Adaptive S-Transform with Chirp-Modulated Window and Its Synchroextracting Transform

In this paper, an adaptive S-transform with chirp-modulated window (ASTCMW) is proposed to improve the energy concentration of the S-transform using the rotation of a function which is the inverse fractional Fourier transform of the chirp-modulated window. The window contains two parameters, the chirp rate parameter and the frequency parameter. The chirp rate parameter varying over time and frequency can control the rotation of the function in the time–frequency plane, and it can be determined by maximizing the amplitude of the ASTCMW. The frequency parameter assists the chirp rate parameter to rotate the function at high frequencies, and it is analyzed by the match between the input signal and the chirp-modulated window. The ASTCMW improves greatly the energy concentration in the instantaneous frequency in noiseless and noisy environments. Furthermore, the instantaneous frequency equation based upon the ASTCMW is developed, and then, a synchroextracting transform is proposed. By extracting the time–frequency points satisfying the equation, the proposed synchroextracting transform sharpens the ASTCMW result and gives a high-resolution time–frequency representation. The experiment results demonstrate the effectiveness of the ASTCMW and the proposed synchroextracting transform.