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 objects, 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 |
---|---|

Block 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 |
---|---|

Fast transversal least-squares adaptation algorithm Sliding window FTF 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 |

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 |
---|---|

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 |
---|---|

Frequency domain adaptation algorithm 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 |
---|---|

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? Adaptive filter objects have a `step`

method
that you use to apply the filter object to data. In the following
sections, various examples of using LMS and RLS adaptive filters show
you how `step`

works with the objects to apply them
to data.

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