Design A DSP Operations Using Vedic Mathematics
ISSN 9-1494www.ijatir.orgDesign A DSP Operations Using Vedic MathematicsBOIENA MADHU1, K.NIRANJAN KUMAR212PG Scholar, Dept of DSCE, PBR VITS, Kavali, AP, India, E-mail: boienamadhu29@gmail.com.Assistant Professor, Dept of ECE, PBR VITS, Kavali, AP, India, E-mail: kkniranjankumar@gmail.com.Abstract: Digital Signal Processing (DSP) operations arevery important part of engineering as well as medicaldiscipline. Designing of DSP operations have manyapproaches. For the designing of DSP operations,multiplication is play important role to perform signalprocessing operations such as Convolution and Correlation.The new approach of this implementation is mentally andeasy to calculate of DSP operations for small length ofsequences. In this paper a fast method for DSP operationsbased on ancient Vedic mathematics is contemplated. Theimplementation of high speed DSP operations of two finitelength sequences using Vedic Urdhava-TriyagbhayamMultiplication Sutra (approach/method) is done. UrdhavaTriyagbhayam Sutra is very efficient multiplication formulaapplicable for all types of multiplication. This algorithm isimplemented in MATLAB and all the operation isperformed in single Graphical User Interface (GUI)window. Vedic mathematics based DSP operations reducethe processing time as compare to inbuilt function ofMATLAB. It reduces the 40-60% time from inbuiltfunction and this algorithm operates in concept of Vedicmultiplier.Keywords: Vedic Mathematics, Vedic Multiplier, VedicConvolution, Vedic Correlation, GUI.I. INTRODUCTIONDSP operation is the heart of the mobile communicationand satellite communication system. The convolution playsa preciously role in Digital Signal Processing and ImageProcessing. It is used for designing of digital filter andcorrelation application. The linear convolution effectivelydesigns by using simple Vedic multiplier. Convolution isbasic concept to designing the finite impulse response filter,Discrete Fourier Transform (DFT) and Fast FourierTransform (FFT) Linear Convolution of two finite lengthsequence normally computed by using the application ofDiscrete Fourier Transform [2,3]. Design of all DSPoperations with the help of high speed Vedic multiplierwhich increase the efficiency of system and reduces theprocessing time. This DSP implementation is design onMatlab with GUI, which is user friendly and easy to use. Inthis method compute the 2N-1 point convolution sequencefrom N point discrete time sequence and N-point circularconvolution of using 2N-1 point Convolution of discretetime sequence. To reduce the processing time of DSP suchas Right–angle circular convolution is operation proposedalternative method.II. VEDIC MATHEMATICSVedic mathematics is an ancient fast calculationmathematics technique which is taken from historicalancient book of wisdom. Vedic mathematics is an ancientVedic mathematics which provides the unique technique ofmental calculation with the help of simple rules andprinciples. Veda rediscovered by the holiness Jagad GuruShree Bharti Krishna Tirtha Ji Maharaj (1884-1960) inbetween 1911-1918. According to Swami-Ji all Vedicmathematics is based on 16-Sutra (Algorithm) and 16- upsutra (Sub-algorithm) after broadly research in AtharvaVeda [5]. It computes all the basic as well as complexmathematical operation easily and quickly also provides apower full mantel technique. It is more consistent thanmodern mathematics and provides an expeditious solution.The term Vedic mathematics is evolving from the word“Veda” which means warehouse of all knowledge. It isbased on sixteen sutras which transact different branches ofmathematics i.e. algebra, geometry, arithmetic.FormerShankrachrya Shree Bharti Krishna Tirtha of India wasdeveloped in to the ancient Vedic text and established thenew method of this system in his pioneering work in Vedicmathematics (1965). Which was the starting point of thenew work in Vedic math’s era? A batter deal of research isalso being transport how to develop more powerful andeasy application of the Vedic sutras geometry, calculus,trigonometric, computing application (property). Modernmathematics is an integral part of the technical educationmost of the engineering system design is based on thevarious mathematical approaches. The necessity forexpeditious processing speed used following Vedicmathematics algorithm. Ekadhikena Purvena – By one more than the previousone. Nikhilam Navatascaramap Dasatah – All from 9 andlast from 10. Urdhva-Tiryagbhyam – Vertically and crosswise. Paravartya Yojayet – Transpose and adjust. Shunyam Samyasamuccaye – When the sum is thesame that sum is zero. (Anurupye) Shunyamanyat – If one is in ratio, theother is zero.Copyright @ 2014 IJATIR. All rights reserved.
