategic planning, project management, or early warning system, but also as a subsidiary element in risk management. The main question is how to effectively integrate weak signals into risk management. The main aim of the paper is to point out the possibilities of weak signals using in small and medium enterprises risk management.

Keywords: early warning system, weak signals, risk management, small and medium enterprises (SMEs)

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Authors: Launcelot.McGrath

Abstract:

A comprehensive understanding of physiological data is a vital aid to the anaesthesiologist in monitoring and maintaining the well-being of a patient undergoing surgery. Biosignal analysis is one of the most important topics that researchers have tried to develop over the last century to understand numerous human diseases. Understanding which biological signals are most important during anaesthesia is critically important. It is important that the anaesthesiologist understand both the signals themselves and the limitations introduced by the processes of acquisition. In this article, we provide an overview of different types of biological signals as well as the mechanisms applied to acquire them.

Keywords: general biosignals, anaesthesia, biological, electroencephalogram

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Authors: Arun Kumar Yadav, Badam Singh Kushvah

Abstract:

In the present work, we investigated displaced periodic orbits in the linear order in the circular restricted three-body Sun-Jupiter system, where the third mass-less body utilizes solar electric sail. The electric solar sail is a new space propulsion concept which uses the solar wind momentum for producing thrust, and it is somewhat like to the more well-known solar radiation pressure sail which is often called simply the solar sail. Moreover, we implement the feedback linearization control scheme to perform the stabilization and trajectory tracking for the nonlinear system. Further, we derived periodic orbits analytically in linear order by introducing a first order approximation. These approximate analytic solutions are utilized in a numerical search to determine displaced periodic orbit in the full nonlinear model. We found the displaced periodic orbit for the defined non-linear model and stabilized the model.

Keywords: solar electric sail, circular restricted three-body problem (CRTBP), displaced orbit, feedback linearization control

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Authors: Launcelot McGrath, Xiaoxiao Liu, Colin Flanagan

Abstract:

It is widely recognised that a comprehensive understanding of physiological data is a vital aid to the anaesthesiologist in monitoring and maintaining the well-being of a patient undergoing surgery. Bio signal analysis is one of the most important topics that researchers have tried to develop over the last century to understand numerous human diseases. There are tremendous biological signals during anaesthesia, and not all of them are important, which to choose to observe is a significant decision. It is important that the anaesthesiologist understand both the signals themselves, and the limitations introduced by the processes of acquisition. In this article, we provide an all-sided overview of different types of biological signals as well as the mechanisms applied to acquire them.

Keywords: general biosignals, anaesthesia, biological, electroencephalogram

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Authors: K. B. Ghazaryan, R. A. Ghazaryan

Abstract:

Based on the constitutive model and anti-plane equations of anisotropic elastic body of monoclinic symmetry we consider the problem of shear wave propagation in multi-layered disordered composite structure with point defect. Using transfer matrix method the analytic expression is obtained providing solutions of shear Floquet wave propagation in periodic disordered anisotropic structure. The usefulness of the obtained analytical expression was discussed also in reflection and refraction problems from multi-layered reflector as well as in vibration problem of multi-layered waveguides. Numerical results are presented highlighting the effects arising in disordered periodic structure due to defects of multi-layered structure.

Keywords: shear elastic waves, monoclinic anisotropic media, periodic structure, disordered multilayer laminae, multi-layered waveguide

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Authors: Yunzhe Tong, Jun Fan, Bin Wang

Abstract:

The vibroacoustic behavior of an immersed infinite cylindrical shell with periodic lengthwise ribs has been studied in this paper. The motions of the shell are described by the Donnell equations. Each lengthwise rib is modeled as an elastic beam. The motions of the bulkheads are decomposed into the longitudinal motions and flexural motions. The analytical expressions of the shell motions can be obtained through circumferential mode expansion, Fourier Transform and periodic boundary condition in the circumferential direction. Furthermore, the far-field radiated pressure has been obtained using the stationary phase. The analysis of wavenumber domain shows that periodic lengthwise stiffeners in the circumferential direction can produce flexural Bloch waves. The dominant feature in far-field pressure amplitude is the resonance of the supersonic components of the flexural Bloch waves in the circumferential direction.

Keywords: flexural Bloch wave, stiffened shell, vibroacoustics, wavenumber analysis

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Authors: Nema M. Salem, Hanan A. Altukhaifi, Amal Mukhtar, Reemaz K. Hetaimish

Abstract:

Recently, BCI field of research has gained a lot of interest. Apart from motor neuroprosthetics, many studies showed the possibility of controlling a virtual environment of a videogame using the acquired electroencephalogram signals (EEG) from the gamer. In addition, another study had successfully moved a farm tractor using the human’s EEG signals. This article utilizes the use of EEG signals, as a source of technology, in controlling a Parallax Boe-Bot robot. The commercial Emotive Epoc headset has been used in acquiring the EEG signals from rested subjects. Because the human's visual cortex can successfully differentiate between different colors, the red and green colors are used as visual stimuli for generating EEG signals using the Epoc. Arduino and Labview are used to translate the virtually pressed keys into instructions controlling the motion and rotation of the robot. Optimistic results have been achieved except for minor delay and accuracy in the robot’s response.

