1.

Record Nr.

UNINA9910480656303321

Autore

Muckenhoupt Benjamin <1933->

Titolo

Transplantation theorems and multiplier theorems for Jacobi series / / Benjamin Muckenhoupt

Pubbl/distr/stampa

Providence, Rhode Island : , : American Mathematical Society, , 1986

©1986

ISBN

1-4704-0772-8

Descrizione fisica

1 online resource (94 p.)

Collana

Memoirs of the American Mathematical Society, , 0065-9266 ; ; Number 356

Disciplina

515/.2433

Soggetti

Jacobi polynomials

Multipliers (Mathematical analysis)

Electronic books.

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

"November 1986, Volume 64, number 356 (first of 2 numbers)."

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

""Table of Contents""; ""1. Introduction""; ""2. Jacobi polynomials""; ""3. A reduction lemma""; ""4. An estimate for separated arguments""; ""5. Kernel estimates for separated arguments""; ""6. An estimate for noncomparable values near 0""; ""7. Kernel estimates for noncomparable values near 0""; ""8. Kernel estimates for comparable values""; ""9. Facts concerning weighted norm inequalities""; ""10. A transplantation lemma without moment conditions""; ""11. A transplantation lemma with moment conditions""; ""12. Proof of the power weight transplantation theorem""



2.

Record Nr.

UNINA9910139041203321

Autore

Wagner Kevin

Titolo

Proportionate-type normalized least mean square algorithms [[electronic resource] /] / Kevin Wagner, Miloš Doroslovački

Pubbl/distr/stampa

London, : ISTE

Hoboken, N.J., : Wiley, c2013

ISBN

1-118-57955-0

1-118-57925-9

1-118-57966-6

Descrizione fisica

1 online resource (184 p.)

Collana

Digital signal and image processing series

Focus Series

Altri autori (Persone)

DoroslovačkiMiloš

Disciplina

511.8

Soggetti

Algorithms

Computer algorithms

Equations, Simultaneous - Numerical solutions

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Title Page; Contents; Preface; Notation; Acronyms; Chapter 1. Introduction to PtNLMS Algorithms; 1.1. Applications motivating PtNLMS algorithms; 1.2. Historical review of existing PtNLMS algorithms; 1.3. Unified framework for representing PtNLMS algorithms; 1.4. Proportionate-type NLMS adaptive filtering algorithms; 1.4.1. Proportionate-type least mean square algorithm; 1.4.2. PNLMS algorithm; 1.4.3. PNLMS++ algorithm; 1.4.4. IPNLMS algorithm; 1.4.5. IIPNLMS algorithm; 1.4.6. IAF-PNLMS algorithm; 1.4.7. MPNLMS algorithm; 1.4.8. EPNLMS algorithm; 1.5. Summary

Chapter 2. LMS Analysis Techniques2.1. LMS analysis based on small adaptation step-size; 2.1.1. Statistical LMS theory: small step-size assumptions; 2.1.2. LMS analysis using stochastic difference equations with constant coefficients; 2.2. LMS analysis based on independent input signal assumptions; 2.2.1. Statistical LMS theory: independent input signal assumptions; 2.2.2. LMS analysis using stochastic difference equations with stochastic coefficients; 2.3. Performance of statistical LMS theory; 2.4. Summary; 3. PtNLMS Analysis Techniques



3.1. Transient analysis of PtNLMS algorithm for white input3.1.1. Link between MSWD and MSE; 3.1.2. Recursive calculation of the MWD and MSWD for PtNLMS algorithms; 3.2. Steady-state analysis of PtNLMS algorithm: bias and MSWD calculation; 3.3. Convergence analysis of the simplified PNLMS algorithm; 3.3.1. Transient theory and results; 3.3.2. Steady-state theory and results; 3.4. Convergence analysis of the PNLMS algorithm; 3.4.1. Transient theory and results; 3.4.2. Steady-state theory and results; 3.5. Summary; 4. Algorithms Designed Based on Minimization of User-Defined Criteria

4.1. PtNLMS algorithms with gain allocation motivated by MSE minimization for white input4.1.1. Optimal gain calculation resulting from MMSE; 4.1.2. Water-filling algorithm simplifications; 4.1.3. Implementation of algorithms; 4.1.4. Simulation results; 4.2. PtNLMS algorithm obtained by minimization of MSE modeled by exponential functions; 4.2.1. WD for proportionate-type steepest descent algorithm; 4.2.2. Water-filling gain allocation for minimization of the MSE modeled by exponential functions; 4.2.3. Simulation results

4.3. PtNLMS algorithm obtained by minimization of the MSWD for colored input4.3.1. Optimal gain algorithm; 4.3.2. Relationship between minimization of MSE and MSWD; 4.3.3. Simulation results; 4.4. Reduced computational complexity suboptimal gain allocation for PtNLMS algorithm with colored input; 4.4.1. Suboptimal gain allocation algorithms; 4.4.2. Simulation results; 4.5. Summary; Chapter 5. Probability Density of WD for PtLMS Algorithms; 5.1. Proportionate-type least mean square algorithms; 5.1.1. Weight deviation recursion

5.2. Derivation of the Conditional PDF of WD for the PtLMS algorithm

Sommario/riassunto

The topic of this book is proportionate-type normalized least mean squares (PtNLMS) adaptive filtering algorithms, which attempt to estimate an unknown impulse response by adaptively giving gains proportionate to an estimate of the impulse response and the current measured error. These algorithms offer low computational complexity and fast convergence times for sparse impulse responses in network and acoustic echo cancellation applications. New PtNLMS algorithms are developed by choosing gains that optimize user-defined criteria, such as mean square error, at all times. PtNLMS algorithms ar