VLSI Architecture for QR Decomposition on MHHT Algoritm

VLSI Architecture for QR Decomposition on MHHT Algoritm A VLSI Architecture for the QR Decomposition based on the MHHT Algorithm s.n.v.sai.pratap1 k.kalyani2 s.rajaram3 Abstract: This paper presents Novel VLSI (Very Large Scale of Integration) architecture for the QR decomposition (QRD) based on the Modified Householder transformation (MHHT) algorithm. QRD of a matrix H is decomposition of matrixHinto a productof an orthogonal matrix Qand an upper triangularR. QRD is often used to solve several engineering problems in many areas. Pre-processing modules based on QRD makes the decoding in signal processing easier and implementing data detection with QRD helps to reduce the complexity of spatial multiplexing MIMO – OFDM detection. The techniques used for implementing QR decomposition are: Givens rotation, Modified GramSchmidt Orthogonalization (MGS), Householder Transformations (HHT), and indeed Modified Householder transformation (MHHT). The proposed MHHT algorithm shows best trade-off between complexity and numerical precision, and also suites for VLSI architectures. The proposed MHHT algorithm reduces computation time and hardware area of the QRD block compared to the existing Householder algorithm. Implementation of this algorithm is carried out in FPGA Virtex6 xc6vlx550tl-1Lff1759 device with the help of Xilinx ISE 14.1. Keywords: MIMO systems,VLSI architecture, QR Decomposition (QRD), Householder Transformation(HHT). 1. INTRODUCTION: The QR decomposition (QRD) is a basic matrix factorization method from matrix-computation theory used to compute two output matrices Q and R from an input matrix H, such that H = QR. QRD is often used to solve many engineering areas like least-square problems, linear system equations etc. For symbol-decoding solutions inside Spatial-Multiplexing Multiple-Input Multiple-Output (SM-MIMO) systems, QRD basically consists in simplifying demodulation tasks in suboptimal and near-optimal solutions by finding an orthogonal matrix Q and an upper-triangular matrix R from an input matrix H. Several techniques towards implementing the QRD are already reported in literature. For instance, and under the context of SM-MIMO systems, the most explored are the Modified Gram-Schmidt Orthogonalization (MGS, as a generalized improvement of the Gram-Schmidt algorithm), Givens rotation, the Modified Householder Transformations (MHHT as an enhancement of the Householder Transformation algorithm). Due to its simplicity and numerical stability, the QR factorization algorithm utilizing Householder transformations has been adopted. An overview of the main steps of the Existing Householder QR algorithm is presented. The purpose of this work is to show that when modifying existing Householder QR factorization to the matrix H, the computational complexity and hardware area gets reduced. Due to its trade-off in complexity, numerical precision, and VLSI implementation suitability, the MHHT is preferred. The contribution of this paper is to present a flexible and scalable FPGA-based VLSI architecture with competitive capabilities against other related approaches, motivated on the context of SM-MIMO demodulation solutions. The organization of this paper is as follows: Section II presents the QRD. In Section III, the exisiting HHT and MHHT algorithm is exposed. Implementation results are reported in Section IV, and conclusions are covered in Section V. 2. QR DECOMPOSITION The QRD constitutes a relevant pre-processing operation in SM-MIMO demodulation tasks [1-2]. The baseband equivalent model can be described in (1) At each symbol time, a vector S with each symbol belonging to the Quadrature Amplitude Modulation (q-QAM) constellation passes through the channel response matrix H. The received vector y at the receiving antenna for each symbol time is a noisy superimposition of the signals contaminated by Additive White Gaussian Noise (AWGN) given by n.The maximum likelihood (ML) detector is the optimum detection algorithm for the MIMO system. It requires finding the signal point from all transmit vector signal sets that minimize the Euclidean distance with respect to the received signal vector. The transmitted symbol s can be estimated by solving (2) This gives the optimal result. However, solving (2) with larger constellations and multiple antennas will result in complex calculations. Instead of solving (2) as such, the symbol estimation can be simplified by using QR decomposition of.That is where resides the usefulness of decomposing matrix H in a QR form, yielding a back-recursive dependency on elements in S without incurring into a BER (Bit Error Rate) loss [3-4]. With this practice, the computational complexity is reduced. The detected vector is computed based on the ML algorithm with QR decomposition as given in (3) (3) where is in upper triangular form, approximation of is computationally simpler with the aid of (3). Note that for MIMO-OFDM systems operated in stationary environments, the channel matrix remains almost the same. Thus, QR decomposition of the channel matrix can be done only once to get matrix. On the other hand, the calculation of must be updated for every incoming signal. 