In this paper, radix-3 algorithm for computation of type-II discrete sine transform (DST-II) of length N =
3푚 (푚 = 1,2, … . ) is presented. The DST-II of length N can be realized from three DST-II sequences, each of
length N/3. A block diagram of for computation of the radix-3 DST-II algorithm is given. Signal flow graph for
DST-II of length 푁 = 32 is shown to clarify the proposed algorithm.
Radix-2 Algorithms for realization of Type-II Discrete Sine Transform and Typ...IJERA Editor
In this paper, radix-2 algorithms for computation of type-II discrete sine transform (DST-II) and type-IV
discrete sine transform (DST-IV), each of length 2 ( 2,3,.....)
m
N m , are presented. The odd-indexed
output components of DST-II can be realized using simple recursive relations. The recursive algorithms are
appropriate for VLSI implementation. The DST-IV of length N can be computed from type-II discrete cosine
transform (DCT-II) and DST-II sequences, each of length N/2.
LADDER AND SUBDIVISION OF LADDER GRAPHS WITH PENDANT EDGES ARE ODD GRACEFULFransiskeran
The ladder graph plays an important role in many applications as Electronics, Electrical and Wireless
communication areas. The aim of this work is to present a new class of odd graceful labeling for the ladder
graph. In particular, we show that the ladder graph Ln with m-pendant Ln mk1 is odd graceful. We also
show that the subdivision of ladder graph Ln with m-pendant S(Ln) mk1 is odd graceful. Finally, we
prove that all the subdivision of triangular snakes ( k snake ) with pendant edges
1
( ) k S snake mk are odd graceful.
The idea of metric dimension in graph theory was introduced by P J Slater in [2]. It has been found
applications in optimization, navigation, network theory, image processing, pattern recognition etc.
Several other authors have studied metric dimension of various standard graphs. In this paper we
introduce a real valued function called generalized metric G X × X × X ® R+ d : where X = r(v /W) =
{(d(v,v1),d(v,v2 ),...,d(v,v ) / v V (G))} k Î , denoted d G and is used to study metric dimension of graphs. It
has been proved that metric dimension of any connected finite simple graph remains constant if d G
numbers of pendant edges are added to the non-basis vertices.
Radix-3 Algorithm for Realization of Discrete Fourier TransformIJERA Editor
In this paper, a new radix-3 algorithm for realization of discrete Fourier transform (DFT) of length N = 3m (m =
1, 2, 3,...) is presented. The DFT of length N can be realized from three DFT sequences, each of length N/3. If
the input signal has length N, direct calculation of DFT requires O (N
2
) complex multiplications (4N
2
real
multiplications) and some additions. This radix-3 algorithm reduces the number of multiplications required for
realizing DFT. For example, the number of complex multiplications required for realizing 9-point DFT using the
proposed radix-3 algorithm is 60. Thus, saving in time can be achieved in the realization of proposed algorithm.
In an earlier paper in 2017, Rastogi and Bajpai[1] defined and studied a special vector field of the first kind in a Finsler space as follows:
Definition 1: A vector field Xi(x), in a Finsler space, is said to be a special vector field of the first kind, if (i) Xi/j = - δij and (ii) Xi hij = Ɵj, where Ɵj is a non-zero vector field in the given Finsler space.
In 2019, some more special vector fields in a Finsler space of two and three dimensions have been defined and studied by the authors Dwivedi et al.[2] and Dwivedi et al.[3] In Dwivedi et al.[3], the authors defined and studied six kinds of special vector fields in a Finsler space of three dimensions and, respectively, called them special vector fields of the second, third, fourth, fifth, sixth, and seventh kind. In the present paper, we shall study some curvature properties of special vector fields of the first and seventh kind in a Finsler space of three dimensions.
JEE Mathematics/ Lakshmikanta Satapathy/ 3D Geometry QA 10/ JEE question on equation of plane passing through the line of intersection of two planes and at a given distance from a given point
Radix-2 Algorithms for realization of Type-II Discrete Sine Transform and Typ...IJERA Editor
In this paper, radix-2 algorithms for computation of type-II discrete sine transform (DST-II) and type-IV
discrete sine transform (DST-IV), each of length 2 ( 2,3,.....)
m
N m , are presented. The odd-indexed
output components of DST-II can be realized using simple recursive relations. The recursive algorithms are
appropriate for VLSI implementation. The DST-IV of length N can be computed from type-II discrete cosine
transform (DCT-II) and DST-II sequences, each of length N/2.
LADDER AND SUBDIVISION OF LADDER GRAPHS WITH PENDANT EDGES ARE ODD GRACEFULFransiskeran
The ladder graph plays an important role in many applications as Electronics, Electrical and Wireless
communication areas. The aim of this work is to present a new class of odd graceful labeling for the ladder
graph. In particular, we show that the ladder graph Ln with m-pendant Ln mk1 is odd graceful. We also
show that the subdivision of ladder graph Ln with m-pendant S(Ln) mk1 is odd graceful. Finally, we
prove that all the subdivision of triangular snakes ( k snake ) with pendant edges
1
( ) k S snake mk are odd graceful.
The idea of metric dimension in graph theory was introduced by P J Slater in [2]. It has been found
applications in optimization, navigation, network theory, image processing, pattern recognition etc.
Several other authors have studied metric dimension of various standard graphs. In this paper we
introduce a real valued function called generalized metric G X × X × X ® R+ d : where X = r(v /W) =
{(d(v,v1),d(v,v2 ),...,d(v,v ) / v V (G))} k Î , denoted d G and is used to study metric dimension of graphs. It
has been proved that metric dimension of any connected finite simple graph remains constant if d G
numbers of pendant edges are added to the non-basis vertices.
