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The short time Fourier transform time-frequency representation (STFT-TFR) method degenerates, and the corresponding short time Fourier transform time-frequency filtering (STFT-TFF) method fails under α stable distribution noise environment. A fractional low order short time Fourier transform (FLOSTFT) which takes advantage of fractional p order moment is proposed for α stable distribution noise environment, and the corresponding FLOSTFT time-frequency representation (FLOSTFT-TFR) algorithm is presented in this paper. We study vector formulation of the FLOSTFT and inverse FLOSTFT (IFLOSTFT) methods and propose a FLOSTFT time-frequency filtering (FLOSTFT-TFF) method which takes advantage of time-frequency localized spectra of the signal in time-frequency domain. The simulation results show that, employing the FLOSTFT-TFR method and the FLOSTFT-TFF method with an adaptive weight function, time-frequency distribution of the signals can be better gotten and time-frequency localized region of the signal can be effectively extracted from α stable distribution noise, and also the original signal can be restored employing the IFLOSTFT method. Their performances are better than the STFT-TFR and STFT-TFF methods, and MSEs are smaller in different α and GSNR cases. Finally, we apply the FLOSTFT-TFR and FLOSTFT-TFF methods to extract fault features of the bearing outer race fault signal and restore the original fault signal from α stable distribution noise; the experimental results illustrate their performances.

Applications of an Improved Time-Frequency Filtering Algorithm to Signal Reconstruction