The S-transform using a new window to improve frequency and time resolutions |
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Authors: | Kamran Kazemi Mohammadreza Amirian Mohammad Javad Dehghani |
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Affiliation: | 1. Department of Electrical and Electronics Engineering, Shiraz University of Technology, Shiraz, Iran
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Abstract: | The S-transform presents arbitrary time series as localized invertible time–frequency spectra. This transformation improves the short-time Fourier transform and the wavelet transform by merging the multiresolution and frequency-dependent analysis properties of wavelet transform with the absolute phase retaining of Fourier transform. The generalized S-transform utilizes a combination of a Fourier transform kernel and a scalable-sliding window. The common S-transform applies a Gaussian window to provide appropriate time and frequency resolution and minimizes the product of these resolutions. However, the Gaussian S-transform is unable to obtain uniform time and frequency resolution for all frequency components. In this paper, a novel window based on the $t$ student distribution is proposed for the S-transform to achieve a more uniform resolution. Simulation results show that the S-transform with the proposed window provides in comparison with the Gaussian window a more uniform resolution for the entire time and frequency range. The result is suitable for applications such as spectrum sensing. |
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