BOIENA MADHU, K.NIRANJAN KUMARUrdhva-Tiryagbhyam sutras are the basic sutras which is Sankalana-Vyavakalanabhyam – By addition and byapplicable for all case of multiplication. This itself is verysubtraction.short and compendious consisting of only one combine Puranapuranabyham – By the completion or noword and means “vertically and crosswise” i.e. the first bitcompletion.of multiplicand and the first bit of multiplier are multiplied Calana-Kalanabyham – Differences and Similarities.with vertically and crosswise method. Vertically and Yaavadunam – Whatever the extent of its deficiency.crosswise multiplication procedure is also known as array Vyastisamanstih – Part and Whole.multiplication technique [7]. Fig.1 represents the 6 6 Sesanyankena Caramena – The remainders by the lastmultiplier using vertically and crosswise method.digit. Sopantyadvayamantyam – The ultimate and twice theIV. DSP OPERATIONSpenultimate.Let us consider two input sequence Ekanyunena Purvena – By one less than the previous(1)one.And Gunitasamuccayah – The product of the sum is equalto the sum of the product.(2) Gunakasamuccayah – The factors of the sum is equalto the sum of the factors.The convolution of the length-L input X with the orderM filter h will output the sequence Y(n).III. URDHAVA - TIRYAGBHYAM(3)(4)(5)(6)Then output sequence y(n) is y [y(0), y(1),.,y(L-1 M)];(7)From equ (3)(8)Adding both side n(9)M must satisfy simultaneously inequalities(10)Equation (5) represents the linear convolution of inputsequence x and h for n 0, 1. L M-1.A. Circular ConvolutionTechnically linear convolution gives an opportunity tocalculate a L-point circular convolution of the two inputsequence. The circular convolution of the L M-1 pointlinearFig. 1.Urdhava-Triyagbhyam Method.International Journal of Advanced Technology and Innovative ResearchVolume. 06, IssueNo.12, December-2014, Pages: 1489-1494
Design A DSP Operations Using Vedic )(17)(26)(18)(27)(19)(28)(20)(21)(29)B. CorrelationDesign of correlation is similarly as linear convolutiononly that we deal with a reflected version of one signal.First input signal is simple but second input signal isreflected. After applying convolution process (Equation (u)is same and reflected the value of equation of (v)) [9]. Letus consider two input sequence are- x(n) [x(0), x(1),.,x(L-2), x(L-1)] and h(n) [h(M 1), h(M), . , h(1), h(0)].Convolution operation with both the input sequences,calculate the correlation operation y (n).(30)V. PROPOSED ALGORITHMA. For Linear ConvolutionThe design of linear convolution has been show in fig.(1).Fortwo6-pointinputsequence.AndThis algorithm is design for any large value of N.(31)Equation (7-17) represents the output value of theconvolution.B. Circular ConvolutionThe Urdhava –Triyagbhyam is always performed foreven number of sequence and gives odd number ofsequences. Circular Convolution perform the followingsteps are done. The middle term of the output ofconvolution is first marked according to fig.2. The outputterm y(5) is circled. Before the middle term outputsequence y(0), y(1), y(2), y(3), y(4) consist array which isleft side of array and after the middle term output sequencey(6), y(7), y(8), y(9), y(10) consist array which is right sideof array. Put up the circled middle term is fixed, and MSBbit of left side array and right side of array will be added.Similarly all the bit position in the right side array will beadded with successively left side bit array position show infig.2. This step will go on until all the bit position in the leftside and right side array of the middle bit according toabove step. After addition we get output of the circularconvolution. Final output calculates by following equation.(32)(33)Show the technique of linear convolution using theUrdhava - Triyagbhyam sutras of Vedic mathematics. Theconvolved outputs sequences are given by the equationshow below.(22)International Journal of Advanced Technology and Innovative ResearchVolume. 06, IssueNo.12, December-2014, Pages: 1489-1494(34)(35)(36)
BOIENA MADHU, K.NIRANJAN KUMAREquation (25-35) represents the output of the cross(37)correlation. For Auto-Correlation both the input sequenceare similar use in above method.VI. IMPLEMENTATION AND RESULTVedic operation is implemented on Graphical UserInterface window. Basically GUI is a program whichprovides the benefits of computer’s graphics capabilities tomake program easy to use. Graphical user Interfaceprovides user a spacious way to interact with software. Themost renowned and essential part of the software that isbeing used today is Graphical User Interface, GUI.Fig. 2. Proposed Circular Convolution technique.C. CorrelationThe design of correlation is based on the linearconvolution has been show in figure (1). For two 6-pointinput sequence x(n) [x(0), x(1), x(2), x(3), x(4), x(5)] andh(n) [h(5), h(4), h(3), h(2), h(1), h(0)]. This algorithm isdesign for any large value of N.Fig. 3. Proposed DSP operations window.A. For ConvolutionTABLE I: For )Fig.4. Proposed convolution operation.International Journal of Advanced Technology and Innovative ResearchVolume. 06, IssueNo.12, December-2014, Pages: 1489-1494