Radix-3 Algorithm for Realization of Discrete Fourier TransformIJERA Editor
In this paper, a new radix-3 algorithm for realization of discrete Fourier transform (DFT) of length N = 3m (m =
1, 2, 3,...) is presented. The DFT of length N can be realized from three DFT sequences, each of length N/3. If
the input signal has length N, direct calculation of DFT requires O (N
2
) complex multiplications (4N
2
real
multiplications) and some additions. This radix-3 algorithm reduces the number of multiplications required for
realizing DFT. For example, the number of complex multiplications required for realizing 9-point DFT using the
proposed radix-3 algorithm is 60. Thus, saving in time can be achieved in the realization of proposed algorithm.
In an earlier paper in 2017, Rastogi and Bajpai[1] defined and studied a special vector field of the first kind in a Finsler space as follows:
Definition 1: A vector field Xi(x), in a Finsler space, is said to be a special vector field of the first kind, if (i) Xi/j = - δij and (ii) Xi hij = Ɵj, where Ɵj is a non-zero vector field in the given Finsler space.
In 2019, some more special vector fields in a Finsler space of two and three dimensions have been defined and studied by the authors Dwivedi et al.[2] and Dwivedi et al.[3] In Dwivedi et al.[3], the authors defined and studied six kinds of special vector fields in a Finsler space of three dimensions and, respectively, called them special vector fields of the second, third, fourth, fifth, sixth, and seventh kind. In the present paper, we shall study some curvature properties of special vector fields of the first and seventh kind in a Finsler space of three dimensions.
JEE Mathematics/ Lakshmikanta Satapathy/ 3D Geometry QA 10/ JEE question on equation of plane passing through the line of intersection of two planes and at a given distance from a given point
Performance Analysis of CRT for Image Encryption ijcisjournal
With the fast advancements of information technology, the security of image data transmitted or stored over
internet is become very difficult. To hide the details, an effective method is encryption, so that only
authorized persons can decrypt the image with the keys available. Since the default features of digital
image such as high capacity data, large redundancy and large similarities among pixels, the conventional
encryption algorithms such as AES, , DES, 3DES, and Blow Fish, are not applicable for real time image
encryption. This paper presents the performance of CRT for image encryption to secure storage and
transmission of image over internet.
Performance Improvement of Vector Quantization with Bit-parallelism HardwareCSCJournals
Vector quantization is an elementary technique for image compression; however, searching for the nearest codeword in a codebook is time-consuming. In this work, we propose a hardware-based scheme by adopting bit-parallelism to prune unnecessary codewords. The new scheme uses a “Bit-mapped Look-up Table” to represent the positional information of the codewords. The lookup procedure can simply refer to the bitmaps to find the candidate codewords. Our simulation results further confirm the effectiveness of the proposed scheme.
Mapping between Discrete Cosine Transform of Type-VI/VII and Discrete Fourier...IJERA Editor
In this paper, the mapping between discrete cosine transform of types VI and VII (DCT-VI/VII) of even length
N and (2N – 1)-point one dimensional discrete Fourier transform (1D-DFT) is presented. The technique used in
this paper is the mapping between the real-valued data sequence to an intermediate sequence used as an input to
DFT
Integral solutions of the ternary cubic equation eSAT Journals
Abstract Urban growth has resulted in increasing demand for energy primarily in form of electricity. With depleting energy resources, growing concern for promotion of alternative energy sources urban housing is going through a transition phase. There is a greater need for promotion of on-site microgeneration systems at community level to ensure a near zero sustainable domestic sector. The paper tries to define three major concerns that need to be addressed in ensuring near zero housing communities – the first being understanding the character of existing renewable energy strategies and promoting them in the context of changing housing typologies, second, identifying the need for development of hybrid energy generation systems in conjunction with renewable energy systems to balance energy demand at times of climatic inconsistencies, the third concern being the integration of on-site microgeneration infrastructure within the context of the built environment without altering the existing character and aesthetics. Keywords: Micro generation, Near Zero Housing Communities, Hybrid Energy Systems, Housing Typologies, Integrated Development
CUBIC RESPONSE SURFACE DESIGNS USING BIBD IN FOUR DIMENSIONS mathsjournal
Response Surface Methodology (RSM) has applications in Chemical, Physical, Meteorological, Industrial and Biological fields. The estimation of slope response surface occurs frequently in practical
situations for the experimenter. The rates of change of the response surface, like rates of change in the yield of crop to various fertilizers, to estimate the rates of change in chemical experiments etc. are of interest. If the fit of second order response is inadequate for the design points, we continue the experiment so as to fit a third order response surface. Higher order response surface designs are
sometimes needed in Industrial andMeteorological applications. Gardiner et al (1959) introduced third order rotatable designs for exploring response surface. Anjaneyulu et al (1994-1995) constructed third order
slope rotatable designs using doubly balanced incomplete block designs. Anjaneyulu etal (2001) introduced third order slope rotatable designs using central composite type design points.Seshu babu et al (2011) studied modified construction of third order slope rotatable designs using central composite designs.Seshu babu et al (2014) constructed TOSRD using BIBD.In view of wide applicability of third order models in RSM and importance of slope rotatability, we introduce. A Cubic Slope Rotatable Designs Using BIBD in four dimensions.
Encryption Quality Analysis and Security Evaluation of CAST-128 Algorithm and...IJNSA Journal
This paper demonstrates analysis of well known block cipher CAST-128 and its modified version using avalanche criterion and other tests namely encryption quality, correlation coefficient, histogram analysis and key sensitivity
tests.