2.1 QRD IMPLEMENTATION The techniques used for QR decomposition are: Gram–Schmidt algorithm obtains the orthogonal basis spanning the column space of the matrix by the orthogonality principle. Using a series of projection, subtraction, norm and division, the column vector of the unitary matrix containing the orthogonal basis can be acquired one by one and upper triangular matrix is also obtained as a by-product. Householder Transformation (HHT) tries to zero out the most elements of each column vector at a stroke by reflection operations. The upper triangular matrix is derived after each transformation matrix being applied to every column vector sequentially. The unitary matrix involves the multiplications of these Householder transformation matrices and thus the complexity is much higher. On the other hand, Givens Rotation (GR) zeros one element of the matrix at a time by two-dimensional rotation. If an identity matrix is fed as an input, the unitary matrix will be calculated by using the same rotation sequence when the upper triangular matrix is obtained (Malstev 2006; Hwang 2008 and Patel 2009).The Gram–Schmidt algorithm has the disadvantage that small imprecisions in the calculation of inner products accumulate quickly and lead to effective loss of orthogonality.HHT method has greater numerical stabilitythan the Gram–Schmidt method. Givens method stores two numbers c and s, for each rotation and thus requires more storage and work than Householder method .Givens rotation requires more complicated implementation in order to overcome this disadvantages. Givens rotation can be beneficial for computing QR factorization only when many entries of matrix are already zero, since nullifying certain matrix elements can be skipped. Unlike Givens Transform, Householder Transform can act on all columns of a matrix, and require less computations for Tridiagonalization and QR decomposition, but cannot be deeply or efficiently parallelized. Householder is used for dense matrices on sequential machines, while Givens is u sed for sparse matrices or/on parallel machines. 3. QRD using Householder Transformation In this section, the existing Householder Transformation algorithm is described, followed by proposed HHT method architecture is demonstrated in detail. 3.1 Householder Transformation Householder QR algorithm gradually transforms H into an upper triangular form R by applying a sequence of Householder matrices (multiplies H from the left with Q). Householder transformation is performed by projecting a multi-dimensional input vector onto a plane zeroes multiple elements at the same time. An nÃâ€"n matrix H of the form , (4) is called a Householder matrix. The vector is called a Householder vector. Pre-multiplication of the coefficient matrix with is used to zero out appropriate elements of. It is easy to verify that Householder matrices are symmetric and orthogonal. The Householder matrix block involves the computation of an outer product which requires complexity operation. However, the practical time requirement of using to zero out elements in is lower than that of computing a full outer product. This is because of the tedious computation of the full matrix which is not necessary in practice. Householder reflections work well for introducing large number of zeros using just one matrix multiplication (computing). Normally, all the elements below the diagonal of an entire column of the matrix are eliminated by one Householder reflection. However, this leads to a difficulty when Householder transforms are implemented on parallelly. One reflection affects multiple rows, and therefore, it is difficult to achieve fine-grained parallelism in the operation. The algorithm for Householder transform is given in Table 1. and its block diagram is given in Figure 2. Fig. 2 Block diagram of HHT Table 1 HHT algorithm End Householder vector block: The conventional method of Householder algorithm for decomposing channel matrix is given in Table 1. Initially, the channel matrix is assigned to matrix. It can be periodically updated by following steps to obtain upper triangular matrix. The first column of is assigned to ‘a’ vector. After that the norm value of ‘a’ is calculated and assigned it to ‘g’. The Householder vector ‘v’ is the division ‘u’ and‘t’ which is the norm operation of vector selection . Householder matrix block: The output of Householder vector is given as input to Householder matrix block. Finally, H is computed by The above operation can be updated upto n times to obtain the upper triangular matrix and unitary matrix. It is given below, (5) Q = (HnHn-1†¦H1) T (6) Here the matrix is given to the input of channel matrix to update its vector value. The orthogonal matrix is computed by the multiplication of ‘n’ Householder matrix. Hence its complexity increases and also it occupy more hardware area. If the matrix size increases, the hardware area also increases tremendously. So there is need to reduce the hardware complexity of this block. 3.2 Proposed HHT method The existing method of Householder reflection requires large hardware area and computation time. Householder transformations also provide the capability of nullifying multiple elements simultaneously by reflecting a multi-dimensional input vector onto a plane. However, VLSI implementation of the Householder algorithm needs square-root, multiplication and division operations, which require high hardware complexity. To resolve this issue, a novel Householder algorithm is presented that use series of simple Householder projections, which can be easily implemented using simple arithmetic operations. The proposed algorithm as given in table2 has lesser number of computations compared to the existing algorithm. In Figure 3, the block diagram of modified method is given. It shows two major sub blocks (i.e.) householder vector block and householder matrix block. Householder vector block is same to the previous method of computing ‘v’ with extra weight vector computation. Here modification taken in the Householder matrix block to eliminate matrix multiplication. The vector ‘v’ subtracted from ‘f’ and column vector of channel matrix to give ‘H’ value. Fig. 3 Block diagram of MHHT. In the first step, matrix H is reduced to with all zeros below the diagonal element in the first column by computing the sign of the pivot element d and weight value w. Compared to the previous algorithm, number of steps required to obtain the first matrix can be reduced. For example, if the initial channel matrix of 4Ãâ€"4 undergone to Householder reflection, then it reduces the matrix with all zeros below the first element. The computation of Householder vector in the existing algorithm requires large memory and area. Because is a 4Ãâ€"4 matrix, multiplication of become complex process. To avoid such a task, column