The method of constructing Hankel matrices and using low-rank approximation has been demonstrated to be an effective approach to audio denoising. However, the significant computational complexity and the trade-off between the denoising quality and the loss of effective signal remain open issues. This paper proposes a denoising method based on frequency-divided Windowed Singular Value Decomposition (WSVD) and exploits the low-rank characteristics and frequency features commonly found in audio signals including speech and music recordings. The method incorporates an improved Lanczos Bidiagonalization algorithm to accelerate the singular value decomposition with low error and high tolerance. Furthermore, techniques are added at the window junctions to maintain the continuity and smoothness of the final audio, thus achieving denoising efficiently and effectively. This paper also assesses the influence of window segmentation length, main frequency domain characteristics, rank selection of Hankel matrix and characteristics of different noises on the final denoising effect. Finally, the denoising algorithm's robustness and effectiveness are validated through simulations and experiments.
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