List of Figures

• 2.1. Transversal adaptive filter structure.
• 2.2. Linear combiner filter structure.
• 2.3. Recursive filter structure.
• 2.4. Block diagram of the lattice predictor.
• 2.5. Block diagram of the joint process estimator.
• 2.6. Block diagram of the general adaptive filtering problem.
• 2.7. Block diagram of the general adaptive system identification (forward modeling) problem.
• 2.8. Block diagram of the general adaptive system identification (forward modeling) problem.
• 2.9. Block diagram of the general forward prediction problem.
• 2.10. Block diagram of the transversal forward prediction problem.
• 2.11. Block diagram of the transversal backward prediction problem.
• 2.12. Autoregressive process modeling.
• 2.13. Block diagram of the adaptive transversal forward prediction error filter.
• 2.14. Block diagram of the network echo canceler.
• 2.15. Block diagram of the acoustic echo canceler.
• 2.16. Block diagram of a communication channel employing both acoustic and network echo cancelers.
• 2.17. Block diagram of the adaptive interference canceling setup.
• 2.18. Block diagram of the power-line adaptive interference canceler.
• 2.19. Input and output signals of an adaptive interference canceler.
• 4.1. The adaptive filter coefficients after convergence and the learning curve for the complex FIR system identification problem using the ARLMSNEWT algorithm.
• 4.2. Block diagram of the Block Frequency Domain Adaptive Filter.
• 4.3. The adaptive filter coefficients after convergence and the learning curve for the complex FIR system identification problem using the BFDAF algorithm.
• 4.4. The adaptive filter coefficients after convergence and the learning curve for the complex FIR system identification problem using the BLMS algorithm.
• 4.5. The adaptive filter coefficients after convergence and the learning curve for the complex FIR system identification problem using the BNLMS algorithm.
• 4.6. The adaptive filter coefficients after convergence and the learning curve for the complex FIR system identification problem using the DRLMS for several values of the data reusing parameter $k$.
• 4.7. The adaptive filter coefficients after convergence and the learning curve for the complex FIR system identification problem using the DRNLMS for several values of the data reusing parameter $k$.
• 4.8. The cascade of the channel and the adaptive filter coefficients after convergence (left), and the learning curve for the inverse modeling problem using the Leaky NLMS algorithm (right).
• 4.9. Sensitivity pattern for a 2-element adaptive array using LCLMS.
• 4.10. The adaptive filter coefficients after convergence and the learning curve for the complex FIR system identification problem using the LMS algorithm.
• 4.11. The adaptive filter coefficients after convergence, the learning curve, and the evolution of the step size for the complex FIR system identification problem using the MVSSLMS algorithm.
• 4.12. The adaptive filter coefficients after convergence and the learning curve for the complex FIR system identification problem using the NLMS algorithm.
• 4.13. The adaptive filter coefficients after convergence and the learning curve for the complex FIR system identification problem using the PBFDAF algorithm.
• 4.14. The adaptive filter coefficients after convergence and the learning curve for the complex FIR system identification problem using the RCPBFDAF algorithm.
• 4.15. The adaptive filter coefficients after convergence and the learning curve for the complex FIR system identification problem using the RDRLMS for several values of the data reusing parameter $k$.
• 4.16. The adaptive filter coefficients after convergence and the learning curve for the complex FIR system identification problem using the RDRNLMS for several values of the data reusing parameter $k$.
• 4.17. The adaptive filter coefficients after convergence and the learning curve for the complex FIR system identification problem using the RLS algorithm.
• 4.18. Block diagram of the Transform Domain Fault Tolerant Adaptive Filter.
• 4.19. Learning curves for the TDLMS and TDFTAF when hardware failure is encountered.
• 4.20. Block diagram of the Transform Domain LMS algorithm.
• 4.21. The adaptive filter coefficients after convergence and the learning curve for the complex FIR system identification problem using the TDLMS algorithm.
• 4.22. The adaptive filter coefficients after convergence, the learning curve, and the evolution of the forgetting factor for the complex system identification problem using the VFFRLS algorithm.
• 4.23. The adaptive filter coefficients after convergence, the learning curve, and the evolution of the mean value of the step size for the complex FIR system identification problem using the VSSLMS algorithm.
• 5.1. The adaptive linear combiner coefficients after convergence and the learning curve for the complex system identification problem using the FTRLS algorithm.
