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Overview of Adaptive Filtering in DSP System Toolbox Software |
DSP System Toolbox™ software contains many objects for constructing and applying adaptive filters to data. As you see in the tables in the next section, the objects use various algorithms to determine the weights for the filter coefficients of the adapting filter. While the algorithms differ in their detail implementations, the LMS and RLS share a common operational approach — minimizing the error between the filter output and the desired signal.
For adaptive filter (adaptfilt) objects, the algorithm string determines which adaptive filter algorithm your adaptfilt object implements. Each available algorithm entry appears in one of the tables along with a brief description of the algorithm. Click on the algorithm in the first column to get more information about the associated adaptive filter technique.
LMS based adaptive filters
RLS based adaptive filters
Affine projection adaptive filters
Adaptive filters in the frequency domain
Lattice based adaptive filters
Least Mean Squares (LMS) Based FIR Adaptive Filters
Adaptive Filter Method | Adapting Algorithm Used to Generate Filter Coefficients During Adaptation |
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Adjoint LMS FIR adaptive filter algorithm | |
Block LMS FIR adaptive filter algorithm | |
FFT-based Block LMS FIR adaptive filter algorithm | |
Delayed LMS FIR adaptive filter algorithm | |
Filtered-x LMS FIR adaptive filter algorithm | |
LMS FIR adaptive filter algorithm | |
Normalized LMS FIR adaptive filter algorithm | |
Sign-data LMS FIR adaptive filter algorithm | |
Sign-error LMS FIR adaptive filter algorithm | |
Sign-sign LMS FIR adaptive filter algorithm |
For further information about an adapting algorithm, refer to the reference page for the algorithm.
Adaptive Filter Method | Adapting Algorithm Used to Generate Filter Coefficients During Adaptation |
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Fast transversal least-squares adaptation algorithm | |
QR-decomposition RLS adaptation algorithm | |
Householder RLS adaptation algorithm | |
Householder SWRLS adaptation algorithm | |
Recursive-least squares (RLS) adaptation algorithm | |
Sliding window (SW) RLS adaptation algorithm | |
Sliding window FTF adaptation algorithm |
For more complete information about an adapting algorithm, refer to the reference page for the algorithm.
Adaptive Filter Method | Adapting Algorithm Used to Generate Filter Coefficients During Adaptation |
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Affine projection algorithm that uses direct matrix inversion | |
Affine projection algorithm that uses recursive matrix updating | |
Block affine projection adaptation algorithm |
To find more information about an adapting algorithm, refer to the reference page for the algorithm.
FIR Adaptive Filters in the Frequency Domain (FD)
Adaptive Filter Method | Description of the Adapting Algorithm Used to Generate Filter Coefficients During Adaptation |
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Frequency domain adaptation algorithm | |
Partition block version of the FDAF algorithm | |
Partition block unconstrained version of the FDAF algorithm | |
Transform domain adaptation algorithm using DCT | |
Transform domain adaptation algorithm using DFT | |
Unconstrained FDAF algorithm for adaptation |
For more information about an adapting algorithm, refer to the reference page for the algorithm.
Lattice-Based (L) FIR Adaptive Filters
Adaptive Filter Method | Description of the Adapting Algorithm Used to Generate Filter Coefficients During Adaptation |
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Gradient adaptive lattice filter adaptation algorithm | |
Least squares lattice adaptation algorithm | |
QR decomposition RLS adaptation algorithm |
For more information about an adapting algorithm, refer to the reference page for the algorithm.
Presenting a detailed derivation of the Wiener-Hopf equation and determining solutions to it is beyond the scope of this User's Guide. Full descriptions of the theory appear in the adaptive filter references provided in the Selected Bibliography.
After you construct an adaptive filter object, how do you apply it to your data or system? Like quantizer objects, adaptive filter objects have a filter method that you use to apply the adaptfilt object to data. In the following sections, various examples of using LMS and RLS adaptive filters show you how filter works with the objects to apply them to data.