Search results for: digital transformation.

Authors: Maria E. de Boyrie, Darlene Nelson, James A. Nelson

Abstract:

The history of money is described in relationship to the history of computing. With the transformation and acceptance of money as information, major challenges to the security of money have involved engineering, computer science, and management. Research opportunities and challenges are described as money continues its transformation into information.

Keywords: Electronic, information, money, risk.

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Authors: Abdulfatah A Raji

Abstract:

This paper started with the definitions of literature, Arabic literature, transformation and went further to highlight the components of educational transformation. The general history of Arabic literature was discussed with focus on how it undergoes some transformations from pre-Islamic period through Quranic era, Abbasid literature to renaissance period in which the modernization of Arabic literature started in Egypt. It also traces the spread of Arabic literature in Nigeria from the pre-colonial era during the Kanuri rulers to Jihad of Usman Dan Fodio and the development of literature which manifested to the Teacher’s Colleges and Bayero University in Northern Nigeria. Also, the establishment of primary and post-primary schools by Muslim organizations in many cities and towns of the Western part of Nigeria. Literary criticism was also discussed in line with Arabic literature. Poetry work of eminent poets were cited to show its importance in line with educational transformation in Nigerian literature and lessons from the cited Arabic poetry works were also highlighted to include: motivation to behave well and to tolerate others, better spirits of interaction, love and co-existence among different sexes, religion etc. All these can help in developing a better educational transformation in Nigeria which can in turn help in how to conduct researches for national development. The paper recommended compulsory Arabic literature at all levels of the nations’ educational system as well as publication of Arabic books and journals to encourage peace in this era of conflicts and further transform Nigeria’s educational system for better.

Keywords: Arabic, literature, peace, development, Nigeria

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Authors: S. Saisundar, Shan Jiang, Kevin T. C. Chai, David Nuttman, Minkyu Je

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Keywords: Analog to digital converter, cyclic, gain-boosting, pipelined.

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Authors: Marita Canina, Carmen Bruno

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Digital Do It Yourself (DIY) is a contemporary socio-technological phenomenon, enabled by technological tools. The nature and potential long-term effects of this phenomenon have been widely studied within the framework of the EU funded project ‘Digital Do It Yourself’, in which the authors have created and experimented a specific Digital Do It Yourself (DiDIY) co-design process. The phenomenon was first studied through a literature research to understand its multiple dimensions and complexity. Therefore, co-design workshops were used to investigate the phenomenon by involving people to achieve a complete understanding of the DiDIY practices and its enabling factors. These analyses allowed the definition of the DiDIY fundamental factors that were then translated into a design tool. The objective of the tool is to shape design concepts by transferring these factors into different environments to achieve innovation. The aim of this paper is to present the ‘DiDIY Factor Stimuli’ tool, describing the research path and the findings behind it.

Keywords: Co-design process, digital DIY, innovation, toolkit.

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Authors: Siamak Rasulzadeh

Abstract:

Graph transformation has recently become more and more popular as a general visual modeling language to formally state the dynamic semantics of the designed models. Especially, it is a very natural formalism for languages which basically are graph (e.g. UML). Using this technique, we present a highly understandable yet precise approach to formally model and analyze the behavioral semantics of UML 2.0 Activity diagrams. In our proposal, AGG is used to design Activities, then using our previous approach to model checking graph transformation systems, designers can verify and analyze designed Activity diagrams by checking the interesting properties as combination of graph rules and LTL (Linear Temporal Logic) formulas on the Activities.

Keywords: UML 2.0 Activity, Verification, Model Checking, Graph Transformation, Dynamic Semantics.