Lattice points on the homogeneous cone 5(x2+y2) 9xy=23z2eSAT Journals
Seven different method s of the non-zero non-negative solutions of homogeneous Diophantine equation 5(x2 + y2) – 9xy = 23z2 are obtained. Introducing the linear transformation x =u + v, y= u – v, u v0 in 5(x2+y2) -9xy = 23z2, it reduces to u2 + 19v2 =23z2. We are solved the above equation through various choices and are obtained seven different methods of solutions which are satisfied it. Some interesting relations among the special numbers and the solutions are exposed.
Effect of Process Parameters of Friction Stir Welded Joint for Similar Alumin...IJERA Editor
In this paper the effect of process parameters of friction stir welded joint for similar aluminium alloys H30 was studied. Taper cylindrical with three flutes all made of High speed steel was used for the friction stir welding (FSW) aluminium alloy H30 and the tensile test of the welded joint were tested by universal testing method. The optimization done using detailed mathematical model is simulated by Minitab17. In this investigation, an effective approach based on Taguchi method, has been developed to determine the optimum conditions leading to higher tensile strength. Experiments were conducted on varying rotational speed, transverse speed, and axial force using L9 orthogonal array of Taguchi method. The present study aims at optimizing process parameters to achieve high tensile strength.
A Low Phase Noise CMOS Quadrature Voltage Control Oscillator Using Clock Gate...IJERA Editor
This project presents the low phase noise cmos quadrature voltage control oscillator using clock gating technique. Here the colpitts vco is used to split the capacitance in the Qvco circuit producing quadrature output. The startup condition in the oscillator is improved by using 퐺푚enhancement [12].This QVCO performs the operation anti phase injection locking fordevice reuse [8]. The new clock gating technique is used to reduce the power with thepower supply 1.5v. The QVCO uses a 0.5m퐴with phase error of 0.4표and exhibits a phase noise of -118dBc/HZ at 1MHZ offset at the centre frequency of 500MHZ.
Index terms: current switching, clock gating, phase noise, Qvco
Sub-Threshold Leakage Current Reduction Techniques In VLSI Circuits -A SurveyIJERA Editor
There is an increasing demand for portable devices powered up by battery, this led the manufacturers of
semiconductor technology to scale down the feature size which results in reduction in threshold voltage and
enables the complex functionality on a single chip. By scaling down the feature size the dynamic power
dissipation has no effect but the static power dissipation has become equal or more than that of Dynamic power
dissipation. So in recent CMOS technologies static power dissipation i.e. power dissipation due to leakage
current has become a challenging area for VLSI chip designers. In order to prolong the battery life and maintain
reliability of circuit, leakage current reduction is the primary goal. A basic overview of techniques used for
reduction of sub-threshold leakages is discussed in this paper. Based on the surveyed techniques, one would be
able to choose required and apt leakage reduction technique.
Limit State Design: IS: 800 2007 a New Challenge for Structural Engineers in ...IJERA Editor
Since last two decades Limit State concept of Design (LSD) of steel structure has been adopted by the structural engineers worldwide. In India it is still a new concept for the practicing structural engineers as the formal publication of IS 800-2007 was made in Dec, 2007, only seven years back. As a result Indian engineers are to face a real challenge to cover-up the gap in between. Publication of ISO: 2943 in 90‟s is a mile stone of global acceptance of LSD. Revision of IS 800-1984 to IS: 800: 2007 is made for a complete change of concept of design hitherto followed. Implementation of LSD was a problem in all most all the countries in the world. India is also facing the same due to delayed introduction of LSD codes when the level of knowledge on limit state developed very fast internationally. Today it becomes an urgent task for the Indian structural engineers to study and review more and more the basic philosophy and concept in contrast to the traditional method of Working Stress Design (WSD) in a documented manner so that this can help everyone in this field for effective application of LSD in practical design. This paper will address this issue as why it becomes a real historical challenge for engineers in India. Here it will also be attempted to highlight the basic philosophical understanding required for successful transformation from the traditional concept to this new concept of LSD. Some comparative design review of both the codes will also be presented for practical understanding of the conceptual changes.
Performance Analysis of CRT for Image Encryption ijcisjournal
With the fast advancements of information technology, the security of image data transmitted or stored over
internet is become very difficult. To hide the details, an effective method is encryption, so that only
authorized persons can decrypt the image with the keys available. Since the default features of digital
image such as high capacity data, large redundancy and large similarities among pixels, the conventional
encryption algorithms such as AES, , DES, 3DES, and Blow Fish, are not applicable for real time image
encryption. This paper presents the performance of CRT for image encryption to secure storage and
transmission of image over internet.
Performance Improvement of Vector Quantization with Bit-parallelism HardwareCSCJournals
Vector quantization is an elementary technique for image compression; however, searching for the nearest codeword in a codebook is time-consuming. In this work, we propose a hardware-based scheme by adopting bit-parallelism to prune unnecessary codewords. The new scheme uses a “Bit-mapped Look-up Table” to represent the positional information of the codewords. The lookup procedure can simply refer to the bitmaps to find the candidate codewords. Our simulation results further confirm the effectiveness of the proposed scheme.