Keywords: BCI, Emotiv Epoc headset, EEG, Labview, Arduino applications, robot

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Authors: Maciej Zaręba, Sławomir Lasota

Abstract:

Understanding the dependencies between the input signal, that controls the production system and signals, that capture its output, is of a great importance in intelligent systems. The method for identification of the relationship between signals in continuous monitoring of production systems is described in the paper. The method discovers the correlation between changes in the states derived from input signals and resulting changes in the states of output signals of the production system. The method is able to handle system inertia, which determines the time shift of the relationship between the input and output.

Keywords: manufacturing operation management, signal relationship, continuous monitoring, production systems

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Authors: H. Namazi, H. T. N. Kuan

Abstract:

Brain activity can be measured by acquiring and analyzing EEG signals from an individual. In fact, the human brain response to external and internal stimuli is mapped in his EEG signals. During years some methods such as Fourier transform, wavelet transform, empirical mode decomposition, etc. have been used to analyze the EEG signals in order to find the effect of stimuli, especially external stimuli. But each of these methods has some weak points in analysis of EEG signals. For instance, Fourier transform and wavelet transform methods are linear signal analysis methods which are not good to be used for analysis of EEG signals as nonlinear signals. In this research we analyze the brain response to auditory stimuli by extracting information in the form of various measures from EEG signals using a software developed by our research group. The used measures are Jeffrey’s measure, Fractal dimension and Hurst exponent. The results of these analyses are useful not only for fundamental understanding of brain response to auditory stimuli but provide us with very good recommendations for clinical purposes.

Keywords: auditory stimuli, brain response, EEG signal, fractal dimension, hurst exponent, Jeffrey’s measure

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Authors: Valentina Narvaez Gaitan, Laura Valentina Rodriguez Leguizamon, Ruben Dario Hernandez B.

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This work describes a physiological signal emulation system that uses electromyography (EMG) signals obtained from muscle sensors in the first instance. These signals are used to extract their characteristics to model and emulate specific arm movements. The main objective of this effort is to develop a new biomedical software system capable of generating physiological signals through the use of embedded systems by establishing the characteristics of the acquired signals. The acquisition system used was Biosignals, which contains two EMG electrodes used to acquire signals from the forearm muscles placed on the extensor and flexor muscles. Processing algorithms were implemented to classify the signals generated by the arm muscles when performing specific movements such as wrist flexion extension, palmar grip, and wrist pronation-supination. Matlab software was used to condition and preprocess the signals for subsequent classification. Subsequently, the mathematical modeling of each signal is performed to be generated by the embedded system, with a validation of the accuracy of the obtained signal using the percentage of cross-correlation, obtaining a precision of 96%. The equations are then discretized to be emulated in the embedded system, obtaining a system capable of generating physiological signals according to the characteristics of medical analysis.

Keywords: classification, electromyography, embedded system, emulation, physiological signals

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Authors: Zahra Abdolkarimi, Naser Zourikalatehsamad,

Abstract:

Up to 40 years ago, after recognition of epilepsy, it was generally believed that these attacks occurred randomly and suddenly. However, thanks to the advance of mathematics and engineering, such attacks can be predicted within a few minutes or hours. In this way, various algorithms for long-term prediction of the time and frequency of the first attack are presented. In this paper, by considering the nonlinear nature of brain signals and dynamic recorded brain signals, ANFIS model is presented to predict the brain signals, since according to physiologic structure of the onset of attacks, more complex neural structures can better model the signal during attacks. Contribution of this work is the co-evolution algorithm for optimization of ANFIS network parameters. Our objective is to predict brain signals based on time series obtained from brain signals of the people suffering from epilepsy using ANFIS. Results reveal that compared to other methods, this method has less sensitivity to uncertainties such as presence of noise and interruption in recorded signals of the brain as well as more accuracy. Long-term prediction capacity of the model illustrates the usage of planted systems for warning medication and preventing brain signals.

Keywords: co-evolution algorithms, brain signals, time series, neural networks, ANFIS model, physiologic structure, time prediction, epilepsy suffering, illustrates model

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Authors: R. Biondi, G. Dys, G. Ferone, T. Renard, M. Zysman

Abstract:

This paper describes an automated implementable system for impulsive signals detection and recognition. The system uses a Digital Signal Processing device for the detection and identification process. Here the system analyses the signals in real time in order to produce a particular response if needed. The system analyses the signals in real time in order to produce a specific output if needed. Detection is achieved through normalizing the inputs and comparing the read signals to a dynamic threshold and thus avoiding detections linked to loud or fluctuating environing noise. Identification is done through neuronal network algorithms. As a setup our system can receive signals to “learn” certain patterns. Through “learning” the system can recognize signals faster, inducing flexibility to new patterns similar to those known. Sound is captured through a simple jack input, and could be changed for an enhanced recording surface such as a wide-area recorder. Furthermore a communication module can be added to the apparatus to send alerts to another interface if needed.

