The S transform is variable window of short time Fourier transform (STFT) or an extension of wavelet transform (WT). It is based on a scalable localizing Gaussian window and supplies the frequency dependent resolution. In this tutorial, we introduce the fundamental function of S transform and the generalized S transform. Furthermore, we present some applications of S transform: seismogram analy...

The S–transform is shown to satisfy a specific twisted multiplicativity property for free random variables in a B–valued Banach noncommutative probability space, for an arbitrary unital complex Banach algebra B. Also, a new proof of the additivity of the R–transform in this setting is given.

In 1983 L. G. Brown introduced a spectral distribution measure for non-normal elements in a nite von Neumann algebra M with respect to a xed normal faithful tracial state. In this paper we compute Brown's spectral distribution measure in case T has a polar decomposition T = UH where U is a Haar unitary and U and H are-free. (When Ker T = f0g this is equivalent to that (T; T) is an R-diagonal pa...

The generalized S transform (GST), a family of reversible integer-to-integer transforms inspired by the S transform, is proposed. This family of transforms is then studied in detail by considering topics such as GST parameter calculation, the effects of using different rounding operators in the GST, and the relationship between the GST and the lifting scheme. Some examples of specific transform...

The algebra Mul[[B]] of formal multilinear function series over an algebra B and its quotient SymMul[[B]] are introduced, as well as corresponding operations of formal composition, which are associative. In the setting of Mul[[B]], the unsymmetrized R– and T–transforms of random variables in B–valued noncommutative probability spaces are introduced. These satisfy properties analogous to the usu...

this paper illustrates the application of s-transform and continuous wavelet transform (cwt) for fault location in combined overhead line and cable distribution networks. the high frequency transient signals originated by faults are analyzed using s-transform and cwt. the s-transform is found to be applicable in transient based fault location in distribution networks. this technique is an expan...

the s-transform has widely been used in the analysis of non-stationary time series. a simple method to obtain depth estimates of gravity field sources is introduced in this study. we have developed a new method based on the spectral characteristics of downward continuation to estimate depth of structures. this calculation procedure is based on replacement of the fourier transform with the s-tra...