vector of matrix has been taken one by one and process it iteratively to obtain the upper triangular matrix. After computation of the first step the matrix size reduced to. After that, the sub matrix of size 3Ãâ€"3 is taken and the steps can be applied repeatedly. The algorithm to compute Householder Vector block is given below. Table 2 HHT algorithm End Repeat above steps for right bottom (n-1)*(n-1) matrix of R Householder vector block: In this Householder reflection algorithm, it transforms the column (7) into the vector of the form (8) where the diagonal element (9) The Householder vector can be computed by, (10) where and This block computation is same as that of previous Householder vector block with a little modification in the weight value. Householder matrix block: After obtaining the Householder vector, the output vector is given to the input of Householder matrix block. The computation of this block is very simple compared to previous method of Householder matrix block computing. The Householder matrix element algorithm is given below, (11) where It reduces the channel matrix to its upper triangular form in steps. To reduce the complexity of computing Q, here the output vector y’ has been taken directly and its algorithm is given below, (12) So the execution time for computing the upper triangular matrix and output vector is very less when compared to conventional Householder reflection algorithm. This reduces the hardware area for the Householder matrix block. The QR decomposition using modified Householder transformation algorithm is simulated by taking ‘a’ as input channel matrix, ‘zb’ as output vector and ‘upper’ as upper triangular matrix. The unitary or orthogonal matrix ‘Q’ need not to be calculated. The output vector in (3) can be computed from the updated Householder vector ‘v’. Also the extra time needed to calculate ‘Q’ can be reduced. So the speed of decomposing the channel matrix can be increased tremendously. 4. Results and Discussion QR decomposition algorithm is required as a pre-processing unit for many MIMO detectors. The accuracy of the channel matrix QR decomposition does not have an impact on the MIMO detection process and finally receiver’s bit-error-rate (BER) performance. The existing and proposed Householder algorithms are downloaded on to Xilinx device xc6vlx550tl-1Lff1759. The synthesis results are compared to show the area efficiency of the proposed one. The channel matrix H elements are represented in floating point representation of 16 bits comprising 1 for sign bit,3 bits for decimal part and 12 bits for fractional part. The 16 bit representation shows an numerical precision oscillates around the interval[10-6,10-5] for both existing and modified algorithms . The computation of column vectors of the R matrix can be parallelised in modified algorithm and thus improvement is obtained in computational time of 49.7% reduction.The computational time for proposed algorithm is about 194.84ns,whereas exisiting algorithm is about 394.56ns. Modified algorithm reduces the matrix computation into vector multilications for some extent and thus reduces the hardware area as obtained from the synthesis report. Table 3 Synthesis report for Conventional Householder algorithm Logic Utilization Used Available Slice LUTs 11142 343680 Bonded IOBs 768 840 BUFG/BUFGCTRL’S 0 32 DSP48E1s 261 864 Table 4 Synthesis report for Proposed Householder algorithm Logic Utilization Used Available Slice LUTs 7634 343680 Bonded IOBs 385 840 BUFG/BUFGCTRL’S 1 32 DSP48E1s 70 864 Table 5 Comparison result Logic Utilization Conventional HHT Proposed HHT % reduced Slice LUTs 11142 7634 31% LUT Flip flops 768 385 49.8% Bonded IOBs 0 1 DSP48E1s 261 70 73% 5. Conclusion To reduce the computational and hardware complexity, Householder transformation algorithm for QRD has been modified. The computation of Q is the tedious process in the existing algorithm. In this work, it can be overcome by directly computing output vector. It reduces the computation time by 52.38% and also reduce in hardware area compared to previous HHT algorithm (Slices – 31%, LUTs – 49.8%) presented in the QRD. Thus it is evident from the comparison result that the number of slices and 4 input LUTs required in FPGA implementation of QR Decomposition is reduced thereby making the low complex design which can meet the specifications of most OFDM communication systems, including VDSL, 802.16, DAB and DVB. In future, this work can be extended to implement K-best LSD and Turbo decoding of LTE receiver. References Lee, K.F. and Williams, D.B.: A space-frequency transmitter diversity technique for OFDM systems. In Proc. Global Telecommunications Conf., San Francisco, CA, pp. 1473-1477. (Nov. 2000) H. Kim, J. Kim, S. Yang, M. Hong, and Y. Shin, â€Å"An effective MIMO–OFDM system for IEEE 802.22 WRAN channels,† IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 55, no. 8, pp. 821–825, Aug. 2008. H.-L. Lin, R. C. Chang, and H.-L. Chen, â€Å"A high speed SDM-MIMO decoder using efficient candidate searching for wireless communication,† IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 55, no. 3, pp. 289–293, Mar. 2008. L. Boher, R. Rabineau, and M. Helard, â€Å"FPGA implementation of an iterative receiver for MIMO–OFDM systems,† IEEE J. Sel. Areas Commun., vol. 26, no. 6, pp. 857–866, Aug. 2008. M.-S. Baek, Y.-H. You, and H.-K. Song, â€Å"Combined QRD-M and DFE detection technique for simple and efficient signal detection in MIMO–OFDM systems,† IEEE Trans. Wireless Commun., vol. 8, no. 4, pp. 1632–1638, Apr. 2009. C. F. T. Tang, K. J. R. Liu, and S. A. Tretter, â€Å"On systolic arrays for recursive complex Householder transformations with applications to array processing,† in Proc. Int. Conf. Acoustics, Speech, and Signal Process., 1991, pp. 1033–1036. K.-L. Chung and W.-M. Yan, â€Å"The complex Householder transform,† IEEE Trans. Signal Process., vol. 45, no. 9, pp. 2374–2376, Sep. 1997. S. Y. Kung, VLSI Array Processors. Upper Saddle River, NJ, USA: Prentice-Hall, 1987.