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Authors: H. M. Côrtes, J. I. Da Silva Filho, M. F. Blos, B. S. Zanon

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In a modern society the factor corresponding to the increase in the level of quality in industrial production demand new techniques of control and machinery automation. In this context, this work presents the implementation of a Paraconsistent-Fuzzy Digital PID controller. The controller is based on the treatment of inconsistencies both in the Paraconsistent Logic and in the Fuzzy Logic. Paraconsistent analysis is performed on the signals applied to the system inputs using concepts from the Paraconsistent Annotated Logic with annotation of two values (PAL2v). The signals resulting from the paraconsistent analysis are two values defined as Dc - Degree of Certainty and Dct - Degree of Contradiction, which receive a treatment according to the Fuzzy Logic theory, and the resulting output of the logic actions is a single value called the crisp value, which is used to control dynamic system. Through an example, it was demonstrated the application of the proposed model. Initially, the Paraconsistent-Fuzzy Digital PID controller was built and tested in an isolated MATLAB environment and then compared to the equivalent Digital PID function of this software for standard step excitation. After this step, a level control plant was modeled to execute the controller function on a physical model, making the tests closer to the actual. For this, the control parameters (proportional, integral and derivative) were determined for the configuration of the conventional Digital PID controller and of the Paraconsistent-Fuzzy Digital PID, and the control meshes in MATLAB were assembled with the respective transfer function of the plant. Finally, the results of the comparison of the level control process between the Paraconsistent-Fuzzy Digital PID controller and the conventional Digital PID controller were presented.

Keywords: Fuzzy logic, paraconsistent annotated logic, level control, digital PID.

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Authors: Youssef Khmou, Said Safi

Abstract:

In this paper, we investigated the effect of real valued transformation of the spectral matrix of the received data for Angles Of Arrival estimation problem.  Indeed, the unitary transformation of Partial Propagator (UPP) for narrowband sources is proposed and applied on Uniform Linear Array (ULA).

Monte Carlo simulations proved the performance of the UPP spectrum comparatively with Forward Backward Partial Propagator (FBPP) and Unitary Propagator (UP). The results demonstrates that when some of the sources are fully correlated and closer than the Rayleigh angular limit resolution of the broadside array, the UPP method outperforms the FBPP in both of spatial resolution and complexity.

Keywords: DOA, Uniform Linear Array, Narrowband, Propagator, Real valued transformation, Subspace, Unitary Operator.

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Authors: Asim Majeed, Anwar Ul Haq, Mike, Lloyd-Williams, Arshad Jamal, Usman Butt

Abstract:

This study aims to investigate the impact of data leak of M&S customers on digital communities. Modern businesses are using digital communities as an important public relations tool for marketing purposes. This form of communication helps companies to build better relationship with their customers which also act as another source of information. The communication between the customers and the organizations is not regulated so users may post positive and negative comments. There are new platforms being developed on a daily basis and it is very crucial for the businesses to not only get themselves familiar with those but also know how to reach their existing and perspective consumers. The driving force of marketing and communication in modern businesses is the digital communities and these are continuously increasing and developing. This phenomenon is changing the way marketing is conducted. The current research has discussed the implications on M&S business performance since the data was exploited on digital communities; users contacted M&S and raised the security concerns. M&S closed down its website for few hours to try to resolve the issue. The next day M&S made a public apology about this incidence. This information was proliferated on various digital communities and it has impacted negatively on M&S brand name, sales and customers. The content analysis approach is being used to collect qualitative data from 100 digital bloggers including social media communities such as Facebook and Twitter. The results and finding provide useful new insights into the nature and form of security concerns of digital users. Findings have theoretical and practical implications. This research will showcase a large corporation utilizing various digital community platforms and can serve as a model for future organizations.

Keywords: Digital, communities, performance, dissemination, implications, data, exploitation.

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Authors: Sukhwinder Singh Billing, Sushma Gupta, Sukhjit Singh Dhaliwal

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the present paper, using the technique of differential subordination, we obtain certain results for analytic functions defined by a multiplier transformation in the open unit disc E = { z : IzI < 1}. We claim that our results extend and generalize the existing results in this particular direction

Keywords: function, Differential subordination, Multiplier transformation.

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Authors: Anindya Roy, Goutam Saha

Abstract:

Rapid progress in audio compression technology has contributed to the explosive growth of music available in digital form today. In a reversal of ideas, this work makes use of a recently proposed efficient audio compression scheme to develop three important applications in the context of Music Information Retrieval (MIR) for the effective manipulation of large music databases, namely automatic music recommendation (AMR), digital rights management (DRM) and audio finger-printing for song identification. The performance of these three applications has been evaluated with respect to a database of songs collected from a diverse set of genres.

Keywords: Audio compression, Music Information Retrieval, Digital Rights Management, Audio Fingerprinting.

