دانلود کتاب الگوریتم‌های فیلتر تطبیقی ​​برای داده‌های مختلط و چهارگانه

Adaptive filters may be described as a class of filtering structures having a mechanism for adjusting the free parameters (i.e. coefficients) based on statistical variations in the environment where the filter operates [1]. Adaptive filters have numerous applications, including adaptive equalization, adaptive noise cancellation, beamforming, system identification, etc. Adaptive filters were originally developed for real signals. Later, an extension to the complex domain was published. In recent years, adaptive filters have been developed for trinions, quaternions, octonions and hyper-complex data. For applications in communications, image processing and biological systems, nonlinear filters are well-suited for modeling the naturally occurring physical characteristics. There is an interest in understanding methods of nonlinear adaptive filtering. Kernel methods are a powerful new approach that can provide considerable complexity reduction for nonlinear filtering, as well as the potential for universal function approximation. The approach is of particular interest for real-time applications. Quaternions, which are an example of hyper-complex data, provide a convenient representation for performing transformations in 3- or 4- dimensional space. Quaternions are particularly well-suited for robotics applications, specifically image pattern recognition and modeling motion in 3-dimensions. However, the use of quaternions for adaptive filtering has been hampered by the fact that multiplication of quaternions is noncommutative, which complicates gradient operations using quaternion based cost functions. In this book, we present linear and nonlinear adaptive algorithms for use with complex and quaternion-valued data. We use kernel adaptive algorithms in cases where nonlinearity is present. Specifically, we present the complex kernel method: Complex Kernel Affine Projection Algorithm (CKAPA), and complex kernel filtering enhancement using widely linear (WL) estimation (i.e. derived WLCKLMS, WL-CKAPA). For quaternion-based kernel methods, we present algorithms such as the Quaternion Kernel LMS (Quat-KLMS) algorithm and Quaternion Kernel Maximum Correntropy (Quat-KMC) algorithm. We present convergence analysis of the algorithms and use simulation to verify the theoretical derivation using various applications of the adaptive filters. The book is organized as follows: Chap. 1 is an introduction, while in Chap. 2, we discuss linear and kernel filter theory, including reproducing kernels and transform spaces applied to adaptive filters. Chapter 3 is about adaptive filters for complex data. Chapter 4 discusses the complex kernel Least Mean Square (CKLMS) adaptive algorithm. Chapter 5 introduces use of quaternions for adaptive filters, while Chap. 6 is an introduction to Information Theoretic Learning. The derivation of the Complex Kernel APA algorithm is in Chap. 7. Chapter 8 presents the development of the Widely Linear CKLMS, CKAPA algorithms. Convergence analysis of the Complex KLMS algorithm is presented in Chap. 9. The derivation of the Quaternion Kernel LMS algorithm is presented in Chap. 10, while Chap. 11 has the derivation of the Quaternion Kernel Maximum Correntropy algorithm. We hope the material here will help educate readers and highlight some of the recent contributions to the field of adaptive signal processing using complex and quaternion data. We thank our families for their love and support during the time to prepare and publish this manuscript.