Synchroextracting Transform Based on the Novel Short-Time Fractional Fourier Transform - Bei Li; Zhuosheng Zhang (Fractal and Fractional)
As a generalization of the short-time Fourier transform (STFT), the novel short-time fractional Fourier transform (NSTFRFT) has been introduced recently. In order to improve the concentration of the time–frequency representation (TFR) generated by the NSTFRFT, two post-processing time–frequency analysis methods, two synchroextracting transforms based on the NSTFRFT with two different fractional Fourier transform (FRFT) angles, are proposed in this paper. One is achieved via an equation where the instantaneous frequency satisfies the condition where the FRFT angle takes <semantics><mstyle scriptlevel="0" displaystyle="true">π2</mstyle></semantics>, and the other one is obtained using the instantaneous frequency estimator in the case that the FRFT angle takes a value related to the chirp rate of the signal. Although the conditions of the two synchroextracting transforms are different, their implementation can be unified into the same algorithm. The proposed synchroextracting transforms supplement existing post-processing time–frequency analysis methods which are based on the NSTFRFT. Experiments are conducted to verify the performance and superiority of the proposed methods.