Keywords: sound detection, impulsive signal, background noise, neural network

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Authors: Saeed Asiri, Yousuf Z. AL-Zahrani

Abstract:

A new class of support structures, called periodic structures, is introduced in this paper as a viable means for isolating the vibration transmitted from the sea waves to offshore platform structures through its legs. A passive approach to reduce transmitted vibration generated by waves is presented. The approach utilizes the property of periodic structural components that creates stop and pass bands. The stop band regions can be tailored to correspond to regions of the frequency spectra that contain harmonics of the wave frequency, attenuating the response in those regions. A periodic structural component is comprised of a repeating array of cells, which are themselves an assembly of elements. The elements may have differing material properties as well as geometric variations. For the purpose of this research, only geometric and material variations are considered and each cell is assumed to be identical. A periodic leg is designed in order to reduce transmitted vibration of sea waves. The effectiveness of the periodicity on the vibration levels of platform will be demonstrated theoretically. The theory governing the operation of this class of periodic structures is introduced using the transfer matrix method. The unique filtering characteristics of periodic structures are demonstrated as functions of their design parameters for structures with geometrical and material discontinuities; and determine the propagation factor by using the spectral finite element analysis and the effectiveness of design on the leg structure by changing the ratio of step length and area interface between the materials is demonstrated in order to find the propagation factor and frequency response.

Keywords: vibrations, periodic structures, offshore, platforms, transfer matrix method

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Authors: Ramonika Sengupta, Stuti Kachhwaha, Asha Adhiya, K. Satya Raja Sekhar, Rajwinder Kaur

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Numerous efforts have been done in the past decade to develop the methods of secure communication that are free from interception and eavesdropping. In fiber optic communication, chaotic optical carrier signals are used for data encryption in secure data transmission. Mach-Zehnder Modulators (MZM) are the key components for generating the chaotic signals to be used as optical carriers. This paper presents the dynamics of a lithium niobate MZM modulator under various biasing conditions. The chaotic fluctuations of the intensity of a laser diode have been generated using the electro-optic MZM modulator operating in a highly nonlinear regime. The modulator is driven in closed loop by its own output at an earlier time. When used as an electro-optic oscillator employing delayed feedback, the MZM displays a wide range of output waveforms of varying complexity. The dynamical behavior of the system ranges from periodic to nonlinear oscillations. The nonlinearity displayed by the system is reproducible and is easily controllable. In this paper, we demonstrate a wide variety of optical signals generated by MZM using easily controllable device parameters in both open and close loop bias conditions.

Keywords: chaotic carrier, fiber optic communication, Mach-Zehnder modulator, secure data transmission

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Authors: Rima A. Ajlouni

Abstract:

The discovery of quasi-periodic structures in material science is revealing an exciting new class of symmetries, which has never been explored before. Due to their unique structural and visual properties, these symmetries are drawing interest from many scientific and design disciplines. Especially, in art and architecture, these symmetries can provide a rich source of geometry for exploring new patterns, forms, systems, and structures. However, the structural systems of these complicated symmetries are still posing a perplexing challenge. While much of their local order has been explored, the global governing system is still unresolved. Understanding their unique global long-range order is essential to their generation and application. The recent discovery of dodecagonal quasi-periodic patterns in historical Islamic architecture is generating a renewed interest into understanding the mathematical principles of traditional Islamic geometry. Astonishingly, many centuries before its description in the modern science, ancient artists, by using the most primitive tools (a compass and a straight edge), were able to construct patterns with quasi-periodic formations. These ancient patterns can be found all over the ancient Islamic world, many of which exhibit formations with 5, 8, 10 and 12 quasi-periodic symmetries. Based on the examination of these historical patterns and derived from the generating principles of Islamic geometry, a global multi-level structural model is presented that is able to describe the global long-range order of dodecagonal quasi-periodic formations in Islamic Architecture. Furthermore, this method is used to construct new quasi-periodic tiling systems as well as generating their deflation and inflation rules. This method can be used as a general guiding principle for constructing infinite patches of dodecagon-based quasi-periodic formations, without the need for local strategies (tiling, matching, grid, substitution, etc.) or complicated mathematics; providing an easy tool for scientists, mathematicians, teachers, designers and artists, to generate and study a wide range of dodecagonal quasi-periodic formations.

Keywords: dodecagonal, Islamic architecture, long-range order, quasi-periodi

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