tailieunhanh - 18 Introduction to Adaptive Filters

An adaptive filter is a computational device that attempts to model the relationship between two signals in real time in an iterative manner. | Douglas . Introduction to Adaptive Filters Digital Signal Processing Handbook Ed. Vijay K. Madisetti and Douglas B. Williams Boca Raton CRC Press LLC 1999 1999 by CRC Press LLC 18 Introduction to Adaptive Filters Scott C. Douglas University of Utah What is an Adaptive Filter The Adaptive Filtering Problem Filter Structures The Task of an Adaptive Filter Applications of Adaptive Filters System Identification Inverse Modeling Linear Prediction Feedforward Control Gradient-Based Adaptive Algorithms General Form of Adaptive FIR Algorithms The Mean-Squared Error Cost Function The Wiener Solution The Method of Steepest Descent The LMS Algorithm Other Stochastic Gradient Algorithms Finite-Precision Effects and Other Implementation Issues System Identification Example Conclusions References What is an Adaptive Filter An adaptive filter is a computational device that attempts to model the relationship between two signals in real time in an iterative manner. Adaptive filters are often realized either as a set of program instructions running on an arithmetical processing device such as a microprocessor or DSP chip or as a set of logic operations implemented in a field-programmable gate array FPGA or in a semicustom or custom VLSI integrated circuit. However ignoring any errors introduced by numerical precision effects in these implementations the fundamental operation of an adaptive filter can be characterized independently of the specific physical realization that it takes. For this reason we shall focus on the mathematical forms of adaptive filters as opposed to their specific realizations in software or hardware. Descriptions of adaptive filters as implemented on DSP chips and on a dedicated integrated circuit can be found in 1 2 3 and 4 respectively. An adaptive filter is defined by four aspects 1. the signals being processed by the filter 2. the structure that defines how the output signal of the filter is computed from its .