An Analysis of The Story of Rahab Essay examples -- Religion Theology

An Analysis of The Story of Rahab The main point of the story of Rahab is that God rewards people, regardless of their station or past sins, who put their faith in Him. The story of Rahab begins when Joshua, after receiving God’s command to enter into the Promised Land, sends two spies into Jericho and the surrounding areas to â€Å"view the land† (Joshua 2:1). The two spies are discovered in Jericho as they enter Rahab’s harlot house. The king of Jericho, being alerted to their presence, sends for the spies. Rahab hides the two spies on her roof under some flax and sends the guards out of the city on a wild goose chase. Rahab then tells the spies that everyone in the land is afraid of their power and that she knows that their God is the One true God. In return for the kindness she showed them Rahab asks for their promise of safety for her family when the Hebrews attack Jericho. The spies promise and escape through Rahab’s window in the city wall and descend down a scarlet rope that is used to signal the Israelites to the location of her home. Rahab’s character is revealed e...

Philosophy of Education :: Philosophy of Education Teaching Essays

Philosophy of Education Educating children profoundly affects their lives and influences the life of anyone who comes into contact with those children. Education provides a foundation for a child to base the rest of his or her life on. Without a solid education, it becomes impossible for an individual to provide for themselves and their family. Also, well-educated people can make decisions that benefit both their own interests and the interests of society as a whole. In this paper, I will address my personal opinions and philosophy about education. First, I will address the nature of the student. Next, I will examine the nature of knowledge, followed by the purpose of public education, and method. Finally, my paper will conclude with a discussion of the curriculum areas that are most important in elementary school. Additionally, I will relate my views to pragmatism and progressivism, and to Plato?s teaching, three valuable theories regarding education. No two students are exactly alike. Nevertheless, they do share one fundamental characteristic -- every student has the ability to learn. The ancient Greek philosopher Plato believed that a student?s learning ability is determined entirely by genetics. According to Plato, people are either golds, silvers, or bronzes. The golds are the smartest and the bronzes are the slower learners. I don?t really agree with this philosophy. Yes, some children are naturally intelligent and others are not. But natural ability is not the only factor to consider. Students differ on their level of motivation regarding learning. Some students will settle for a ?C? while others push themselves to get an ?A.? Others are perfectly happy with failing grades. Motivation, or lack of it, can be blamed on one of two causes: environment and genetics. Some feel that a child?s desire to learn is most influenced by their home environment. Genes have also been blamed for a child?s longing to l earn. I feel that both factors play a role in how a child approaches education. In a home where education is strongly emphasized, a child is probably going to want to learn. However, this is not always true.