Mapping between Discrete Cosine Transform of Type-VI/VII and Discrete Fourier...IJERA Editor
In this paper, the mapping between discrete cosine transform of types VI and VII (DCT-VI/VII) of even length
N and (2N – 1)-point one dimensional discrete Fourier transform (1D-DFT) is presented. The technique used in
this paper is the mapping between the real-valued data sequence to an intermediate sequence used as an input to
DFT
Integral solutions of the ternary cubic equation eSAT Journals
Abstract Urban growth has resulted in increasing demand for energy primarily in form of electricity. With depleting energy resources, growing concern for promotion of alternative energy sources urban housing is going through a transition phase. There is a greater need for promotion of on-site microgeneration systems at community level to ensure a near zero sustainable domestic sector. The paper tries to define three major concerns that need to be addressed in ensuring near zero housing communities – the first being understanding the character of existing renewable energy strategies and promoting them in the context of changing housing typologies, second, identifying the need for development of hybrid energy generation systems in conjunction with renewable energy systems to balance energy demand at times of climatic inconsistencies, the third concern being the integration of on-site microgeneration infrastructure within the context of the built environment without altering the existing character and aesthetics. Keywords: Micro generation, Near Zero Housing Communities, Hybrid Energy Systems, Housing Typologies, Integrated Development
CUBIC RESPONSE SURFACE DESIGNS USING BIBD IN FOUR DIMENSIONS mathsjournal
Response Surface Methodology (RSM) has applications in Chemical, Physical, Meteorological, Industrial and Biological fields. The estimation of slope response surface occurs frequently in practical
situations for the experimenter. The rates of change of the response surface, like rates of change in the yield of crop to various fertilizers, to estimate the rates of change in chemical experiments etc. are of interest. If the fit of second order response is inadequate for the design points, we continue the experiment so as to fit a third order response surface. Higher order response surface designs are
sometimes needed in Industrial andMeteorological applications. Gardiner et al (1959) introduced third order rotatable designs for exploring response surface. Anjaneyulu et al (1994-1995) constructed third order
slope rotatable designs using doubly balanced incomplete block designs. Anjaneyulu etal (2001) introduced third order slope rotatable designs using central composite type design points.Seshu babu et al (2011) studied modified construction of third order slope rotatable designs using central composite designs.Seshu babu et al (2014) constructed TOSRD using BIBD.In view of wide applicability of third order models in RSM and importance of slope rotatability, we introduce. A Cubic Slope Rotatable Designs Using BIBD in four dimensions.
Encryption Quality Analysis and Security Evaluation of CAST-128 Algorithm and...IJNSA Journal
This paper demonstrates analysis of well known block cipher CAST-128 and its modified version using avalanche criterion and other tests namely encryption quality, correlation coefficient, histogram analysis and key sensitivity
tests.
Lattice points on the homogeneous cone 5(x2+y2) 9xy=23z2eSAT Journals
Seven different method s of the non-zero non-negative solutions of homogeneous Diophantine equation 5(x2 + y2) – 9xy = 23z2 are obtained. Introducing the linear transformation x =u + v, y= u – v, u v0 in 5(x2+y2) -9xy = 23z2, it reduces to u2 + 19v2 =23z2. We are solved the above equation through various choices and are obtained seven different methods of solutions which are satisfied it. Some interesting relations among the special numbers and the solutions are exposed.
Effect of Process Parameters of Friction Stir Welded Joint for Similar Alumin...IJERA Editor
In this paper the effect of process parameters of friction stir welded joint for similar aluminium alloys H30 was studied. Taper cylindrical with three flutes all made of High speed steel was used for the friction stir welding (FSW) aluminium alloy H30 and the tensile test of the welded joint were tested by universal testing method. The optimization done using detailed mathematical model is simulated by Minitab17. In this investigation, an effective approach based on Taguchi method, has been developed to determine the optimum conditions leading to higher tensile strength. Experiments were conducted on varying rotational speed, transverse speed, and axial force using L9 orthogonal array of Taguchi method. The present study aims at optimizing process parameters to achieve high tensile strength.
A Low Phase Noise CMOS Quadrature Voltage Control Oscillator Using Clock Gate...IJERA Editor
This project presents the low phase noise cmos quadrature voltage control oscillator using clock gating technique. Here the colpitts vco is used to split the capacitance in the Qvco circuit producing quadrature output. The startup condition in the oscillator is improved by using 퐺푚enhancement [12].This QVCO performs the operation anti phase injection locking fordevice reuse [8]. The new clock gating technique is used to reduce the power with thepower supply 1.5v. The QVCO uses a 0.5m퐴with phase error of 0.4표and exhibits a phase noise of -118dBc/HZ at 1MHZ offset at the centre frequency of 500MHZ.
Index terms: current switching, clock gating, phase noise, Qvco
Sub-Threshold Leakage Current Reduction Techniques In VLSI Circuits -A SurveyIJERA Editor
There is an increasing demand for portable devices powered up by battery, this led the manufacturers of
semiconductor technology to scale down the feature size which results in reduction in threshold voltage and
enables the complex functionality on a single chip. By scaling down the feature size the dynamic power
dissipation has no effect but the static power dissipation has become equal or more than that of Dynamic power
dissipation. So in recent CMOS technologies static power dissipation i.e. power dissipation due to leakage
current has become a challenging area for VLSI chip designers. In order to prolong the battery life and maintain
reliability of circuit, leakage current reduction is the primary goal. A basic overview of techniques used for
reduction of sub-threshold leakages is discussed in this paper. Based on the surveyed techniques, one would be
able to choose required and apt leakage reduction technique.
Limit State Design: IS: 800 2007 a New Challenge for Structural Engineers in ...IJERA Editor
Since last two decades Limit State concept of Design (LSD) of steel structure has been adopted by the structural engineers worldwide. In India it is still a new concept for the practicing structural engineers as the formal publication of IS 800-2007 was made in Dec, 2007, only seven years back. As a result Indian engineers are to face a real challenge to cover-up the gap in between. Publication of ISO: 2943 in 90‟s is a mile stone of global acceptance of LSD. Revision of IS 800-1984 to IS: 800: 2007 is made for a complete change of concept of design hitherto followed. Implementation of LSD was a problem in all most all the countries in the world. India is also facing the same due to delayed introduction of LSD codes when the level of knowledge on limit state developed very fast internationally. Today it becomes an urgent task for the Indian structural engineers to study and review more and more the basic philosophy and concept in contrast to the traditional method of Working Stress Design (WSD) in a documented manner so that this can help everyone in this field for effective application of LSD in practical design. This paper will address this issue as why it becomes a real historical challenge for engineers in India. Here it will also be attempted to highlight the basic philosophical understanding required for successful transformation from the traditional concept to this new concept of LSD. Some comparative design review of both the codes will also be presented for practical understanding of the conceptual changes.
