LEADER 01212nam--2200349---450- 001 990003196520203316 005 20090213132341.0 010 $a978-92-79-08587-1 035 $a000319652 035 $aUSA01000319652 035 $a(ALEPH)000319652USA01 035 $a000319652 100 $a20090213d2008----km-y0itaa50------ba 101 0 $aeng 102 $aLU 105 $aa---z---001yy 200 1 $aBeing part of it$eEuropean research for an inclusive information society$fEuropean Commission, Information society and media 210 $aLuxembourg$cOffice for official publications of the European Communities$d2008 215 $a33 p.$d21x21 cm 606 0 $aInformazione comunitaria$xDiffusione 606 0 $aTelecomunicazioni$yEuropa 676 $a302.23094 699 $a19.01$bTecnologie di comunicazione e delle informazioni 710 02$aCOMMISSIONE EUROPEA :$bDirezione generale Societą dell?informazione e media$0596910 801 0$aIT$bsalbc$gISBD 912 $a990003196520203316 951 $aCDE 19.01 (XXXIX)$bCDE 2107$cCDE 19.01$d00151396 959 $aBK 969 $aCDE 979 $aMARIAS$b90$c20090213$lUSA01$h1323 996 $aBeing part of it$91015015 997 $aUNISA LEADER 06745nam 2200457 450 001 9910497087203321 005 20220727163845.0 010 $a9781447175094 010 $z9781447175087 035 $a(CKB)4940000000610934 035 $a(MiAaPQ)EBC6719235 035 $a(Au-PeEL)EBL6719235 035 $a(OCoLC)1267298987 035 $a(PPN)258057505 035 $a(EXLCZ)994940000000610934 100 $a20220610d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aQuaternions for computer graphics /$fJohn Vince 205 $aSecond edition. 210 1$aLondon, England :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (188 pages) 320 $aIncludes bibliographical references and index. 327 $aIntro -- Preface -- Contents -- 1 Introduction -- 1.1 Rotation Transforms -- 1.2 The Reader -- 1.3 Aims and Objectives of This Book -- 1.4 Mathematical Techniques -- 1.5 Assumptions Made in This Book -- References -- 2 Number Sets and Algebra -- 2.1 Introduction -- 2.2 Number Sets -- 2.2.1 Natural Numbers -- 2.2.2 Real Numbers -- 2.2.3 Integers -- 2.2.4 Rational Numbers -- 2.3 Arithmetic Operations -- 2.4 Axioms -- 2.5 Expressions -- 2.6 Equations -- 2.7 Ordered Pairs -- 2.8 Groups, Rings and Fields -- 2.8.1 Groups -- 2.8.2 Abelian Group -- 2.8.3 Rings -- 2.8.4 Fields -- 2.8.5 Division Ring -- 2.9 Summary -- 2.9.1 Summary of Definitions -- Reference -- 3 Complex Numbers -- 3.1 Introduction -- 3.2 Imaginary Numbers -- 3.3 Powers of i -- 3.4 Definition of a Complex Number -- 3.4.1 Addition and Subtraction of Complex Numbers -- 3.4.2 Multiplying a Complex Number by a Scalar -- 3.4.3 Product of Complex Numbers -- 3.4.4 Square of a Complex Number -- 3.4.5 Norm of a Complex Number -- 3.4.6 Complex Conjugate of a Complex Number -- 3.4.7 Quotient of Complex Numbers -- 3.4.8 Inverse of a Complex Number -- 3.4.9 Square-Root of pmi -- 3.5 Field Structure of Complex Numbers -- 3.6 Ordered Pairs -- 3.6.1 Addition and Subtraction of Ordered Pairs -- 3.6.2 Multiplying an Ordered Pair by a Scalar -- 3.6.3 Product of Ordered Pairs -- 3.6.4 Square of an Ordered Pair -- 3.6.5 Norm of an Ordered Pair -- 3.6.6 Complex Conjugate of an Ordered Pair -- 3.6.7 Quotient of an Ordered Pair -- 3.6.8 Inverse of an Ordered Pair -- 3.6.9 Square-Root of pmi -- 3.7 Matrix Representation of a Complex Number -- 3.7.1 Adding and Subtracting Complex Numbers -- 3.7.2 Product of Two Complex Numbers -- 3.7.3 Norm Squared of a Complex Number -- 3.7.4 Complex Conjugate of a Complex Number -- 3.7.5 Inverse of a Complex Number -- 3.7.6 Quotient of a Complex Number. 