On Arabian Culture Essay

The literature on social diversity and cleavages in Arab society and the Middle East as a whole suffers from several fallacies, two of which are most pertinent here. One is the tendency, particularly among Orientalists, to speak both of the mosaic nature of Arab society and of the existence of a unified mentality, or one Arab mind, without any awareness of the contradiction between these two abstractions. The other is the emphasis either on communal cleavages or on class conflicts, with the result that one becomes explanatory while the other is ignored. The interplay and coincidence of these two cleavages are rarely examined in their historical and social contexts. How can an individual define the diversity of Arab society? The diversity that characterizes Arab society needs to be analyzed within a three-dimensional framework: (a) a homogeneity-heterogeneity continuum; (b) the processes of conflict-accommodation-assimilation; and (c) social class cleavages. The continuum that covers the range from a completely homogeneous society to one of great heterogeneity encompasses a complex system of vertical loyalties and communal differentiations (ethnic, linguistic, sectarian, tribal, local, regional, and the like) that coincides as well as conflicts with social class cleavages. Arab society has historically been highly heterogeneous. Certainly, one may argue that there has recently been a resurgence of communal loyalties and mobilization, confirming the mosaic and segmentary structures of society. What cannot be granted is the static conception of these loyalties and cleavage as permanent, unchanging forms of differentiation. What is Arab society in general? The characterization of Arab society as heterogeneous, however, needs to be accompanied by an explicit clarification that not all Arab countries are similar in this respect. In fact, they differ widely in regard to their positions on the homogeneity-heterogeneity continuum. Compared to other Arab countries, Egypt and Tunisia, for instance, may be described as rather homogeneous as far as communal cleavages are concerned. These two countries tend to have fewer ethnic, religious, and tribal differences (and, hence, conflicts) than other Arab societies, and are characterized more by social complexity and social class cleavages. A second group of Arab countries, such as Lebanon and Sudan, occupy a position close to the opposite end of the continuum, each being more of a mosaic in structure and social composition. A third set, such as Syria, Algeria, Arabia, and Morocco, tend to occupy positions more in the middle of the continuum. Conventional Western literature on Arab and other Middle Eastern societies has persistently avoided any serious discussion of social class structure. Instead, it has conceived of Arab societies simply as a mosaic. At the margin of this mainstream discourse, however, there has been some occasional speculation on problems of social stratification. Whenever a discussion of this nature has taken place, it has evolved into a heated exchange. One point of view reaffirms the conclusions of the mosaic model and questions the relevance of class analysis. For instance, C. A. O. van Niewenhuijze and James Bill, in separate works, dismiss class analysis in economic terms and instead use Weberian concepts of status and power. Similarly, Iliya Harik has more recently dismissed the thesis put forward by some writers that the Lebanese civil war is actually a class struggle and expressed his â€Å"belief that class distinctions in Lebanon are too obscure to sustain the class struggle argument†. Bryan S. Turner, by contrast, has pointed out that anyone â€Å"who wants to develop a Marxist analysis of North Africa and the Middle East must start with a critique of the mosaic theory and all its related assumptions†. Such a critique, he explains, is required because mosaic analysts believe â€Å"that traditional Middle Eastern societies were not class dominated and that in the modern Middle East social class is only in the process of emerging alongside other forms of social stratification†. Nicholas S. Hopkins has applied ideas of class derived from the Marxist tradition to changes in the social structure of an agricultural town in Tunisia, concluding that essential changes in the mechanization of agriculture and in the improvement of communications â€Å"led to a shift in the organization of work away from a pattern based on mobilization of labor within the household or the extended kindred . . . and toward a pattern of labor determined by wage labor†. Consequently, this Tunisian agricultural town has shifted from a society in which rank was based â€Å"on vertical rather than on horizontal links† to one â€Å"based on class†. Hopkins argues further that not only is there class in the objective sense, â€Å"there is also class consciousness, at least in embryonic, symbolic form†. My own view is that the persistence of communal cleavages complicates rather than nullifies social class consciousness and struggle. This persistence of communal cleavages and vertical loyalties in some Arab countries is owing to the perpetuation of traditional systems in which communities are linked to their local za’ims (traditional leaders) through patron-client relationships. To the extent that constructive change can be introduced in these areas, such traditional systems will give way, increasingly, to other social and class relationships. Reference: Gutas, D. (1998). Greek Thought, Arab Culture : The Graeco-Arabic Translation Movement in Baghdad and Early Abbasid Society (2nd-4th & 8th-10th C. ): Routledge. Rejwan, N. (1998). Arabs Face the Modern World: Religious, Cultural, and Political Responses to the West: Gainesville University Press of Florida. Szarmach, P. E. (1979). Aspects of Jewish Culture in the Middle Ages: Albany State University of New York Press

Perseverance: Harriet Tubman