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Authors: Hyungkeun Jee, Jooyoung Lee, Dowon Hong

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The most common forensic activity is searching a hard disk for string of data. Nowadays, investigators and analysts are increasingly experiencing large, even terabyte sized data sets when conducting digital investigations. Therefore consecutive searching can take weeks to complete successfully. There are two primary search methods: index-based search and bitwise search. Index-based searching is very fast after the initial indexing but initial indexing takes a long time. In this paper, we discuss a high speed bitwise search model for large-scale digital forensic investigations. We used pattern matching board, which is generally used for network security, to search for string and complex regular expressions. Our results indicate that in many cases, the use of pattern matching board can substantially increase the performance of digital forensic search tools.

Keywords: Digital forensics, search, regular expression.

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Authors: Do-Jin Jang, Sung-Ah Kim

Abstract:

In designing a kinetic façade, it is hard for the designer to make digital models due to its complex geometry with motion. This paper aims to present a methodology of converting a point cloud of a physical model into a single digital model with a certain topology and motion. The method uses a Microsoft Kinect sensor, and color markers were defined and applied to three paper folding-inspired designs. Although the resulted digital model cannot represent the whole folding range of the physical model, the method supports the designer to conduct a performance-oriented design process with the rough physical model in the reduced folding range.

Keywords: Design media, kinetic façades, tangible user interface, 3D scanning.

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Authors: Nerey H. Mvungi, Justinian Anatory, Fatuma Simba

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Digital broadcasting has been an area of active research, development, innovation and business models development in recent years. This paper presents a survey on the characteristics of the digital terrestrial television broadcasting (DTTB) standards, and implementation status of DTTB worldwide showing the standards adopted. It is clear that only the developed countries and some in the developing ones shall be able to beat the ITU set analogue to digital broadcasting migration deadline because of the challenges that these countries faces in digitizing their terrestrial broadcasting. The challenges to keep on track the DTTB migration plan are also discussed in this paper. They include financial, technology gap, policies alignment with DTTB technology, etc. The reported performance comparisons for the different standards are also presented. The interesting part is that the results for many comparative studies depends to a large extent on the objective behind such studies, hence counter claims are common.

Keywords: Digital terrestrial television broadcasting (DTTB) technologies, DTTB standards comparison, DTTB implementation.

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Authors: Bokyung Sung, Kwanghyo Koo, Jungsoo Kim, Myung-Bum Jung, Jinman Kwon, Ilju Ko

Abstract:

In this paper, we propose effective system for digital music retrieval. We divided proposed system into Client and Server. Client part consists of pre-processing and Content-based feature extraction stages. In pre-processing stage, we minimized Time code Gap that is occurred among same music contents. As content-based feature, first-order differentiated MFCC were used. These presented approximately envelop of music feature sequences. Server part included Music Server and Music Matching stage. Extracted features from 1,000 digital music files were stored in Music Server. In Music Matching stage, we found retrieval result through similarity measure by DTW. In experiment, we used 450 queries. These were made by mixing different compression standards and sound qualities from 50 digital music files. Retrieval accurate indicated 97% and retrieval time was average 15ms in every single query. Out experiment proved that proposed system is effective in retrieve digital music and robust at various user environments of web.

Keywords: Music Retrieval, Content-based, Music Feature and Digital Music.

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Authors: Syed Musharaf Ali, Muhammad Younus Javed, Naveed Sarfraz Khattak, Athar Mohsin, UmarFarooq

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This paper introduces the effective speckle reduction of synthetic aperture radar (SAR) images using inner product spaces in undecimated wavelet domain. There are two major areas in projection onto span algorithm where improvement can be made. First is the use of undecimated wavelet transformation instead of discrete wavelet transformation. And second area is the use of smoothing filter namely directional smoothing filter which is an additional step. Proposed method does not need any noise estimation and thresholding technique. More over proposed method gives good results on both single polarimetric and fully polarimetric SAR images.

Keywords: Directional Smoothing, Inner product, Length ofvector, Undecimated wavelet transformation.

