Enhancing time-frequency resolution via deep-learning framework

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.