reedom, and in her quest for freeing others. I will also describe the obstacles she overcame, and who supported her in her cause of being free. Harriet Tubman was an African-American abolitionist, humanitarian, and Union spy during the American Civil War. Her biggest accomplishment was her escape to freedom, and not only did she free herself, but also others. She was the most famous â€Å"conductor† of the Underground Railroad. Throughout a 10-year span, Tubman made more than 20 trips down to the South and led over 300 slaves from bondage to freedom.Perhaps the most shocking fact about Tubman's journeys back and forth from the South was that she never lost a single passenger. This is the most shocking because there were more obstacles facing her then, that a murderer now! Her biggest fear then, was being caught. The only way she could persevere through this, is going on regardless. Regardless of what happened, regardless of what she or anybody else believed, she went on becaus e she had the courage and will power to do it. Throughout her journey, she overcame many obstacles. Fear being the biggest one and her priorities the next.As stated before, I believe that she overcame fear by going on, no matter how hard she tried, or how tired she grew, she kept going on. Her next obstacle in line was taking care of her followers. It has been stated that, there were many times, when her passengers wanted to turn around, give up. They were tired, they were hungry, and there was no way, that she could take care of them alone. I firmly believe that the Underground Railroad was a gift from God. I believe he saw that she struggled, he saw that she was tired, but he also so the cause of her going on and fighting.The Underground Railroad was her way through her obstacles. It was a safe haven for not only her, but her passengers too. She had the will power, and the faith to do it, but faith without work to me, is dead. The Underground Railroad also allowed her to meet vari ous people. Being a slave in the South, you'd think that all Caucasian men were slave owners, but it surprised and inspired her, when she met Caucasian men in the North. She was surprised because these men were standing against and standing for what she hoped and believed in, freedom.It was men like former President John Quincy Adams, William Lloyd Garrison, and Thomas Garrett. They took part in speaking against it, and abolishing it. Most abolitionists were Caucasian, but the ones who actually valued freedom most, were the ones who escaped. It was people like Sojourner Truth and Frederick Douglass who inspired her to go on, and fight against what was right. In her lifetime, Harriet Tubman showed perseverance by not only freeing herself, but also over 300 passengers. She overcame many obstacles, but with the help of her supporters in her cause of being free, she made it through.

Mba Research Methodology Mb 0050

RESEARCH METHODOLOGY MB 0050 [pic] Name: XXXXX Roll number: XXXX Learning centre: XXXX Subject: MB 0050- RESEARCH METHODOLOGY Assignment No. : Set 1 Date of submission at learning centre: [pic] ASSIGNMENTS Subject code: MB0050 (4 credits) Marks 60 subject NAME: RESEARCH METHODOLOGY Note: Each Question carries 10 marks Q1)a. Differentiate between nominal, ordinal, interval and ratio scales, with an example of each. b. What are the purposes of measurement in social science research? a. Types of scales: Ans) There are four types of data that may be gathered in social research, each one adding more to the next. Thus ordinal data is also nominal, and so on. Nominal The name ‘Nominal' comes from the Latin nomen, meaning ‘name' and nominal data are items which are differentiated by a simple naming system. The only thing a nominal scale does is to say that items being measured have something in common, although this may not be described. Nominal items may have numbers assigned to them. This may appear ordinal but is not — these are used to simplify capture and referencing. Nominal items are usually categorical, in that they belong to a definable category, such as 'employees'. Example The number pinned on a sports person. A set of countries. Ordinal Items on an ordinal scale are set into some kind of order by their position on the scale. This may indicate such as temporal position, superiority, etc. The order of items is often defined by assigning numbers to them to show their relative position. Letters or other sequential symbols may also be used as appropriate. Ordinal items are usually categorical, in that they belong to a definable category, such as ‘1956 marathon runners'. You cannot do arithmetic with ordinal numbers — they show sequence only. Example The first, third and fifth person in a race. Pay bands in an organization, as denoted by A, B, C and D. Interval Interval data (also sometimes called integer) is measured along a scale in which each position is equidistant from one another. This allows for the distance between two pairs to be equivalent in some way. This is often used in psychological experiments that measure attributes along an arbitrary scale between two extremes. Interval data cannot be multiplied or divided. Example My level of happiness, rated from 1 to 10. Temperature, in degrees Fahrenheit. Ratio In a ratio scale, numbers can be compared as multiples of one another. Thus one person can be twice as tall as another person. Important also, the number zero has meaning. Thus the difference between a person of 35 and a person 38 is the same as the difference between people who are 12 and 15. A person can also have an age of zero. Ratio data can be multiplied and divided because not only is the difference between 1 and 2 the same as between 3 and 4, but also that 4 is twice as much as 2. Interval and ratio data measure quantities and hence are quantitative. Because they can be measured on a scale, they are also called scale data. Example A person's weight The number of pizzas I can eat before fainting b. Purpose of measurement in social science. One of the primary purposes of classifying variables according to their level or scale of measurement is to facilitate the choice of a statistical test used to analyze the data. There are certain statistical analyses which are only meaningful for data which are measured at certain measurement scales. For example, it is generally inappropriate to compute the mean for Nominal variables. Suppose you had 20 subjects, 12 of which were male, and 8 of which were female. If you assigned males a value of ‘1' and females a value of ‘2', could you compute the mean sex of subjects in your sample? It is possible to compute a mean value, but how meaningful would that be? How would you interpret a mean sex of 1. 