Which algorithm, evolved from Widrow and Hoff’s LMS, accounts for secondary path distortion in ANC?

Answer

Filtered-X LMS (FXLMS).

The Filtered-X Least Mean Squares (FXLMS) algorithm is foundational to modern, robust ANC systems, especially in feedforward configurations. It evolved from the original LMS algorithm developed by Widrow and Hoff in 1959. The critical enhancement provided by FXLMS is its ability to mathematically model and compensate for the delay and distortion introduced by the secondary path—which includes the loudspeaker and amplifier system used to generate the anti-noise. By factoring in this secondary path distortion via filtering before minimizing the error, the system ensures that the inverted sound wave arrives at the error point (the ear) perfectly timed and phased to achieve effective cancellation against the original noise.

Which algorithm, evolved from Widrow and Hoff’s LMS, accounts for secondary path distortion in ANC?

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