327 $a3.7.7 Square-Root of pmi -- 3.8 Summary -- 3.8.1 Summary of Definitions -- 3.9 Worked Examples -- 3.9.1 Adding and Subtracting Complex Numbers -- 3.9.2 Product of Complex Numbers -- 3.9.3 Multiplying a Complex Number by i -- 3.9.4 The Norm of a Complex Number -- 3.9.5 The Complex Conjugate of a Complex Number -- 3.9.6 The Quotient of Two Complex Numbers -- 3.9.7 Divide a Complex Number by i -- 3.9.8 Divide a Complex Number by -i -- 3.9.9 The Inverse of a Complex Number -- 3.9.10 The Inverse of i -- 3.9.11 The Inverse of -i -- References -- 4 The Complex Plane -- 4.1 Introduction -- 4.2 Some History -- 4.3 The Complex Plane -- 4.4 Polar Representation -- 4.5 Rotors -- 4.6 Summary -- 4.6.1 Summary of Definitions -- 4.7 Worked Examples -- 4.7.1 Rotate a Complex Number by i -- 4.7.2 Product and Quotient Using Polar Form -- 4.7.3 Design a Rotor to Rotate a Complex Number 30° -- 4.7.4 Design a Rotor to Rotate a Complex Number -60° -- References -- 5 Triples and Quaternions -- 5.1 Introduction -- 5.2 Some History -- 5.3 Triples -- 5.3.1 Adding and Subtracting Triples -- 5.4 The Birth of Quaternions -- References -- 6 Quaternion Algebra -- 6.1 Introduction -- 6.2 Some History -- 6.3 Defining a Quaternion -- 6.3.1 The Quaternion Units -- 6.3.2 Example of Quaternion Products -- 6.4 Algebraic Definition -- 6.5 Adding and Subtracting Quaternions -- 6.6 Real Quaternion -- 6.7 Multiplying a Quaternion by a Scalar -- 6.8 Pure Quaternion -- 6.9 Unit Quaternion -- 6.10 Additive Form of a Quaternion -- 6.11 Binary Form of a Quaternion -- 6.12 The Complex Conjugate of a Quaternion -- 6.13 Norm of a Quaternion -- 6.14 Normalised Quaternion -- 6.15 Quaternion Products -- 6.15.1 Product of Pure Quaternions -- 6.15.2 Product of Unit-Norm Quaternions -- 6.15.3 Square of a Quaternion -- 6.15.4 Norm of the Quaternion Product -- 6.16 Inverse Quaternion -- 6.17 Matrices. 327 $a6.17.1 Orthogonal Matrix -- 6.18 Quaternion Algebra -- 6.19 Summary -- 6.19.1 Summary of Definitions -- 6.20 Worked Examples -- 6.20.1 Adding and Subtracting Quaternions -- 6.20.2 Norm of a Quaternion -- 6.20.3 Unit-Norm Quaternions -- 6.20.4 Quaternion Product -- 6.20.5 Square of a Quaternion -- 6.20.6 Inverse of a Quaternion -- References -- 7 3-D Rotation Transforms -- 7.1 Introduction -- 7.2 3-D Rotation Transforms -- 7.3 Rotating About a Cartesian Axis -- 7.4 Rotate About an Off-Set Axis -- 7.5 Composite Rotations -- 7.6 Rotating About an Arbitrary Axis -- 7.6.1 Matrices -- 7.6.2 Vectors -- 7.7 Rodrigues' Rotation Formula -- 7.8 Summary -- 7.8.1 Summary of Definitions -- 7.9 Worked Examples -- 7.9.1 Rotation Transform About an Off-Set Axis -- 7.9.2 Test for Gimbal Lock -- 7.9.3 The General Rotation Matrix -- 7.9.4 Testing the Rotation Matrix -- References -- 8 Quaternions in Space -- 8.1 Introduction -- 8.2 Some History -- 8.2.1 Composition Algebras -- 8.3 Quaternion Products -- 8.3.1 Special Case -- 8.3.2 General Case -- 8.3.3 Double Angle -- 8.4 Quaternions in Matrix Form -- 8.4.1 Vector Method -- 8.4.2 Matrix Method -- 8.4.3 Geometric Verification -- 8.5 Multiple Rotations -- 8.6 Rotating About an Off-Set Axis -- 8.7 Frames of Reference -- 8.8 Interpolating -- 8.8.1 Linear Interpolation -- 8.9 Interpolating Vectors -- 8.10 Interpolating Quaternions -- 8.11 Converting a Rotation Matrix to a Quaternion -- 8.12 Euler Angles to Quaternion -- 8.13 Summary -- 8.13.1 Summary of Definitions -- 8.14 Worked Examples -- 8.14.1 Special Case Quaternion -- 8.14.2 Rotating a Vector Using a Quaternion -- 8.14.3 Evaluate qpq-1 -- 8.14.4 Evaluate qpq-1 Using a Matrix -- 8.14.5 Slerp Interpolation -- 8.14.6 Rotation Matrix into a Quaternion -- References -- 9 Conclusion -- Index. 