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Authors: Daniel Schwarz, Jan Fivaz, Alessia Neuroni

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Although digitization is a buzzword in almost every election campaign, the political parties leave voters largely in the dark about their specific positions on digital issues. In the run-up to the 2019 elections in Switzerland, the ‘Digitization Monitor’ project (DMP) was launched in order to change this situation. Within the framework of the DMP, all 4,736 candidates were surveyed about their digital policy positions and values. The DMP is designed as a digital policy supplement to the existing ‘smartvote’ voting advice application. This enabled a direct comparison of the digital policy attitudes according to the DMP with the topics of the ‘smartvote’ questionnaire which are comprehensive in content but mainly related to conventional policy areas. This paper’s main research goal is to analyze and visualize possible differences between conventional and digital policy areas in terms of response patterns between and within political parties. The analysis is based on dimensionality reduction methods (multidimensional scaling and principal component analysis) for the visualization of inter-party differences, and on standard deviation as a measure of variation for the evaluation of intra-party unity. The results reveal that digital issues show a lower degree of inter-party polarization compared to conventional policy areas. Thus, the parties have more common ground in issues on digitization than in conventional policy areas. In contrast, the study reveals a mixed picture regarding intra-party unity. Homogeneous parties show a lower degree of unity in digitization issues whereas parties with heterogeneous positions in conventional areas have more united positions in digital areas. All things considered, the findings are encouraging as less polarized conditions apply to the debate on digital development compared to conventional politics. For the future, it would be desirable if in further countries similar projects to the DMP could emerge to broaden the basis for conclusions.

Keywords: Comparison of political issue dimensions, digital awareness of candidates, digital policy space, party positions on digital issues.

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Authors: N. Popovich, P. Yan

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In this paper a controller for the pitch angle of an aircraft regarding to the elevator deflection angle is designed. The way how the elevator angle affects pitching motion of the aircraft is pointed out, as well as, how a pitch controller can be applied for the aircraft to reach certain pitch angle. In this digital optimal system, the elevator deflection angle and pitching angle of the plane are considered to be input and output respectively. A single input single output (SISO) system is presented. A digital pitch aircraft control is demonstrated. A simulation for the whole system has been performed. The optimal control weighting vectors, Q and R have been determined.

Keywords: Aircraft, control, digital, optimal, Q and Rmatrices.

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Authors: F. Amin, S. Feizi

Abstract:

This paper describes the complex nature of organizational culture and its role in telecom organizations. To set the stage for culture change, the literature is reviewed for perspective on the role and function of culture in organizations. Organizational the­orists as well as business consultants report that a strong organizational culture is essential for success because the shared assumptions, values and culture of an organization influence the behavior of its individual members.

Keywords: Component, Telecommunication, Management, Cultural, Transformation.

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Authors: Aber Salem Aboalgasm, Rupert Ward

Abstract:

The aim of this research is to explore how pupils in art classes can use creative digital art tools to redesign Tamazight fonts, in order to develop children’s artistic creativity, enable them to learn about a new culture, and to help the teacher assess the creativity of pupils in the art class. It can also help students to improve their talents in drawing. The study could relate to research in Libya among the Amazigh people (better known as Berber) and possibly the development of Tamazight fonts with new uses in art. The research involved students aged 9-10 years old working with digital art tools, and was designed to explore the potential of digital technology by discovering suitable tools and techniques to develop children’s artistic performance using Tamazight fonts. The project also sought to show the aesthetic aspects of these characters and to stimulate the artistic creativity of these young people.

Keywords: Artistic creativity, Tamazight fonts, Technology acceptance model, Traditional and digital art tools.

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Authors: Aishwarya Ravichandra, Kirtana Kirtivasan, Adithi Mahesh, Ashwini S.Savanth

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A Non-Contact Digital Music System has been conceptualized and implemented to create a new era of digital music. This system replaces the strings of a traditional stringed instrument with laser beams to avoid bruising of the user’s hand. The system consists of seven laser modules, detector modules and distance sensors that form the basic hardware blocks of this instrument. Arduino ATmega2560 microcontroller is used as the primary interface between the hardware and the software. MIDI (Musical Instrument Digital Interface) is used as the protocol to establish communication between the instrument and the virtual synthesizer software.

Keywords: Arduino, Detector, Laser, MIDI, NOTE ON, NOTE OFF, PITCH BEND, Sharp IR distance sensor.

