It was proposed by Oliveira  in 2010, based on the modified FXLMS (MFXLMS) algorithm.
For example, a frequency domain implementation of the FXLMS algorithm was developed .
Similar idea was described by Duan, to develop the time-frequencydomain FXLMS (TF-FXLMS) algorithm.
The first is to place an identical filter in the reference signal path to the weight update of the LMS algorithm, which realizes the FXLMS algorithm.
It is noted that, for most powertrain active noise control system, the FXLMS algorithm is not directly used due to the computational cost.