Abstract
Energy concentration of the S-transform in the time-frequency domain has been addressed in this paper by optimizing the width of the window function used. A new scheme is developed and referred to as a window width optimized S-transform. Two optimization schemes have been proposed, one for a constant window width, the other for time-varying window width. The former is intended for signals with constant or slowly varying frequencies, while the latter can deal with signals with fast changing frequency components. The proposed scheme has been evaluated using a set of test signals. The results have indicated that the new scheme can provide much improved energy concentration in the time-frequency domain in comparison with the standard S-transform. It is also shown using the test signals that the proposed scheme can lead to higher energy concentration in comparison with other standard linear techniques, such as short-time Fourier transform and its adaptive forms. Finally, the method has been demonstrated on engine knock signal analysis to show its effectiveness.
Highlights
In the analysis of the nonstationary signals, one often needs to examine their time-varying spectral characteristics
In contrast to wavelet transform, the phase information provided by the S-transform is referenced to the time origin, and provides supplementary information about spectra which is not available from locally referenced phase information obtained by the continuous wavelet transform [5]
The scheme is based on the optimization of the width of the window used in the transform
Summary
In the analysis of the nonstationary signals, one often needs to examine their time-varying spectral characteristics. In contrast to wavelet transform, the phase information provided by the S-transform is referenced to the time origin, and provides supplementary information about spectra which is not available from locally referenced phase information obtained by the continuous wavelet transform [5] For these reasons, the S-transform has already been considered in many fields such as geophysics [6,7,8], cardiovascular time-series analysis [9,10,11], signal processing for mechanical systems [12, 13], power system engineering [14], and pattern recognition [15]. Several window functions are considered, including two types of exponential functions: amplitude modulation and phase modulation by cosine functions Another form of the generalized S-transform is developed in [7], where the window scale and shape are a function of frequency. It is shown that the WWOST produces the time-frequency representation with a higher concentration than other standard linear techniques, such as the short-time Fourier transform and its adaptive forms.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
