The characteristic property of white Gaussian noise (WGN) is derived in S-transformation domain. The results show that the distribution of normalized S-spectrum of WGN follows X2 distribution with two degrees of freedom. The conclusion has been confirmed through both theoretical derivations and numerical simulations. Combined with different criteria, an effective signal detection in S-transformation can be realized.
 R. G. Stockwell, L. Mansinha and R. P. Lowe, “Localization of the Complex Spectrum: The S-Transform,” IEEE Transactions on Signal Processing, Vol. 44, No. 4, 1996, pp. 998-1001. http://dx.doi.org/10.1109/78.492555
 C. R. Pinnegar and L. Mansinha, “The S-Transform with Windows of Arbitrary and Varying Shape,” Geophysics, Vol. 68, No. 1, 2003, pp. 381-385. http://dx.doi.org/10.1190/1.1543223
 A. G. Rehorn, E. Sejdic and J. Jiang, “Fault Diagnosis in Machine Tools Using Selective Regional Correlation,” Mechanical Systems and Signal Processing, Vol. 20, No. 5, 2006, pp. 1221-1238. http://dx.doi.org/10.1016/j.ymssp.2005.01.010
 C. R. Pinnegar and L. Mansinha, “The Bi-Gaussian S-Transform,” SIAM: SIAM Journal on Scientific Computing, Vol. 24, No. 5, 2003, pp. 1678-1692. http://dx.doi.org/10.1137/S1064827500369803
 C.R. Pinnegar, L. Mansinha, “Time-Local Fourier Analysis with a Scalable, Phase-Modulated Analyzing Function: The S-Transform with a Complex Window,” Signal Process, Vol. 84, No. 7, 2004, pp. 1167-1176. http://dx.doi.org/10.1016/j.sigpro.2004.03.015
 M. Schimmel and J. Gallart, “The Inverse S-Transform in Filters with Time-Frequency Localization,” IEEE Transactions on Signal Process, Vol. 53, No. 11, 2005, pp. 4417-4422. http://dx.doi.org/10.1109/TSP.2005.857065
 C. Si-mon, S. Ventosa, M. Schimmel, A. Heldring, J. J. Da?obeitia, J. Gallart and A. Mànuel, “The S-Transform and Its Inverses: Side Effects of Discretizing and Filtering,” IEEE Transactions on Signal Processing, Vol. 55, No. 10, 2007, pp. 4928-4937.