LEADER 00928cam0-22003251i-450- 001 990002663120403321 005 20070319133020.0 010 $a025601423X 035 $a000266312 035 $aFED01000266312 035 $a(Aleph)000266312FED01 035 $a000266312 100 $a20030910d1973----km-y0itay50------ba 101 0 $aeng 102 $aUS 200 1 $aPrinciples of auditing$fby Walter B. Meigs, E. John Larsen, Robert F. Meigs 205 $a5nd ed. 210 $aHomewood$cR. D. Irwin$d1973 215 $a777 p.$d24 cm 225 1 $a<>Willard J. Graham series in accounting 700 1$aMeigs,$bWalter B.$0112391 701 1$aMeigs,$bRobert F.$0112392 701 1$aLarsen,$bE. John$0299784 801 0$aIT$bUNINA$gRICA$2UNIMARC 901 $aBK 912 $a990002663120403321 952 $a1-BIS-283-TB$bs.i.$fECA 959 $aECA 996 $aPrinciples of auditing$9425584 997 $aUNINA LEADER 06011nam 2200829Ia 450 001 9910143132303321 005 20200520144314.0 010 $a9786612123375 010 $a9781282123373 010 $a1282123378 010 $a9780470742624 010 $a0470742623 010 $a9780470742631 010 $a0470742631 035 $a(CKB)1000000000766913 035 $a(EBL)470268 035 $a(SSID)ssj0000354051 035 $a(PQKBManifestationID)11236656 035 $a(PQKBTitleCode)TC0000354051 035 $a(PQKBWorkID)10302182 035 $a(PQKB)10102083 035 $a(Au-PeEL)EBL470268 035 $a(CaPaEBR)ebr10308014 035 $a(CaONFJC)MIL212337 035 $a(iGPub)WILEYB0024191 035 $a(MiAaPQ)EBC470268 035 $a(OCoLC)352829734 035 $a(Perlego)2755861 035 $a(EXLCZ)991000000000766913 100 $a20090123d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aComplex valued nonlinear adaptive filters $enoncircularity, widely linear, and neural models /$fDanilo P. Mandic, Vanessa Su Lee Goh 205 $a1st ed. 210 $aHoboken, N.J. $cWiley$dc2009 215 $a1 online resource (345 p.) 225 1 $aAdaptive and Learning Systems for Signal Processing, Communications and Control Series ;$vv.59 300 $aDescription based upon print version of record. 311 08$a9780470066355 311 08$a0470066350 320 $aIncludes bibliographical references and index. 327 $aComplex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models; Series Page; Contents; Preface; Acknowledgements; 1 The Magic of Complex Numbers; 1.1 History of Complex Numbers; 1.1.1 Hypercomplex Numbers; 1.2 History of Mathematical Notation; 1.3 Development of Complex Valued Adaptive Signal Processing; 2 Why Signal Processing in the Complex Domain?; 2.1 Some Examples of Complex Valued Signal Processing; 2.1.1 Duality Between Signal Representations in R and C; 2.2 Modelling in C is Not Only Convenient But Also Natural 327 $a2.3 Why Complex Modelling of Real Valued Processes?2.3.1 Phase Information in Imaging; 2.3.2 Modelling of Directional Processes; 2.4 Exploiting the Phase Information; 2.4.1 Synchronisation of Real Valued Processes; 2.4.2 Adaptive Filtering by Incorporating Phase Information; 2.5 Other Applications of Complex Domain Processing of Real Valued Signals; 2.6 Additional Benefits of Complex Domain Processing; 3 Adaptive Filtering Architectures; 3.1 Linear and Nonlinear Stochastic Models; 3.2 Linear and Nonlinear Adaptive Filtering Architectures; 3.2.1 Feedforward Neural Networks 327 $a3.2.2 Recurrent Neural Networks3.2.3 Neural Networks and Polynomial Filters; 3.3 State Space Representation and Canonical Forms; 4 Complex Nonlinear Activation Functions; 4.1 Properties of Complex Functions; 4.1.1 Singularities of Complex Functions; 4.2 Universal Function Approximation; 4.2.1 Universal Approximation in R; 4.3 Nonlinear Activation Functions for Complex Neural Networks; 4.3.1 Split-complex Approach; 4.3.2 Fully Complex Nonlinear Activation Functions; 4.4 Generalised Splitting Activation Functions (GSAF); 4.4.1 The Clifford Neuron 327 $a4.5 Summary: Choice of the Complex Activation Function5 Elements of CR Calculus; 5.1 Continuous Complex Functions; 5.2 The Cauchy-Riemann Equations; 5.3 Generalised Derivatives of Functions of Complex Variable; 5.3.1 CR Calculus; 5.3.2 Link between R- and C-derivatives; 5.4 CR-derivatives of Cost Functions; 5.4.1 The Complex Gradient; 5.4.2 The Complex Hessian; 5.4.3 The Complex Jacobian and Complex Differential; 5.4.4 Gradient of a Cost Function; 6 Complex Valued Adaptive Filters; 6.1 Adaptive Filtering Configurations; 6.2 The Complex Least Mean Square Algorithm 327 $a6.2.1 Convergence of the CLMS Algorithm6.3 Nonlinear Feedforward Complex Adaptive Filters; 6.3.1 Fully Complex Nonlinear Adaptive Filters; 6.3.2 Derivation of CNGD using CR calculus; 6.3.3 Split-complex Approach; 6.3.4 Dual Univariate Adaptive Filtering Approach (DUAF); 6.4 Normalisation of Learning Algorithms; 6.5 Performance of Feedforward Nonlinear Adaptive Filters; 6.6 Summary: Choice of a Nonlinear Adaptive Filter; 7 Adaptive Filters with Feedback; 7.1 Training of IIR Adaptive Filters; 7.1.1 Coefficient Update for Linear Adaptive IIR Filters 327 $a7.1.2 Training of IIR filters with Reduced Computational Complexity 330 $aThis book was written in response to the growing demand for a text that provides a unified treatment of linear and nonlinear complex valued adaptive filters, and methods for the processing of general complex signals (circular and noncircular). It brings together adaptive filtering algorithms for feedforward (transversal) and feedback architectures and the recent developments in the statistics of complex variable, under the powerful frameworks of CR (Wirtinger) calculus and augmented complex statistics. This offers a number of theoretical performance gains, which is illustrated on both stochast 410 0$aAdaptive and Learning Systems for Signal Processing, Communications and Control Series 606 $aFunctions of complex variables 606 $aAdaptive filters$xMathematical models 606 $aFilters (Mathematics) 606 $aNonlinear theories 606 $aNeural networks (Computer science) 615 0$aFunctions of complex variables. 615 0$aAdaptive filters$xMathematical models. 615 0$aFilters (Mathematics) 615 0$aNonlinear theories. 615 0$aNeural networks (Computer science) 676 $a621.382/2 700 $aMandic$b Danilo P$0320346 701 $aGoh$b Vanessa Su Lee$0320347 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910143132303321 996 $aComplex valued nonlinear adaptive filters$9803366 997 $aUNINA