Radix-2 Algorithms for realization of Type-II Discrete Sine Transform and Typ...IJERA Editor
In this paper, radix-2 algorithms for computation of type-II discrete sine transform (DST-II) and type-IV
discrete sine transform (DST-IV), each of length 2 ( 2,3,.....)
m
N m , are presented. The odd-indexed
output components of DST-II can be realized using simple recursive relations. The recursive algorithms are
appropriate for VLSI implementation. The DST-IV of length N can be computed from type-II discrete cosine
transform (DCT-II) and DST-II sequences, each of length N/2.
DISTANCE TWO LABELING FOR MULTI-STOREY GRAPHSgraphhoc
An L (2, 1)-labeling of a graph G (also called distance two labeling) is a function f from the vertex set V (G) to the non negative integers {0,1,…, k }such that |f(x)-f(y)| ≥2 if d(x, y) =1 and | f(x)- f(y)| ≥1 if d(x, y) =2. The L (2, 1)-labeling number λ (G) or span of G is the smallest k such that there is a f with
max {f (v) : vє V(G)}= k. In this paper we introduce a new type of graph called multi-storey graph. The distance two labeling of multi-storey of path, cycle, Star graph, Grid, Planar graph with maximal edges and its span value is determined. Further maximum upper bound span value for Multi-storey of simple
graph are discussed.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
JAVA BASED VISUALIZATION AND ANIMATION FOR TEACHING THE DIJKSTRA SHORTEST PAT...ijseajournal
Shortest path (SP) algorithms, such as the popular Dijkstra algorithm has been considered as the “basic
building blocks” for many advanced transportation network models. Dijkstra algorithm will find the
shortest time (ST) and the corresponding SP to travel from a source node to a destination node.
Applications of SP algorithms include real-time GPS and the Frank-Wolfe network equilibrium.
For transportation engineering students, the Dijkstra algorithm is not easily understood. This paper
discusses the design and development of a software that will help the students to fully understand the key
components involved in the Dijkstra SP algorithm. The software presents an intuitive interface for
generating transportation network nodes/links, and how the SP can be updated in each iteration. The
software provides multiple visual representations of colour mapping and tabular display. The software can
be executed in each single step or in continuous run, making it easy for students to understand the Dijkstra
algorithm. Voice narratives in different languages (English, Chinese and Spanish) are available.A demo
video of the Dijkstra Algorithm’s animation and result can be viewed online from any web browser using
the website: http://www.lions.odu.edu/~imako001/dijkstra/demo/index.html.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
A graph with n vertex and m edges is said to be cubic graceful labeling if its vertices are labeled with distinct integers {0,1,2,3,……..,m3} such that for each edge f*( uv) induces edge mappings are {13,23,33,……,m3}. A graph admits a cubic graceful labeling is called a cubic graceful graph. In this paper, we proved that < K1,a , K1,b , K1c , K1,d>, associate urp with u(r+1)1 of K1,P, fixed vertices vr and ur of two copies of Pn are cubic graceful.
Closed-Form Performance Analysis of Dual Polarization Based MIMO System in Sh...IJERA Editor
In this paper, the problem of dual polarization based MIMO Processing in Shadowed-Rician (SR) fading land mobile satellite (LMS) channels is studied. It is shown in literature that polarization is used as a interference rejection method; and, most of the existing analytical results are not in closed-form. In this paper, we derive the closed-form expressions of the moment generating (MGF) function of the received signal-to-noise ratio of the MRC based receiver in SR fading LMS channels. Then we provide closed-form expressions of the symbol error rate (SER) by using MGF approach. The analytical diversity order and capacity of the considered scheme is also derived. It is shown by by derived closed-form capacity expression that the capacity of the considered dual polarization based scheme is improved; and it is found very useful in practical satellite communication systems.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
K-means Clustering Algorithm with Matlab Source codegokulprasath06
K-means algorithm
The most common method to classify unlabeled data.
Also Checkout: http://bit.ly/2Mub6xP
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ALEXANDER FRACTIONAL INTEGRAL FILTERING OF WAVELET COEFFICIENTS FOR IMAGE DEN...sipij
The present paper, proposes an efficient denoising algorithm which works well for images corrupted with
Gaussian and speckle noise. The denoising algorithm utilizes the alexander fractional integral filter which
works by the construction of fractional masks window computed using alexander polynomial. Prior to the
application of the designed filter, the corrupted image is decomposed using symlet wavelet from which only
the horizontal, vertical and diagonal components are denoised using the alexander integral filter.
Significant increase in the reconstruction quality was noticed when the approach was applied on the
wavelet decomposed image rather than applying it directly on the noisy image. Quantitatively the results
are evaluated using the peak signal to noise ratio (PSNR) which was 30.8059 on an average for images
corrupted with Gaussian noise and 36.52 for images corrupted with speckle noise, which clearly
outperforms the existing methods.
A generalized Dai-Liao type CG-method with a new monotone line search for unc...TELKOMNIKA JOURNAL
In this paper, we presented two developments, the first deals with generalizing the modernization of the damped Dai-Liao formula in an optimized manner. The second development is by suggesting a monotone line search formula for our new algorithms. These new algorithms with the new monotone line search yielded good numerical results when compared to the standard Dai-Liao (DL) and minimum description length (MDL) algorithms. Through several theorems, the new algorithms proved to have a faster convergence to reach the optimum point. These comparisons are drawn in the results section for the tools (Iter, Eval-F, Time) which are a comprehensive measure of the efficiency of the new algorithms with the basic algorithms that we used in the paper.