• 5.2. Block diagram of the backward prediction error filter.
• 5.3. The frequency response of the PEF after convergence and the filter output for the adaptive line enhancer using LBPEF.
• 5.4. Block diagram of the forward prediction error filter.
• 5.5. The frequency response of the PEF after convergence and the filter output for the adaptive line enhancer using LFPEF.
• 5.6. Block diagram of the adaptive Joint Process Estimator.
• 5.7. The adaptive linear combiner coefficients after convergence and the learning curve for the complex system identification problem using the LMSLATTICE algorithm.
• 5.8. Block diagram of the RLS adaptive Joint Process Estimator.
• 5.9. The adaptive linear combiner coefficients after convergence and the learning curve for the complex system identification problem using the RLSLATTICE algorithm.
• 5.10. Block diagram of the RLS adaptive Joint Process Estimator.
• 5.11. The adaptive linear combiner coefficients after convergence and the learning curve for the complex system identification problem using the RLSLATTICE-2 algorithm.
• 5.12. Block diagram of the backward prediction error filter.
• 5.13. The frequency response of the PEF after convergence and the filter output for the adaptive line enhancer using RLSLBPEF.
• 5.14. Block diagram of the forward prediction error filter.
• 5.15. The frequency response of the PEF after convergence and the filter output for the adaptive line enhancer using RLSLFPEF.
• 5.16. Block diagram of the lattice predictor.
• 5.17. Block diagram of the lattice predictor.
• 5.18. Block diagram of the LMS-LATTICE Joint Process Estimator.
• 5.19. Block diagram of the RLS-LATTICE adaptive Joint Process Estimator.
• 5.20. Block diagram of the RLSLATTICE-2 adaptive Joint Process Estimator.
• 5.21. Block diagram of the backward prediction error filter.
• 5.22. Block diagram of the forward prediction error filter.
• 6.1. Block diagram of the cascaded second order IIR adaptive line enhancer.
• 6.2. The adaptive filters frequency responses after convergence and the filter output for the cascaded adaptive line enhancer.
• 6.3. Block diagram of the equation error algorithm.
• 6.4. The adaptive filter impulse response after convergence and the learning curve for the IIR system identification problem using the equation error algorithm.
• 6.5. Block diagram of the output error algorithm.
• 6.6. The adaptive filter response after convergence and the learning curve for the IIR system identification problem using the output error algorithm.
• 6.7. Block diagram of the SHARF algorithm.
• 6.8. The adaptive filter impulse response after convergence and the learning curve for the IIR system identification problem using the SHARF algorithm.
• 6.9. Block diagram of the second order IIR algorithm in an adaptive line enhancer configuration.
• 6.10. The adaptive filter frequency response after convergence and the filter output for the adaptive line enhancer problem using the second order IIR type-1 algorithm.
• 6.11. Block diagram of the second order IIR algorithm in an adaptive line enhancer configuration.
• 6.12. The adaptive filter frequency response after convergence and the filter output for the adaptive line enhancer problem using the second order IIR type-2 filter.
• 7.1. Block diagram of the Adjoint-LMS algorithm.
• 7.2. Sensor signal before and after applying the adaptive controller in a single channel ANVC system using the adjoint LMS algorithm.
• 7.3. Block diagram of the Frequency Domain Adjoint-LMS algorithm.
• 7.4. Sensor signal before and after applying the adaptive controller in a single channel ANVC system using the frequency domain adjoint LMS algorithm.
• 7.5. Block diagram of the Frequency Domain Filtered-X LMS algorithm.
• 7.6. Sensor signal before and after applying the adaptive controller in a single channel ANVC system using the frequency domain filtered-x LMS algorithm.
• 7.7. Block diagram of the Filtered-x LMS algorithm.
• 7.8. Sensor signal before and after applying the adaptive controller in a single channel ANVC system using the filtered-x LMS algorithm.
• 7.9. Block diagram of the Multichannel Adjoint-LMS algorithm.
• 7.10. Signals recorded by the sensors before and after applying the adaptive controller in a Multichannel ANVC system using the multichannel adjoint LMS algorithm.
• 7.11. Block diagram of the Multi-Channel Frequency Domain Adjoint-LMS algorithm.
• 7.12. Signals recorded by the sensors before and after applying the adaptive controller in a Multichannel ANVC system using the multichannel frequency domain adjoint LMS algorithm.
