The Discrete Stockwell Transforms for Infinite-Length Signals and Their Real-Time Implementations

The various forms of the Stockwell transforms (ST) introduced in the literature have been developed for off-line signal processing on finite-length signals. However, in many applications such as audio, medical or radar signal processing, signals to be analyzed are of large sizes or received in real-time, time-frequency representations of such a signal cannot be calculated using the entire signal. The common approach is to calculate the spectrum segment-by-segment. This may result obvious boundary effects or lose absolute-referenced phase information in their time-frequency representations. In this paper, new formulations of the discrete ST for infinite-length signals are proposed. Based on the new definitions, fast algorithms are implemented using the fast Fourier transform. Our proposed computational schemes make it possible to process an infinite-length/large size signal segment-by-segment at low computational cost without any boundary effects. More importantly, the absolute-referenced phase information is reserved in this approach. These properties make the infinite-length STs more suitable for real-time signal processing.

[1]  R. P. Lowe,et al.  Local S-spectrum analysis of 1-D and 2-D data , 1997 .

[2]  K. R. Krishnanand,et al.  A New Real-Time Fast Discrete S-Transform for Cross-Differential Protection of Shunt-Compensated Power Systems , 2013, IEEE Transactions on Power Delivery.

[3]  Lalu Mansinha,et al.  Localization of the complex spectrum: the S transform , 1996, IEEE Trans. Signal Process..

[4]  Jing-Hua Gao,et al.  Generalized S Transform and Seismic Response Analysis of Thin Interbedss Surrounding Regions by Gps , 2003 .

[5]  Martin Vetterli,et al.  Fast Fourier transforms: a tutorial review and a state of the art , 1990 .

[6]  Jicheng Liu,et al.  Generalized S Transform with Adaptive Optimized Window and its Application in Seismic Signal Analysis , 2013 .

[7]  Dusmanta Kumar Mohanta,et al.  Power System Disturbance Recognition Using Wavelet and S-Transform Techniques , 2004 .

[8]  Lalu Mansinha,et al.  Space‐local spectral texture segmentation applied to characterizing the heterogeneity of hydraulic conductivity , 2002 .

[9]  E. Ferrara.  Fast implementations of LMS adaptive filters , 1980 .

[10]  Ralph F. Milliff,et al.  Resonant inertial oscillations in moored buoy ocean surface winds , 2004 .

[11]  Robert Glenn Stockwell,et al.  A basis for efficient representation of the S-transform , 2007, Digit. Signal Process..

[12]  Subhransu Ranjan Samantaray.  Fast S-transform based distance relaying in transmission line , 2013 .

[13]  Hongmei Zhu,et al.  The generalization of discrete Stockwell transforms , 2011, 2011 19th European Signal Processing Conference.

[14]  M. L. Lauzon,et al.  A General Description of Linear Time-Frequency Transforms and Formulation of a Fast, Invertible Transform That Samples the Continuous S-Transform Spectrum Nonredundantly , 2010, IEEE Transactions on Signal Processing.

[15]  Sylvia Drabycz,et al.  Image Texture Characterization Using the Discrete Orthonormal S-Transform , 2008, Journal of Digital Imaging.

[16]  Yanwei Wang,et al.  Fast Discrete Orthonormal Stockwell Transform , 2009, SIAM J. Sci. Comput..

[17]  A. W. M. van den Enden,et al.  Discrete Time Signal Processing , 1989 .

[18]  Joseph Ross Mitchell,et al.  T2 MRI texture analysis is a sensitive measure of tissue injury and recovery resulting from acute inflammatory lesions in multiple sclerosis , 2009, NeuroImage.