On the Odd Gracefulness of Cyclic Snakes With Pendant EdgesGiselleginaGloria
Graceful and odd gracefulness of a graph are two entirely different concepts. A graph may posses one or both of these or neither. We present four new families of odd graceful graphs. In particular we show an odd graceful labeling of the linear 4 1 kC snake mK − e and therefore we introduce the odd graceful labeling of 4 1 kC snake mK − e ( for the general case ). We prove that the subdivision of linear 3 kC snake − is odd graceful. We also prove that the subdivision of linear 3 kC snake − with m-pendant edges is odd graceful. Finally, we present an odd graceful labeling of the crown graph P mK n 1 e .
AN APPLICATION OF Gd -METRIC SPACES AND METRIC DIMENSION OF GRAPHSFransiskeran
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Radix-3 Algorithm for Realization of Type-II Discrete Sine Transform
1. M. N. Murty Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 5, Issue 6, ( Part -1) June 2015, pp.09-15
www.ijera.com 9 | P a g e
Radix-3 Algorithm for Realization of Type-II Discrete Sine
Transform
M. N. Murty*
and B. Padhy**
*
(Department of Physics, National Institute of Science and Technology, Palur Hills, Berhampur-761008, Odisha,
India)
**
(Department of Physics, Khallikote Autonomous College, Berhampur, Odisha, India)
ABSTRACT
In this paper, radix-3 algorithm for computation of type-II discrete sine transform (DST-II) of length N =
3 𝑚
(𝑚 = 1,2, … . ) is presented. The DST-II of length N can be realized from three DST-II sequences, each of
length N/3. A block diagram of for computation of the radix-3 DST-II algorithm is given. Signal flow graph for
DST-II of length 𝑁 = 32
is shown to clarify the proposed algorithm.
Keywords - Discrete cosine transform, discrete sine transform, radix-3 algorithm.
I. INTRODUCTION
Discrete transforms play a significant role in digital signal processing. Discrete cosine transform (DCT)
and discrete sine transform (DST) are used as key functions in many signal and image processing applications.
There are eight types of DCT and DST. Of these, the DCT-II, DST-II, DCT-IV, and DST-IV have gained
popularity. The DCT and DST transform of types I, II, III and IV, form a group of so-called “even” sinusoidal
transforms. Much less known is group of so-called “odd” sinusoidal transforms: DCT and DST of types V, VI,
VII and VIII.
The original definition of the DCT introduced by Ahmed et al. in 1974 [1] was one-dimensional (1-D) and
suitable for 1-D digital signal processing. The DCT has found wide applications in speech and image processing
as well as telecommunication signal processing for the purpose of data compression, feature extraction, image
reconstruction, and filtering. Thus, many algorithms and VLSI architectures for the fast computation of DCT
have been proposed [2]-[7]. Among those algorithms [6] and [7] are believed to be most efficient two-
dimensional DCT algorithms in the sense of minimizing any measure of computational complexity.
The DST was first introduced to the signal processing by Jain [8], and several versions of this original DST
were later developed by Kekre et al. [9], Jain [10] and Wang et al. [11]. Ever since the introduction of the first
version of the DST, the different DST’s have found wide applications in several areas in Digital signal
processing (DSP), such as image processing[8,12,13], adaptive digital filtering[14] and interpolation[15]. The
performance of DST can be compared to that of the DCT and it may therefore be considered as a viable
alternative to the DCT. For images with high correlation, the DCT yields better results; however, for images
with a low correlation of coefficients, the DST yields lower bit rates [16]. Yip and Rao [17] have proven that for
large sequence length (N ≥ 32) and low correlation coefficient (< 0.6), the DST performs even better than the
DCT.
In this paper, a new radix-3 algorithm for computation of DST-II of length N = 3 𝑚
(𝑚 = 1,2, … . ) is
presented. The DST-II of length N is realized from three DST sequences, each of length N/3.
The rest of the paper is organized as follows. The proposed radix-3 algorithm for DST-II is presented in
Section-II. An example for computation of DST-II of length 𝑁 = 32
is given in Section-III. Conclusion is given
in Section-IV.
II. PROPOSED RADIX-3 ALGORITHM FOR DST-II
The type-II DST for input data array 𝑥 𝑛 , 1 ≤ 𝑛 ≤ 𝑁, is defined as
1
2 (2 1)
( ) ( ) sin
2
N
k
n
n k
Y k x nC
N N
(1)
for 1,2,....,k N
RESEARCH ARTICLE OPEN ACCESS
2. M. N. Murty Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 5, Issue 6, ( Part -1) June 2015, pp.09-15
www.ijera.com 10 | P a g e
where ,
1
2
1 1,2,..., 1
k
if k N
C
if k N
The ( )II
kY values represent the transformed data. Without loss of generality, the scale factors in (1) are
ignored in the rest of the paper. After ignoring scale factors, (1) can be written as
1
(2 1)
( ) ( )sin
2
N
n
n k
Y k x n
N
(2)
for 1,2,....,k N .