606 $aQuaternions 615 0$aQuaternions. 676 $a512.5 700 $aVince$b John$g(John A.),$0471760 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910497087203321 996 $aQuaternions for computer graphics$92870222 997 $aUNINA LEADER 03869nam 22006735 450 001 9910299578303321 005 20200702152659.0 010 $a981-10-4262-4 024 7 $a10.1007/978-981-10-4262-1 035 $a(CKB)3710000001388876 035 $a(DE-He213)978-981-10-4262-1 035 $a(MiAaPQ)EBC4867931 035 $a(PPN)20146960X 035 $a(EXLCZ)993710000001388876 100 $a20170530d2018 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAcoustics of Bangla Speech Sounds /$fby Asoke Kumar Datta 205 $a1st ed. 2018. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2018. 215 $a1 online resource (XIV, 133 p. 210 illus., 137 illus. in color.) 225 1 $aSignals and Communication Technology,$x1860-4862 311 $a981-10-4261-6 320 $aIncludes bibliographical references. 327 $aPart 1: Vowel, Semi-vowels, Diphthongs -- Introduction -- Vowel -- Nasal Vowels -- Aspirated Vowels -- Diphthongs -- Semi-Vowels -- Part 2: Consonants -- Introduction -- Experimental Procedure -- Speech Material -- Acoustic Analysis -- EPG Analysis -- Summary. 330 $aThis book presents the consolidated acoustic data for all phones in Standard Colloquial Bengali (SCB), commonly known as Bangla, a Bengali language used by 350 million people in India, Bangladesh and the Bengali diaspora. The book analyzes the real speech of selected native speakers of the Bangla dialect to ensure that a proper acoustical database is available for the development of speech technologies. The acoustic data presented here consists of averages and their normal spread, represented by the standard deviations of necessary acoustic parameters including e.g. formant information for multiple native speakers of both sexes. The study employs two important speech technologies, namely (1) text to speech synthesis (TTS) and (2) automatic speech recognition (ASR). The procedures, particularly related to the use of technologies, are described in sufficient detail that researchers can use them in the creation of technical acoustic databases for any other Indian dialect. The book offers a unique resource for scientists and industrial practitioners who are interested in the acoustic analysis and processing of Indian dialects to develop similar dialect databases of their own. 410 0$aSignals and Communication Technology,$x1860-4862 606 $aSignal processing 606 $aImage processing 606 $aSpeech processing systems 606 $aAcoustics 606 $aComputational linguistics 606 $aPattern perception 606 $aSignal, Image and Speech Processing$3https://scigraph.springernature.com/ontologies/product-market-codes/T24051 606 $aAcoustics$3https://scigraph.springernature.com/ontologies/product-market-codes/P21069 606 $aComputational Linguistics$3https://scigraph.springernature.com/ontologies/product-market-codes/N22000 606 $aPattern Recognition$3https://scigraph.springernature.com/ontologies/product-market-codes/I2203X 615 0$aSignal processing. 615 0$aImage processing. 615 0$aSpeech processing systems. 615 0$aAcoustics. 615 0$aComputational linguistics. 615 0$aPattern perception. 615 14$aSignal, Image and Speech Processing. 615 24$aAcoustics. 615 24$aComputational Linguistics. 615 24$aPattern Recognition. 676 $a491.4483421 700 $aDatta$b Asoke Kumar$4aut$4http://id.loc.gov/vocabulary/relators/aut$0941416 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299578303321 996 $aAcoustics of Bangla Speech Sounds$92522101 997 $aUNINA