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Complex valued nonlinear adaptive filters : noncircularity, widely linear, and neural models / / Danilo P. Mandic, Vanessa Su Lee Goh
| Complex valued nonlinear adaptive filters : noncircularity, widely linear, and neural models / / Danilo P. Mandic, Vanessa Su Lee Goh |
| Autore | Mandic Danilo P |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, c2009 |
| Descrizione fisica | 1 online resource (345 p.) |
| Disciplina | 621.382/2 |
| Altri autori (Persone) | GohVanessa Su Lee |
| Collana | Adaptive and Learning Systems for Signal Processing, Communications and Control Series |
| Soggetto topico |
Functions of complex variables
Adaptive filters - Mathematical models Filters (Mathematics) Nonlinear theories Neural networks (Computer science) |
| ISBN |
9786612123375
9781282123373 1282123378 9780470742624 0470742623 9780470742631 0470742631 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Complex 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
2.3 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 3.2.2 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 4.5 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 6.2.1 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 7.1.2 Training of IIR filters with Reduced Computational Complexity |
| Record Nr. | UNINA-9910143132303321 |
Mandic Danilo P
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| Hoboken, N.J., : Wiley, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Recurrent neural networks for prediction / / Danilo P. Mandic, Jonathon A. Chambers
| Recurrent neural networks for prediction / / Danilo P. Mandic, Jonathon A. Chambers |
| Autore | Mandic Danilo P |
| Pubbl/distr/stampa | Chichester : , : John Wiley & Sons Ltd., , [2001] |
| Descrizione fisica | 1 online resource (280 pages) |
| Disciplina | 6.32 |
| Collana | Wiley series in adaptive and learning systems for signal processing , communications, and control |
| Soggetto topico |
Neural networks (Computer science)
Machine learning |
| ISBN |
9786610554539
9780470845356 047084535X 9781280554537 1280554533 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9911019096603321 |
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Mandic Danilo P
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| Chichester : , : John Wiley & Sons Ltd., , [2001] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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