Taking N = 3 𝑚
(𝑚 = 1,2, … . ), 𝑌(𝑘) can be decomposed as
𝑌 3𝑘 = 𝑃(𝑛) sin
2𝑛−1
2
𝑘𝜋
𝑁 3
𝑁 3
𝑛=1 (3)
𝑌 3𝑘 − 1 = 𝑄(𝑛) sin
2𝑛−1
2
𝑘𝜋
𝑁 3
𝑁 3
𝑛=1 − 𝑅(𝑛) sin
𝑁
3
+ 𝑘
2𝑛−1
2
𝜋
𝑁 3
𝑁 3
𝑛=1 (4)
𝑌 𝑁 − 3𝑘 + 1 = 𝑇(𝑛) sin
𝑁
3
+ 𝑘
2𝑛−1
2
𝜋
𝑁 3
𝑁 3
𝑛=1 + 𝑊(𝑛) sin
2𝑛−1
2
𝑘𝜋
𝑁 3
𝑁 3
𝑛=1 (5)
for k = 1,2, … ,
𝑁
3
.
where
𝑃 𝑛 = 𝑥 𝑛 − 𝑥
2𝑁
3
+ 1 − 𝑛) + 𝑥 𝑛 +
2𝑁
3
(6)
𝑄 𝑛 = 𝑥 𝑛 cos
2𝑛−1
2
𝜋
𝑁
− 𝑥
2𝑁
3
+ 1 − 𝑛 cos
2𝜋
3
−
2𝑛−1
2
𝜋
𝑁
+ 𝑥 𝑛 +
2𝑁
3
cos
2𝜋
3
+
2𝑛−1
2
𝜋
𝑁
(7)
𝑅 𝑛 = 𝑥 𝑛 sin
2𝑛−1
2
𝜋
𝑁
+ 𝑥
2𝑁
3
+ 1 − 𝑛 sin
2π
3
−
2n−1
2
π
N
+𝑥 𝑛 +
2𝑁
3
sin
2𝜋
3
+
2𝑛−1
2
𝜋
𝑁
(8)
𝑇 𝑛 = −1 𝑛+1
𝑄(𝑛) (9)
𝑊 𝑛 = −1 𝑛+1
𝑅(𝑛) (10)
for 𝑛 = 1,2, … ,
𝑁
3
Define
𝐶1𝑛 = cos
2𝑛−1
2
𝜋
𝑁
(11)
𝐶2𝑛 = cos
2𝜋
3
−
2𝑛−1
2
𝜋
𝑁
(12)
𝐶3𝑛 = cos
2𝜋
3
+
2𝑛−1
2
𝜋
𝑁
(13)
𝑆1𝑛 = sin
2𝑛−1
2
𝜋
𝑁
(14)
𝑆2𝑛 = sin
2𝜋
3
−
2𝑛−1
2
𝜋
𝑁
(15)
𝑆3𝑛 = sin
2𝜋
3
+
2𝑛−1
2
𝜋
𝑁
(16)
Using (11), (12) and (13) in (7), we have
𝑄 𝑛 = 𝑥 𝑛 𝐶1𝑛 − 𝑥
2𝑁
3
+ 1 − 𝑛 𝐶2𝑛 + 𝑥 𝑛 +
2𝑁
3
𝐶3𝑛 (17)
3. M. N. Murty Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 5, Issue 6, ( Part -1) June 2015, pp.09-15
www.ijera.com 11 | P a g e
for 𝑛 = 1,2, … ,
𝑁
3
Using (14), (15) and (16) in (8), we get
𝑅 𝑛 = 𝑥 𝑛 𝑆1𝑛 + 𝑥
2𝑁
3
+ 1 − 𝑛 𝑆2𝑛 + 𝑥 𝑛 +
2𝑁
3
𝑆3𝑛 (18)
for 𝑛 = 1,2, … ,
𝑁
3
The type-II DSTs of 𝑄 𝑛 , 𝑅 𝑛 , 𝑇 𝑛 &𝑊(𝑛) of length 𝑁 3 can be expressed as
𝑌𝑄 𝑘 = 𝑄(𝑛) sin
2𝑛−1
2
𝑘𝜋
𝑁 3
𝑁 3
𝑛=1 = DST-II of 𝑄(𝑛)of length 𝑁 3 (19)
𝑌𝑅
𝑁
3
+ 𝑘 = 𝑅(𝑛) sin
𝑁
3
+ 𝑘
2𝑛−1
2
𝜋
𝑁 3
𝑁 3
𝑛=1 = DST-II of 𝑅(𝑛)of length 𝑁 3 (20)
𝑌𝑇
𝑁
3
+ 𝑘 = 𝑇(𝑛) sin
𝑁
3
+ 𝑘
2𝑛−1
2
𝜋
𝑁 3
𝑁 3
𝑛=1 = DST-II of 𝑇(𝑛)of length 𝑁 3 (21)
𝑌 𝑊 𝑘 = 𝑊(𝑛) sin
2𝑛−1
2
𝑘𝜋
𝑁 3
𝑁 3
𝑛=1 = DST-II of 𝑊(𝑛)of length 𝑁 3 (22)
for k = 1,2, … ,
𝑁
3
.
Using (19) and (20) in (4), we obtain
𝑌 3𝑘 − 1 = 𝑌𝑄 𝑘 − 𝑌𝑅
𝑁
3
+ 𝑘 (23)
for k = 1,2, … ,
𝑁
3
.
Using (21) and (22) in (5), we have
𝑌 𝑁 − 3𝑘 + 1 = 𝑌𝑇
𝑁
3
+ 𝑘 + 𝑌 𝑊(𝑘) (24)
for k = 1,2, … ,
𝑁
3
.
Thus the DST-II of length N = 3 𝑚
(𝑚 = 1,2, … . ) can be realized from three DSTs, each of length N/3.
𝑌(3𝑘) in (3) is the DST of 𝑃(𝑛) of length N/3. It can be realized using (6). 𝑌(3𝑘 − 1) in (4) can be realized
using (17), (18), (19), (20) and (23). Similarly, using (9), (10), (17), (18), (21), (22) and (24), 𝑌(𝑁 − 3𝑘 + 1)
can be realized.
