Abstract The S transform, which is a time-frequency representation known for its local spectral phase properties in signal processing, uniquely combines elements of wavelet transforms and the short-time Fourier transform (STFT). The fractional Fourier transform is a tool for non-stationary signal analysis. In this paper, we defi ne the concept of the fractional S transform (FRST) of a signal, based on the idea of the fractional Fourier transform (FRFT) and S transform (ST), extend the S transform to the time-fractional frequency domain from the timefrequency domain to obtain the inverse transform, and study the FRST mathematical properties. The FRST, which has the advantages of FRFT and ST, can enhance the ST fl exibility to process signals. Compared to the S transform, the FRST can effectively improve the signal timefrequency resolution capacity. Simulation results show that the proposed method is effective.
This work was supported by Scientifi c Research Fund of Sichuan Provincial Education Department and the National Nature Science Foundation of China (No. 40873035)
Cite this article:
XU De-Ping,GUO Ke. Fractional S transform – Part 1: Theory*[J]. APPLIED GEOPHYSICS, 2012, 9(1): 73-79.
[1]
Akan, A., and Çekiç, Y., 2003, A fractional Gabor expansion: Journal of the Franklin Institute, 340(5), 391 - 397.
[2]
Akan, A., and Önen, E., 2007, A discrete fractional Gabor expansion for multi-component signals: AEUInternational
[3]
Journal of Electronics and Communications, 61(5), 279 - 285.
[4]
Almeida, L., 1994, The fractional Fourier transform and time-frequency representations: IEEE Trans. Signal
[5]
Process., 42(11), 3084 - 3091.
[6]
Capus, C., and Brown, K., 2003, Short-time fractional Fourier methods for the time-frequency representation
[7]
of chirp signals: Acoustical Society of America Journal, 113(6), 3253 - 3263.
[8]
Durak, L., and Arikan, O., 2003, Short-time Fourier transform: two fundamental properties and optimal
[9]
implementation: IEEE Trans. on Signal Processing, 51(5), 1231 - 1242.
[10]
Huang, Y., and Suter, B., 1998, The fractional wave packet transform: Multi-dimensional Systems and Signal
[11]
Processing, 9(4), 399 - 402.
[12]
Li, Y., and Zheng, X., 2007, Wigner-Ville distribution and its application in seismic attenuation estimation: Applied
[13]
Geophysics, 4(4), 245 - 254
[14]
Mendlovic, D., Zalevsky, Z., Mas, D., García, J., and Ferreira, C., 1997, Fractional wavelet transform: Applied
[15]
Optics, 36(20), 4801 - 4806.
[16]
Rioul, O., and Vetterli, M., 1991, Wavelets and signal processing: IEEE Signal Processing, 8(4), 14 - 38.
[17]
Stockwell, R. G., Mansinha, L., and Lowe, R. P., 1996, Localization of the complex spectrum: the S transform:
[18]
IEEE Trans. on Signal Processing, 44(4), 998 - 1001.
[19]
Tao, R., Li, Y. L., and Wang, Y., 2010, Short-time fractional Fourier transform and its applications: IEEE Trans.
[20]
Signal Process., 58(5), 2568 - 2580.
[21]
Wexler, R., 1990, Discrete Gabor expansions: Signal Processing, 21(3), 207 - 220.
2012, Vol. 9 
