Enhancing time‐frequency resolution via deep‐learning framework
Zixin Wang, Lixing Chen, Peng Xiao, Lingji Xu, Zhenglin Li
Abstract
Abstract The fixed window function used in the short‐time Fourier transform (STFT) does not guarantee both time and frequency resolution, exerting a negative impact on the subsequent study of time‐frequency analysis (TFA). To avoid these limitations, a post‐processing method that enhances the time‐frequency resolution using a deep‐learning (DL) framework is proposed. Initially, the deconvolution theoretical formula is derived and a post‐processing operation is performed on the time‐frequency representation (TFR) of the STFT via deconvolution, a theoretical calculation to obtain the ideal time‐frequency representation (ITFR). Then, aiming at the adverse influence of the window function, a novel fully‐convolutional encoder‐decoder network is trained to preserve effective features and acquire the optimal time‐frequency kernel. In essence, the generation of the optimal time‐frequency kernel can be regarded as a deconvolution process. The authors conducted the qualitative and quantitative analyses of numerical simulations, with experimental results demonstrate that the proposed method achieves satisfactory TFR, possesses strong anti‐noise capabilities, and exhibits high steady‐state generalisation capability. Furthermore, results of a comparative experiment with several TFA methods indicate that the proposed method yields significantly improved performance in terms of time‐frequency resolution, energy concentration, and computational load.