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You must consider both convergence speed and computational resource requirements when choosing an adaptive filter algorithm. For example, the sign least mean squares (LMS) algorithms require the fewest computational resources. However, the corresponding convergence speed is slow. The QR decomposition-based recursive least squares (QR-RLS) algorithm requires the most computational resources. However, the corresponding convergence speed is fast.

For most applications, experiment with the standard LMS or normalized LMS (NLMS) algorithm first. If the resulting convergence speed does not meet the application requirements, consider other adaptive filter algorithms. For active noise control applications, you must use the filtered-x LMS algorithms.

The following table lists the computational resource requirements and relative convergence speed for different adaptive filter algorithms.

Algorithm | Computational Resource Requirements | Relative Convergence Speed | ||||
---|---|---|---|---|---|---|

Memory Usage | Multiplication | Addition | Division | Shift | ||

Standard LMS | 2n |
2n+1 |
2n+1 |
0 | 0 | Fast |

NLMS | 2n |
2n+4 |
2n+3 |
1 | 0 | Fast |

Leaky LMS | 2n |
3n+1 |
2n+2 |
0 | 0 | Fast |

Normalized Leaky LMS | 2n |
3n+4 |
2n+2 |
1 | 0 | Fast |

Sign-Error LMS | 2n |
n |
2n+1 |
0 | n |
Slow |

Sign-Data LMS | 2n |
n |
2n+1 |
0 | n |
Slow |

Sign-Sign LMS | 2n |
n |
2n+1 |
0 | 0 | Slow |

Fast Block LMS (Constraint) | 14n |
10log_{2}n+26 |
N/A | 0 | 0 | Fast |

Fast Block LMS (Unconstraint) | 14n |
6log_{2}n+26 |
N/A | 0 | 0 | Fast |

Filtered-X LMS | 2n+M |
2n+M+2 |
2n+M+2 |
0 | 0 | Fast |

Normalized Filtered-X LMS | 2n+M |
2n+M+5 |
2n+M+4 |
1 | 0 | Fast |

Recursive Least Squares (RLS) | n^{2}+2n |
2n^{2}+4n |
1.5n^{2}+2.5n |
0 | 0 | Very Fast |

QR-RLS | n^{2}+2n |
5n^{2}+9n |
2n^{2}+3n |
2n |
0 | Very Fast |

n is the length of the adaptive filter and M is the length of the estimated impulse response of the secondary path. |