A multi-resolution filtered-x LMS algorithm based on discrete wavelet transform for active noise control

•A new active control algorithm based on discrete wavelet transform (DWT) is proposed, which update the adaptive filter coefficients in frequency domain.•The proposed active control algorithm, so-called DWT-FFT-FXLMS algorithm is verified and compared with TD-FXLMS and FD-FXLMS algorithms.•Simulation results suggest that the DWT-FFT-FXLMS algorithm is effective for both stationary and non-stationary noise cancellation.

We have developed a new active control algorithm based on discrete wavelet transform (DWT) for both stationary and non-stationary noise control. First, the Mallat pyramidal algorithm is introduced to implement the DWT, which can decompose the reference signal into several sub-bands with multi-resolution and provides a perfect reconstruction (PR) procedure. To reduce the extra computational complexity introduced by DWT, an efficient strategy is proposed that updates the adaptive filter coefficients in the frequency domainDeepthi B.B using a fast Fourier transform (FFT). Based on the reference noise source, a ‘Haar’ wavelet is employed and by decomposing the noise signal into two sub-band (3-band), the proposed DWT-FFT-based FXLMS (DWT-FFT-FXLMS) algorithm has greatly reduced complexity and a better convergence performance compared to a time domain filtered-x least mean square (TD-FXLMS) algorithm. As a result of the outstanding time-frequency characteristics of wavelet analysis, the proposed DWT-FFT-FXLMS algorithm can effectively cancel both stationary and non-stationary noise, whereas the frequency domain FXLMS (FD-FXLMS) algorithm cannot approach this point.