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Authors: Kyunghoon Kim, Sungjoon Shim, Jun Tae Kim, Jong Tae Kim

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In a wireless communication system, a predistorter(PD) is often employed to alleviate nonlinear distortions due to operating a power amplifier near saturation, thereby improving the system performance and reducing the interference to adjacent channels. This paper presents a new adaptive polynomial digital predistorter(DPD). The proposed DPD uses Coordinate Rotation Digital Computing(CORDIC) processors and PD process by pipelined architecture. It is simpler and faster than conventional adaptive polynomial DPD. The performance of the proposed DPD is proved by MATLAB simulation.

Keywords: DPD, CORDIC.

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Authors: Jakub Havlicek, Jiri Cajthaml

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The article describes the effect of the replacement of the used reference coordinate system in the georeferencing of an old map of Europe. The map was georeferenced into three types of projection – the equal-area conic (original cartographic projection), cylindrical Plate Carrée and cylindrical Mercator map projection. The map was georeferenced by means of the affine and the second-order polynomial transformation. The resulting georeferenced raster datasets from the Plate Carrée and Mercator projection were projected into the equal-area conic projection by means of projection equations. The output is the comparison of drawn graphics, the magnitude of standard deviations for individual projections and types of transformation.

Keywords: Georeferencing, reference coordinate system, transformation, standard deviation.

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Authors: Sadife Güngör, Sevilay Konya, Zeynep Karaçor

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Inflation and foreign trade are the most important economic indicator of a country. In this study, Turkey's economy with the policies adopted after 2000, given how performs an economic transformation. This transformation of the economy is discussed with inflation and foreign trade. In this context, attention is drawn to 2001 Strong Economy and Transition Program and 2006 Inflation Targeting Regime. The evaluation was performed of after the year 2000 inflation and foreign trade figures in Turkey economy. When we looked the progress, after 2000 in Turkey economy, we can say a new process was built up.

Keywords: Inflation, foreign trade, 2001 strong economy program, 2006 ınflation targeting regime.

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Authors: Jianqiao. Yu, Jianbo. Wang, Xinzhen. He

Abstract:

This paper presents a longitudinal quasi-linear model for the ADMIRE model. The ADMIRE model is a nonlinear model of aircraft flying in the condition of high angle of attack. So it can-t be considered to be a linear system approximately. In this paper, for getting the longitudinal quasi-linear model of the ADMIRE, a state transformation based on differentiable functions of the nonscheduling states and control inputs is performed, with the goal of removing any nonlinear terms not dependent on the scheduling parameter. Since it needn-t linear approximation and can obtain the exact transformations of the nonlinear states, the above-mentioned approach is thought to be appropriate to establish the mathematical model of ADMIRE. To verify this conclusion, simulation experiments are done. And the result shows that this quasi-linear model is accurate enough.

Keywords: quasi-linear model, simulation, state transformation approach, the ADMIRE model.

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Authors: Peyman Sindareh Esfahani, Jeffery Kurt Pieper

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In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the l₂-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.

Keywords: Linear fractional transformation, linear matrix inequality, robust model predictive control, state feedback control.

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Authors: Hossam El-din H. Ahmed, Hamdy M. Kalash, Osama S. Farag Allah

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This paper investigates the encryption efficiency of RC6 block cipher application to digital images, providing a new mathematical measure for encryption efficiency, which we will call the encryption quality instead of visual inspection, The encryption quality of RC6 block cipher is investigated among its several design parameters such as word size, number of rounds, and secret key length and the optimal choices for the best values of such design parameters are given. Also, the security analysis of RC6 block cipher for digital images is investigated from strict cryptographic viewpoint. The security estimations of RC6 block cipher for digital images against brute-force, statistical, and differential attacks are explored. Experiments are made to test the security of RC6 block cipher for digital images against all aforementioned types of attacks. Experiments and results verify and prove that RC6 block cipher is highly secure for real-time image encryption from cryptographic viewpoint. Thorough experimental tests are carried out with detailed analysis, demonstrating the high security of RC6 block cipher algorithm. So, RC6 block cipher can be considered to be a real-time secure symmetric encryption for digital images.

Keywords: Block cipher, Image encryption, Encryption quality, and Security analysis.