• 7.13. Block diagram of the Multichannel Frequency Domain Filtered-X LMS algorithm.
• 7.14. Signals recorded by the sensors before and after applying the adaptive controller in a Multichannel ANVC system using the multichannel frequency domain filtered-x LMS algorithm.
• 7.15. Block diagram of the Multichannel Adjoint-LMS algorithm.
• 7.16. Signals recorded by the sensors before and after applying the adaptive controller in a Multichannel ANVC system using the multichannel filtered-x LMS algorithm.
• 7.17. Block diagram of the Adjoint-LMS algorithm.
• 7.18. Block diagram of the Frequency Domain Adjoint-LMS algorithm.
• 7.19. Block diagram of the Frequency Domain Filtered-X LMS algorithm.
• 7.20. Block diagram of the Filtered-x LMS algorithm.
• 7.21. Block diagram of the Multichannel Adjoint-LMS algorithm.
• 7.22. Block diagram of the Multichannel Frequency Domain Adjoint-LMS algorithm.
• 7.23. Block diagram of the MultChannel Frequency Domain Filtered-X LMS algorithm.
• 7.24. Block diagram of the MultChannel Filtered-X LMS algorithm.
• 8.1. The adaptive filter coefficients after convergence and the learning curve for the FIR system identification problem using the SOVLMS algorithm.
• 8.2. The adaptive filter coefficients after convergence and the learning curve for the FIR system identification problem using the SOVNLMS algorithm.
• 8.3. The adaptive filter coefficients after convergence and the learning curve for the FIR system identification problem using the SOVRLS algorithm.
• 8.4. The adaptive filter coefficients after convergence and the learning curve for the FIR system identification problem using the SOVTDLMS algorithm.
• 8.5. The adaptive filter coefficients after convergence, the evolution of the step size, and the learning curve for the FIR system identification problem using the SOVVSSLMS algorithm.
• 9.1. The iteration progress window.
• 9.2. A multichannel system with two actuators and three sensors.
• 9.3. The adaptive line enhancer graph window.
• 9.4. The active noise and vibration control graph window.
• 9.5. The adaptive beam former graph window.
• 9.6. The echo canceler graph window.
• 9.7. The inverse modeling (equalizer) graph window.
• 9.8. The modeling (system identification) graph window.
• 9.9. The adaptive prediction graph window.
• 9.10. The frequency contents of the input and output of a second order Volterra filter.
• 9.11. The iteration progress window.
• 10.1. Block diagram of a Cascade of M second order adaptive line enhancer sections.
• 10.2. Convergence and tracking behavior of the cascade second order type-2 IIR adaptive line enhancer.
• 10.3. Block diagram of an adaptive line enhancer implemented using the second order type-1 IIR adaptive filter.
• 10.4. Performance of the second order type-1 IIR adaptive line enhancer.
• 10.5. Block diagram of an adaptive line enhancer implemented using the second order type-2 IIR adaptive filter.
• 10.6. Performance of the second order type-2 IIR adaptive line enhancer.
• 10.7. Block diagram of a single channel noise cancellation application using the Adjoint-LMS algorithm.
• 10.8. Performance of the ADJLMS algorithm.
• 10.9. Block diagram of a single channel noise cancellation application using the Frequency Domain ADJoint-LMS algorithm.
• 10.10. Performance of the FDADJLMS algorithm.
• 10.11. Block diagram of a single channel noise cancellation application using the Frequency Domain Filtered-X LMS algorithm.
• 10.12. Performance of the FDFXLMS algorithm.
• 10.13. Block diagram of a single channel noise cancellation application using the Filtered-x LMS algorithm.
• 10.14. Performance of the FXLMS algorithm.
• 10.15. Block diagram of a multichannel noise cancellation application using the Multichannel Adjoint-LMS algorithm.
• 10.16. Performance of the MCADJLMS algorithm.
• 10.17. Block diagram of a multichannel noise cancellation application using the Multi Channel Frequency Domain Adjoint LMS algorithm.
• 10.18. Performance of the MCFDADJLMS algorithm.
• 10.19. Block diagram of a multichannel noise cancellation application using the Multi Channel Frequency Domain Filtered-X LMS algorithm.
• 10.20. Performance of the MCFDFXLMS algorithm.
