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Adaptive Filter Design & Implementation
Digital Signal Processing Project Dr. Pawan K. Ajmera EEE F434 Adaptive Filter Design & Implementation Rishabh Bhardwaj 2014A3PS179P Aditya Manglik 2014A3PS296P
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Linear Filters Linear filters :
filter output is a linear function of the filter input . Design methods: The classical approach:- frequency-selective filters such as high pass/ low pass / band pass / notch filters etc.
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What is a Digital Filter?
A Digital Filter is a system that performs mathematical operations on a sampled discrete-time signal to reduce or enhance certain aspects of that signal.
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Limitations of fixed coefficient digital filter
Time varying noise frequency cannot be filtered easily, as is usually the case in practical signals Overlapping bands of signals and noise, which is a critical problem in real time systems
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Optimal filter design Coefficients are updated at every iteration according to the error function Mostly based on minimizing the mean-square value of the error signal
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Adaptive filter Signal and/or noise characteristics are often nonstationary and the statistical parameters vary with time Adaptive filter has an adaptation algorithm, that is meant to monitor the environment and vary the filter transfer function accordingly Based on the actual signals received, the algorithm attempts to find the optimum filter design
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Weiner Filter In a stationary environment, the filter is expected to converge, to the Wiener filter In a nonstationary environment, the filter is expected to track time variations and vary its filter coefficients accordingly!
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Adaptive filter The basic operation now involves two processes :
1. Filtering process, which produces an output signal in response to a given input signal. 2. 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
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Why not IIR? The generalization to adaptive IIR filters leads to stability problems It’s common to use a FIR digital filter with adjustable coefficients.
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Adaptive Filter Filtering Principle
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Least Mean Squares(LMS) Algorithm
Most popular adaptation algorithm is LMS. Defines cost function as mean-squared error. Based on the method of steepest descent “Move towards the minimum on the error surface to get to minimum gradient of the error surface estimated at every iteration!”
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LMS implementation Widrow-Hoff LMS Algorithm
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LMS Algorithm
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RLS implementation
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NLMS (Normalized Least Mean Squares) Algorithm
The main drawback of the simple LMS algorithm is that it is sensitive to the scaling of its input. This makes it very hard to choose a learning rate µ that guarantees stability of the algorithm. The Normalized least mean squares (NLMS) filter is a variant of the LMS algorithm. The benefit is that it solves this problem by normalizing with the power of the input.
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Performance Comparisons between different algorithms
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Applications of Adaptive Digital Signal Processing
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Four Typical Applications of Adaptive Filters
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Acoustic Echo Cancellation
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New Trends in Adaptive Filtering
Partial Updating Weights. Sub-band adaptive filtering. Adaptive Kalman filtering. Affine Projection Method. Time-Space adaptive processing. Non-Linear adaptive filtering:- Neural Networks. The Volterra Series Algorithm . Genetic & Fuzzy. Blind Adaptive Filtering.
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Thank You
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