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Authors: Ju-Hong Lee, Chong-Jia Ciou

Abstract:

This paper deals with the problem of two-dimensional (2-D) recursive two-channel quincunx quadrature mirror filter (QQMF) banks design. The analysis and synthesis filters of the 2-D recursive QQMF bank are composed of 2-D recursive digital allpass lattice filters (DALFs) with symmetric half-plane (SHP) support regions. Using the 2-D doubly complementary half-band (DC-HB) property possessed by the analysis and synthesis filters, we facilitate the design of the proposed QQMF bank. For finding the coefficients of the 2-D recursive SHP DALFs, we present a structure of 2-D recursive digital allpass filters by using 2-D SHP recursive digital all-pass lattice filters (DALFs). The novelty of using 2-D SHP recursive DALFs to construct a 2-D recursive QQMF bank is that the resulting 2-D recursive QQMF bank provides better performance than the existing 2-D recursive QQMF banks. Simulation results are also presented for illustration and comparison.

Keywords: All-pass digital filter, doubly complementary, lattice structure, symmetric half-plane digital filter, quincunx QMF bank.

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Authors: Abhimanyu Pati, Prabir K. Bandyopadhyay

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The paper intends to highlight the significance of Digital Manufacturing (DM) strategy in support and achievement of business strategy and goals of any manufacturing organization. Towards this end, DM initiatives have been given a process perspective, while not undermining its technological significance, with a view to link its benefits directly with fulfilment of customer needs and expectations in a responsive and cost-effective manner. A digital process model has been proposed to categorize digitally enabled organizational processes with a view to create synergistic groups, which adopt and use digital tools having similar characteristics and functionalities. This will throw future opportunities for researchers and developers to create a unified technology environment for integration and orchestration of processes. Secondly, an effort has been made to apply “what” and “how” features of Quality Function Deployment (QFD) framework to establish the relationship between customers’ needs – both for external and internal customers, and the features of various digital processes, which support for the achievement of these customer expectations. The paper finally concludes that in the present highly competitive environment, business organizations cannot thrive to sustain unless they understand the significance of digital strategy and integrate it with their business strategy with a clearly defined implementation roadmap. A process-oriented approach to DM strategy will help business executives and leaders to appreciate its value propositions and its direct link to organization’s competitiveness.

Keywords: Digital manufacturing, digital process model, quality function deployment, business strategy.

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Authors: Michael Zimba, Darlison Nyirenda

Abstract:

A novel copy-move image forgery, CMIF, detection method is proposed. The proposed method presents a new approach which relies on electrostatic field theory, EFT. Solely for the purpose of reducing the dimension of a suspicious image, the proposed algorithm firstly performs discrete wavelet transform, DWT, of the suspicious image and extracts only the approximation subband. The extracted subband is then bijectively mapped onto a virtual electrostatic field where concepts of EFT are utilized to extract robust features. The extracted features are invariant to additive noise, JPEG compression, and affine transformation. Finally, same affine transformation selection, SATS, a duplication verification method, is applied to detect duplicated regions. SATS is a better option than the common shift vector method because SATS is insensitive to affine transformation. Consequently, the proposed CMIF algorithm is not only fast but also more robust to attacks compared to the existing related CMIF algorithms. The experimental results show high detection rates, as high as 100% in some cases.

Keywords: Affine transformation, Radix sort, SATS, Virtual electrostatic field.

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Authors: T. Sakamoto, N. Hori

Abstract:

A multi-rate discrete-time model, whose response agrees exactly with that of a continuous-time original at all sampling instants for any sampling periods, is developed for a linear system, which is assumed to have multiple real eigenvalues. The sampling rates can be chosen arbitrarily and individually, so that their ratios can even be irrational. The state space model is obtained as a combination of a linear diagonal state equation and a nonlinear output equation. Unlike the usual lifted model, the order of the proposed model is the same as the number of sampling rates, which is less than or equal to the order of the original continuous-time system. The method is based on a nonlinear variable transformation, which can be considered as a generalization of linear similarity transformation, which cannot be applied to systems with multiple eigenvalues in general. An example and its simulation result show that the proposed multi-rate model gives exact responses at all sampling instants.

Keywords: Multi-rate discretization, linear systems, triangularization, similarity transformation, diagonalization, exponential transformation, multiple eigenvalues

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