4? When you are examining a Nominal variable such as sex, it is more appropriate to compute a statistic such as a percentage (60% of the sample was male). When a research wishes to examine the relationship or association between two variables, there are also guidelines concerning which statistical tests are appropriate. For example, let's say a University administrator was interested in the relationship between student gender (a Nominal variable) and major field of study (another Nominal variable). In this case, the most appropriate measure of association between gender and major would be a Chi-Square test. Let's say our University administrator was interested in the relationship between undergraduate major and starting salary of students' first job after graduation. In this case, salary is not a Nominal variable; it is a ratio level variable. The appropriate test of association between undergraduate major and salary would be a one-way Analysis of Variance (ANOVA), to see if the mean starting salary is related to undergraduate major. Finally, suppose we were interested in the relationship between undergraduate grade point average and starting salary. In this case, both grade point average and starting salary are ratio level variables. Now, neither Chi-square nor ANOVA would be appropriate; instead, we would look at the relationship between these two variables using the Pearson correlation coefficient. Q2) a. What are the sources from which one may be able to identify research problems? b. Why literature survey is important in research? Ans: Identifying research Problem This involves the identification of a general topic and formulating it into a specific research problem. It requires thorough understanding of the problem and rephrasing it in meaningful terms from an analytical point of view. Types of Research Projects †¢ those that relate to states of nature those which relate to relationships between variables In understanding the problem, it is helpful to discuss it with colleagues or experts in the field. It is also necessary to examine conceptual and empirical literature on the subject. After the literature review, the researcher is able to focus on the problem and phrase it in analytical or operational terms. The task of defining the research problem is of greatest importance in the entire research process. Being able to define the problem unambiguously helps the researc her in discriminating relevant data from irrelevant ones. Extensive literature review Review of literature is a systematic process that requires careful and perceptive reading and attention to detail. In the review of the literature, the researcher attempts to determine what others have learned about similar research problems. It is important in the following ways: †¢ specifically limiting and identifying the research problem and possible hypothesis or research questions i. e. sharpening the focus of the research. †¢ informing the researcher of what has already been done in the area. This helps to avoid exact duplication. If one had the literature and exercised enough patience and industry in reviewing available literature, it may well be that his problem has already been solved by someone somewhere some time ago and he will save himself the trouble. † Nwana (1982). †¢ Providing insights into possible research designs and methods of conducting the research and interpreting the results. †¢ Providing suggestions for possible modifications in the research to avoid unanticipated difficulties. The library is the most likely physical location for the research literature. Within the library there is access to books, periodicals, technical reports and academic theses. Other sources are the Education Index and the Educational Resources information centre (ERIC). Computer-assisted searchers of literature have become very common today. They have the advantage of comprehensiveness and speed. They are also very cost-effective in terms of time and effort although access to some of the databases requires payment. Irrespective of the sources of the literature, ethics of research require that the source is acknowledged through a clear system of referencing. . Why Literature survey is important in research? Doing a literature survey before you begin your investigation enables you to take advantage of the unique human capacity to pass on detailed written information from one generation to another. Reading all the knowledge that's accumulated so far on the problem you want to study can be time-consuming and even tedious. But careful evaluation of that material hel ps make your investigation worthwhile by alerting you to knowledge already gained and problems already encountered in your areas of interest. A literature survey amounts to reading available material on a given topic, analyzing and organizing findings, and producing a summary. There are many sources for literature reviews, including journals of general interest in each discipline, such as the American Political Science Review. There are also journals for specific topics such as the Leadership and Organization Development Journal. Governments publish great quantities of data on many topics. The United Nations and the United States Government Printing Office are two major sources. In addition, businesses and private organizations gather and publish information you might find useful. For certain problems you may want to search through popular or non-scholarly periodicals as well. While it's customary to include only data from sources that actually research the problem in a precise fashion, articles in more popular sources may provide interesting insight or orientations. Talking to knowledgeable people may also give you information that helps you formulate your problem. Thoroughness is the key. Most libraries have staff trained in information retrieval who can help find sources and suggest strategies to review the iterature. The Internet, of course, now allows easy access to limitless information on given topics. Thoroughness in your review means not only finding all current publications on a topic but locating earlier writing as well. There's no easy rule for how long ago literature was published on your topic. The time varies from problem to problem. A useful way to locate past as well as current writing is to begin with the most current sources likely to contain relevant material. Then, follow these authors' footnotes and bibliographies. At some point in this search you'll find the material is beginning to be only peripherally related to your current interest or that authors claim originality for their work. Of course, doing a goodliterature surveyis easier when you know a great deal about the subject already. In such a case you'd probably be familiar with publications and even other people who do research in your area of interest. But for the novice, efficient use of library/Internet services and organizing how they check sources are especially important skills. Having located literature, keeping a checklist of useful information will help you read each source. You might ask yourself, particularly for research articles: 1. What was the exact problem studied? 