The Fig.1 shows the block diagram for realization of the output components 𝑌(3𝑘) and 𝑌(3𝑘 − 1) of radix-
3 DST-II of length N. The Fig.2 shows the block diagram for realization of the output components 𝑌(𝑁 − 3𝑘 +
1) of radix-3 DST-II of length N.
4. M. N. Murty Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 5, Issue 6, ( Part -1) June 2015, pp.09-15
www.ijera.com 12 | P a g e
Figure 1: Block diagram for realization of output components 3Y k and 3 1Y k of radix-3 DST-II of
length N .
Figure 2: Block diagram for realization of output components 3 1Y N k of radix-3 DST-II of length N .
5. M. N. Murty Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 5, Issue 6, ( Part -1) June 2015, pp.09-15
www.ijera.com 13 | P a g e
III. EXAMPLE FOR REALIZING DST-II OF LENGTH N = 9
To clarify the proposed radix-3 algorithm, the DST of length 𝑁 = 32
is taken. Using (6), the values of 𝑃(𝑛)
for 𝑛 = 1,2 & 3 are given by
𝑃 1 = 𝑥 1 − 𝑥 6 + 𝑥(7) (25)
𝑃 2 = 𝑥 2 − 𝑥 5 + 𝑥(8) (26)
𝑃 3 = 𝑥 3 − 𝑥 4 + 𝑥(9) (27)
The output components 𝑌 3 , 𝑌 6 & 𝑌(9) of DST-II are realized using (25), (26) and (27) in (3) for
𝑘 = 1,2 & 3 and 𝑛 = 1,2 & 3 as shown in the signal flow graph of Fig.3.
Putting successively 𝑛 = 1, 2 & 3 in (17), the values of 𝑄(𝑛) are given by
𝑄 1 = 𝑥 1 𝐶11 − 𝑥 6 𝐶21 + 𝑥(7)𝐶31 (28)
𝑄 2 = 𝑥 2 𝐶12 − 𝑥 5 𝐶22 + 𝑥(8)𝐶32 (29)
𝑄 3 = 𝑥 3 𝐶13 − 𝑥 4 𝐶23 + 𝑥(9)𝐶33 (30)
Using (18), the values of 𝑅(𝑛) for 𝑛 = 1, 2 & 3 are given by
𝑅 1 = 𝑥 1 𝑆11 + 𝑥 6 𝑆21 + 𝑥(7)𝑆31 (31)
𝑅 2 = 𝑥 2 𝑆12 + 𝑥 5 𝑆22 + 𝑥(8)𝑆32 (32)
𝑅 3 = 𝑥 3 𝑆13 + 𝑥 4 𝑆23 + 𝑥(9)𝑆33 (33)
For k =1, 2 and 3, we have from (23)
𝑌 2 = 𝑌𝑄(1) − 𝑌𝑅(4) (34)
𝑌 5 = 𝑌𝑄(2) − 𝑌𝑅(5) (35)
𝑌 8 = 𝑌𝑄(3) − 𝑌𝑅(6) (36)
The output components 𝑌 2 , 𝑌 5 & 𝑌(8) of DST-II given in (34), (35) & (36) are realized using (28) to (33) in
(4) for 𝑘 = 1,2 & 3 and 𝑛 = 1,2 & 3 as shown in the signal flow graph of Fig.3.
Using (17) in (9), the values of 𝑇(𝑛) for 𝑛 = 1,2 & 3 are given by
𝑇 1 = 𝑥 1 𝐶11 − 𝑥 6 𝐶21 + 𝑥(7)𝐶31 (37)
𝑇 2 = −𝑥 2 𝐶12 + 𝑥 5 𝐶22 − 𝑥(8)𝐶32 (38)
𝑇 3 = 𝑥 3 𝐶13 − 𝑥 4 𝐶23 + 𝑥(9)𝐶33 (39)
Using (18) in (10), the values of 𝑊(𝑛) for 𝑛 = 1, 2 & 3 are given by
𝑊 1 = 𝑥 1 𝑆11 + 𝑥 6 𝑆21 + 𝑥(7)𝑆31 (40)
𝑊 2 = −𝑥 2 𝑆12 − 𝑥 5 𝑆22 − 𝑥(8)𝑆32 (41)
𝑊 3 = 𝑥 3 𝑆13 + 𝑥 4 𝑆23 + 𝑥(9)𝑆33 (42)
For k = 1, 2 and 3, we obtain from (24)
𝑌 7 = 𝑌𝑇(4) + 𝑌 𝑊(1) (43)
𝑌 4 = 𝑌𝑇(5) + 𝑌 𝑊(2) (44)
𝑌 1 = 𝑌𝑇(6) + 𝑌 𝑊(3) (45)
The output components 𝑌 7 , 𝑌 4 & 𝑌(1) of DST-II given in (43), (44) & (45) are realized using (37) to
(42) in (5) for 𝑘 = 1,2 & 3 and 𝑛 = 1,2 & 3 as shown in the signal flow graph of Fig.4.
6. M. N. Murty Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 5, Issue 6, ( Part -1) June 2015, pp.09-15
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Figure 3: Signal flow graph for realization of the output components 2 ,Y 3 ,Y 5 ,Y 6 ,Y 8Y
and 9Y of radix-3 DST-II of length N=9.
Figure 4: Signal flow graph for realization of the output components 1 ,Y 4 ,Y and 7Y of radix-3
DST-II of length N=9.
7. M. N. Murty Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 5, Issue 6, ( Part -1) June 2015, pp.09-15
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IV. CONCLUSION
A new radix-3 algorithm for realization of DST-II of length N = 3 𝑚
(𝑚 = 1,2, … . ) has been presented. A
block diagram for implementation of this algorithm is shown and the signal flow graph for DST of length
𝑁 = 32
is given to clarify the proposal. This algorithm can easily be implemented due its simple and regular
structure.
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