文档介绍：信号与图像处理基础
中国科学技术大学自动化系
曹洋
Adaptive Filter
Outline
Overview of Adaptive Filter
Wiener Filter
LMS Filter
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Filters may be used for three information-processing tasks
Filtering
Smoothing
Prediction
overview of Adaptive Filter
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The Filtering Problem
The signal and/or noise characteristics are often nonstationary and the statistical parameters vary with time
An adaptive filter has an adaptation algorithm, that is meant to monitor the environment and vary the filter transfer function accordingly
Based in the actual signals received, attempts to find the optimum filter design
Adaptive Filter
Adaptive Filter
Given an optimality criteria we often can design optimal filters
Requires a priori information about the environment
Adaptive filters are self-designing using a recursive algorithm
Useful plete knowledge of environment is not available a priori
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The basic operation now involves two processes :
1. a filtering process, which produces an output signal in response to a given input signal.
2. an adaptation process, which aims to adjust the filter parameters (filter transfer function) to the (possibly time-varying) environment
Often, the (average) square value of the error signal is used as the optimization criterion
Adaptive Filter
Applications of Adaptive Filters: Identification
Used to provide a linear model of an unknown plant
Parameters
u=input of adaptive filter=input to plant
y=output of adaptive filter
d=desired response=output of plant
e=d-y=estimation error
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Applications of Adaptive Filters: Inverse Modeling
Used to provide an inverse model of an unknown plant
Parameters
u=input of adaptive filter=output to plant
y=output of adaptive filter
d=desired response=delayed system input
e=d-y=estimation error
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Applications of Adaptive Filters: Prediction
Used to provide a prediction of the present value of a random signal
Parameters
u=input of adaptive filter=delayed version of random signal
y=output of adaptive filter
d=