2. How were the topics of interest defined? 3. What did the authors expect to find? 4. How were things measured? 5. What research did this author cite? Have you read it? 6. Who were the subjects of study? 7. What do the results show? 8. Do the data presented agree with the written conclusions? 9. What were the limitations of the study? A thorough literature survey should demonstrate that you've carefully read and evaluated each article or book. Because research reports can be tedious and difficult to understand for new researchers, many tend to read others' conclusions or summaries and take the author's word that the data actually support the conclusions. Careful reading of both tables and text for awhile will convince you they don't always agree. Sometimes data are grossly misinterpreted in the text, but on other occasions authors are more subtle. Consider, for example, the following statements: Fully 30 percent of the sample said they did not vote. Only 30 percent of the sample said they did not vote. The percentage is the same, but the impression conveyed is decidedly different. Reading the actual data before accepting the author's conclusions will help prevent some of these errors of interpretation from creeping into your own research. It's important that after you finish your reading, you're able to write your literature survey in a way that's clear, organizing what you know about the content and methods used to study your problem. You may find it helpful to record information about each source on a separate card or piece of paper so that information can later be reshuffled, compared, and otherwise reorganized. Note in most journal articles that what probably began as a long literature survey is usually condensed on the first few pages of the research report, explaining previous research on the problem and how the current study will contribute. You, too, want to add to this growing body of knowledge we call social science by a creative summary of what's been accomplished by others as well as by your own research. Q3) a. What are the characteristics of a good research design? b. What are the components of a research design? Ans) Research Design – Definition A research design is the arrangement of conditions for collection and analysis of data in a manner that aims to combine relevance to the research purpose witheconomy in procedure†Is the conceptual structure within which research is conducted; it constitutes theblueprint for the collection, measurement and analysis of data more explicitly: i. What is the study about? ii. Why is the study being conducted? iii. Where will the st udy be carried out? iv. What type of data is required? v. Where can the required data be found? Components of research design http://www. google. co. in/url? a=t=j=components%20of%20research%20design=web=3=0CDIQFjAC=http%3A%2F%2Fposta. marmara. edu. tr%2F~sozmen%2F2003-2004%2Fresearch_methodology%2Fweek_4. doc= KgOgTo-aEofqrAeFkbWNAw=AFQjCNG1ctNqNjUq_ils-O4muicz4Z2eBA=RFuXRcsnlsSIOe9zWHhr5A=rja 4. a. Distinguish between Doubles sampling and multiphase sampling. [ 5 marks] b. What is replicated or interpenetrating sampling? [ 5 marks] http://wiki. answers. com/Q/What_is_double_sampling http://en. wikipedia. org/wiki/Multistage_sampling http://en. wikipedia. org/wiki/Replication_(statistics) https://onlinecourses. science. psu. du/stat506/node/54 5. a. How is secondary data useful to researcher? [ 5 marks] b. What are the criteria used for evaluation of secondary data? [ 5 marks] http://www. steppingstones. ca/artman/publish/article_60. shtml http://www. change. freeuk. com/learning/r esmeth/secondary. html 6. What are the differences between observation and interviewing as methods of data collection? Give two specific examples of situations where either observation or interviewing would be more appropriate. [10 marks]. †¢ http://www. differencebetween. com/difference-between-observation-and-vs-interviewing-as-methods-of-data-collection/

Motivation in the Work Place Essay Example | Topics and Well Written Essays - 500 words

Motivation in the Work Place - Essay Example Components of this model, from lowest to the highest are in the order, physical needs, safety and security needs, social needs of love and belonging, esteem needs of respect and confidence, and finally self-actualization needs of knowledge and understanding. Baumeister (p.88) asserts that esteem needs are required to enhance a person’s overall personality by providing a sense of achievement and shielding negative emotions. Self-esteem is associated with confidence and high expectations of success; high self-esteem is associated with optimism and lower anxiety. It also provides a sense of integrity and adequacy. Maslow’s theory points towards need for respect from others and from self. Respect from others confers recognition, acceptance and appreciation. Realizing that human being is a social animal, the Sociometer theory proposes that man continually tries to seek inclusion into social groups. Psychologically, it reduces anxiety and improves health (Baumeister, 89). Employees’ self-esteem is enhanced by gaining recognition in the form of awards and appreciations, and a need to enhance self-esteem, in order for the employees to feel included in the virtual social ‘wanted’ circles, is an effective motivat or (Marriner-Tomey, 92). Self-actualization needs refer to self-fulfilment in terms of all the activities a person can do or is capable of doing. This is driven by individual’s desires, interests and passion towards specific activity or job. Self-actualization needs occupy the topmost position in Maslow’s hierarchy. While the other motives are sought in order to fill deficiencies in one’s life or work, the self-actualization needs are sought in order to pursue growth and development (Gordon, 244). However, without realization of the other needs, self-actualization needs may not be very motivating to the employees. Achieving self-actualization in the work sphere is highly motivating for the employees because