Design A DSP Operations Using Vedic MathematicsB. For Circular ConvolutionD. for Auto CorrelationTABLE II: For Circular ConvolutionTABLE IV: for Auto CorrelationFig. 5. Proposed circular convolution operation.Fig. 7. Proposed auto correlation operation.C. For Cross CorrelationTABLE III: For Cross CorrelationFig.8.simulation output for linear convolution.Fig. 6. Proposed cross correlation operation.International Journal of Advanced Technology and Innovative ResearchVolume. 06, IssueNo.12, December-2014, Pages: 1489-1494
BOIENA MADHU, K.NIRANJAN KUMARFig. (3) represent the main window for DSPs operationdiscrete convolution / correlation and string matching, andand performing the convolution operation for sequence oneexploring the possibility of a deterministic linear-timealgorithm for discrete convolution/correlation” in Proc.x(n) [4,5,6,7,8,0,3,1,2,3], h(n) [3,1,0,3,4,5,6,1,0,8].IETE Journal of education, vol.51, April 2010.Display the convolution result[10] Isabella1and Emi Retna, “Study paper on test casegeneration for GUI based testing” in proc. Int. Journaly(n) [12,19,23,39,62,66,103,122,115,Software Engineering & Applications, Vol.3, Jan 2012, pp.140,133,81,96,95,28,44,11,16,24].3-8.Fig. 4-7 represents the graph between the time consumedby Vedic operation and conventional operation. In abovefigure the red graph show the time value for conventionaloperation and blue graph represent the value for Vedicoperation. Table 1-4 show the time comparison betweenconventional versus Vedic operation for different inputsequences and operations.VII. CONCLUSIONA fast computation of DSP operations of two finite lengthsequences implemented with the help of single GUIwindow. DSP operations are based on UrdhavaTriyagbhyam method of Vedic mathematics, which reducesthe processing time as compare to inbuilt function ofMatlab. Proposed algorithm provide average processingtime in micro second and conventional operation provideaverage time in mili second. Mathematics operation timegive in Graphical User Interface window is easy to use anduser friendly. In future, the Fast Fourier Transform andFilter operation is design with the help of Vedic UrdhavaTriyagbhyam method.VIII. REFERENCES[1] A.Kumar, A. Raman, Dr. Sarin, “Small areareconfigurable FFT design by Vedic math” in Proc. 2ndIEEE Int. Conf. Computer and Automatic Engineering,India vol. 5, 2010, pp.836-838.[2] L. R. Rabiner and B. Gold, “Theory and Application ofDigital Signal Processing”. Englewood Cliffs, NJ: PrenticeHall, 1975.[3] J.G. Proakis and D.G. Monolakis, “Digital SignalProcessing”. Prentice- Hall International, Inc., 1996.[4] W.Li, “The Modified fermat number transform and itsapplication” in Proc. IEEE Int. Symposium on Circuit andSystem, Bethlehem, 1990, vol.3, pp. 2365-2368.[5] Jagadguru Swami Sri Bharath, Krishna Tirathji, “VedicMathematics o Sixteen Simple Sutras from The Vedas”,Motilal Banarsidas, Varanasi (India), 1992.[6] Jeganathan Sriskandarajah, “Secrets of Ancient Maths:Vedic Mathematics”, Journal of Indic Studies Foundation,California, 2003 pp. 15-16.[7] Parth Mehta, Dhanashri Gawali, “Conventional versusVedic mathematical method for Hardware implementationof a multiplier” ; in Proc. IEEE Int. Conf. Advances es, India, Dec. 2009, pp. 640-642.[8] Sophocles J. Orfanidis “Introduction to SignalProcessing” Prentice Hall, Inc.,1996–2009 [9] SumantraDutta Roy, Poonam Suryanarayan, “The Relation betweenInternational Journal of Advanced Technology and Innovative ResearchVolume. 06, IssueNo.12, December-2014, Pages: 1489-1494
Vedic mathematics is an ancient Vedic mathematics which provides the unique technique of mental calculation with the help of simple rules and principles. Veda rediscovered by the holiness Jagad Guru Shree Bharti Krishna Tirtha Ji Maharaj (1884-1960) in between 1911-1918. According to Swami-Ji all Vedic mathematics is based on 16-Sutra .
Component Dsp codec wrapper Component Dsp render. HIFI4 Core. Dsp codecs. SAI/ESAI/DMA DAC. Figure 2. Software architecture for DSP processor The DSP-related code includes the DSP framework, DSP remoteproc driver, DSP wrapper, unit test, DSP codec wrapper, and DSP codec. The DSP framework is a firmware code which runs on the DSP core.
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