• 10.21. Block diagram of a multichannel noise cancellation application using the Multichannel Filtered-X LMS algorithm.
• 10.22. Performance of the MCFXLMS algorithm.
• 10.23. Block diagram of an adaptive array using the Linearly Constrained LMS algorithm.
• 10.24. Sensitivity pattern of an adaptive array adapted at the base-band frequency using the Linearly Constrained LMS algorithms.
• 10.25. Block diagram of an adaptive array functioning as a sidelobe canceler.
• 10.26. Performance of an adaptive sidelobe canceler implemented using the LMS algorithm.
• 10.27. Block diagram of an acoustic echo canceler implemented using the block frequency domain adaptive filter (BFDAF).
• 10.28. Performance of an Acoustic Echo Canceler implemented using the BFDAF algorithm.
• 10.29. Block diagram of an acoustic echo canceler implemented using the Leaky NLMS adaptive filter.
• 10.30. Performance of an Acoustic Echo Canceler implemented using the Leaky NLMS adaptive filter.
• 10.31. Block diagram of an acoustic echo canceler implemented using the NLMS algorithm.
• 10.32. Performance of an Acoustic Echo Canceler implemented using the NLMS algorithm.
• 10.33. Block diagram of an acoustic echo canceler implemented using the Partitioned Block Frequency Domain Adaptive Filter (PBFDAF).
• 10.34. Performance of an Acoustic Echo Canceler implemented using the PBFDAF algorithm.
• 10.35. Block diagram of an acoustic echo canceler implemented using the (Reduced Complexity) partitioned block frequency domain adaptive filter (RCPBFDAF).
• 10.36. Performance of an Acoustic Echo Canceler implemented using the RCPBFDAF algorithm with two partitions out of eight are constrained each block and a block length equals to half the partition length.
• 10.37. Block diagram of the inverse modeling application.
• 10.38. Performance of the NLMS adaptive algorithm in an inverse modeling application.
• 10.39. Block diagram of the inverse modeling application.
• 10.40. Performance of the RLS algorithm in a a channel equalization application.
• 10.41. Block diagram of a forward modeling application using the autoregressive LMS-Newton algorithm.
• 10.42. Performance of the autoregressive LMS-Newton adaptive filter in a system identification application.
• 10.43. Block diagram of the forward modeling application using the Equation Error recursive adaptive filter.
• 10.44. Performance of the equation error adaptive filter in a system identification application.
• 10.45. Block diagram of the Lattice joint process estimator in a forward modeling application.
• 10.46. Performance of the LMS Lattice adaptive filter in a system identification application.
• 10.47. Block diagram of an FIR forward modeling using the MVSSLMS adaptive algorithm.
• 10.48. Performance of the Modified Variable Step Size LMS (MVSSLMS) adaptive filter in a system identification application.
• 10.49. Block diagram of the forward modeling application using the Output Error recursive adaptive filter.
• 10.50. Performance of the output error algorithm in a system identification application.
• 10.51. Block diagram of the RLS Lattice joint process estimator in a forward modeling application.
• 10.52. Performance of the RLS-Lattice algorithm in a system identification application.
• 10.53. Block diagram of the forward modeling application using the SHARF algorithm.
• 10.54. Performance of the SHARF IIR adaptive filter in a system identification application.
• 10.55. Block diagram of an FIR forward modeling using the TDLMS adaptive algorithm.
• 10.56. Performance of the Transform Domain LMS (TDLMS) adaptive filter in a system identification application.
• 10.57. Block diagram of an FIR forward modeling using the VSSLMS adaptive algorithm.
• 10.58. Performance of the variable step size LMS (VSSLMS) adaptive filter in a system identification application.
• 10.59. Block diagram of a prediction application using the lattice backward prediction error filter.
• 10.60. Performance of the Lattice Backward Prediction Error Filter in a prediction application.
• 10.61. Block diagram of a prediction application using the lattice forward prediction error filter.
• 10.62. Performance of the Lattice Forward Prediction Error Filter in a prediction application.
• 10.63. Block diagram of a prediction application using the RLS lattice backward prediction error filter.
• 10.64. Performance of the RLS Lattice Backward Prediction Error Filter in a prediction application.
• 10.65. Block diagram of a prediction application using the RLS lattice forward prediction error filter.
• 10.66. Performance of the RLS Lattice Forward Prediction Error Filter in a prediction application.