Topic

# S transform

About: S transform is a research topic. Over the lifetime, 3220 publications have been published within this topic receiving 61831 citations.

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TL;DR: The S transform is shown to have some desirable characteristics that are absent in the continuous wavelet transform, and provides frequency-dependent resolution while maintaining a direct relationship with the Fourier spectrum.

Abstract: The S transform, which is introduced in the present correspondence, is an extension of the ideas of the continuous wavelet transform (CWT) and is based on a moving and scalable localizing Gaussian window. It is shown to have some desirable characteristics that are absent in the continuous wavelet transform. The S transform is unique in that it provides frequency-dependent resolution while maintaining a direct relationship with the Fourier spectrum. These advantages of the S transform are due to the fact that the modulating sinusoids are fixed with respect to the time axis, whereas the localizing scalable Gaussian window dilates and translates.

2,752 citations

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TL;DR: The S transform as discussed by the authors is an extension to the ideas of the Gabor transform and the Wavelet transform, based on a moving and scalable localising Gaussian window and is shown here to have characteristics that are superior to either of the transforms.

Abstract: The S transform, an extension to the ideas of the Gabor transform and the Wavelet transform, is based on a moving and scalable localising Gaussian window and is shown here to have characteristics that are superior to either of the transforms. The S transform is fully convertible both forward and inverse from the time domain to the 2-D frequency translation (time) domain and to the familiar Fourier frequency domain. Parallel to the translation (time) axis, the S transform collapses as the Fourier transform. The amplitude frequency-time spectrum and the phase frequency-time spectrum are both useful in defining local spectral characteristics. The superior properties of the S transform are due to the fact that the modulating sinusoids are fixed with respect to the time axis while the localising scalable Gaussian window dilates and translates. As a result, the phase spectrum is absolute in the sense that it is always referred to the origin of the time axis, the fixed reference point. The real and imaginary spectrum can be localised independently with a resolution in time corresponding to the period of the basis functions in question. Changes in the absolute phase ofa constituent frequency can be followed along the time axis and useful information can be extracted. An analysis of a sum of two oppositely progressing chirp signals provides a spectacular example of the power of the S transform. Other examples of the applications of the Stransform to synthetic as well as real data are provided.

2,323 citations

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TL;DR: The paper compares the two possible forms of model-based transforms: unconstrained, where any combination of mean and variance transform may be used, and constrained, which requires the variance transform to have the same form as the mean transform.

Abstract: This paper examines the application of linear transformations for speaker and environmental adaptation in an HMM-based speech recognition system. In particular, transformations that are trained in a maximum likelihood sense on adaptation data are investigated. Only model-based linear transforms are considered, since, for linear transforms, they subsume the appropriate feature–space transforms. The paper compares the two possible forms of model-based transforms: (i) unconstrained, where any combination of mean and variance transform may be used, and (ii) constrained, which requires the variance transform to have the same form as the mean transform. Re-estimation formulae for all appropriate cases of transform are given. This includes a new and efficient full variance transform and the extension of the constrained model–space transform from the simple diagonal case to the full or block–diagonal case. The constrained and unconstrained transforms are evaluated in terms of computational cost, recognition time efficiency, and use for speaker adaptive training. The recognition performance of the two model–space transforms on a large vocabulary speech recognition task using incremental adaptation is investigated. In addition, initial experiments using the constrained model–space transform for speaker adaptive training are detailed.

1,755 citations

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TL;DR: A tutorial review of both linear and quadratic representations is given, and examples of the application of these representations to typical problems encountered in time-varying signal processing are provided.

Abstract: A tutorial review of both linear and quadratic representations is given. The linear representations discussed are the short-time Fourier transform and the wavelet transform. The discussion of quadratic representations concentrates on the Wigner distribution, the ambiguity function, smoothed versions of the Wigner distribution, and various classes of quadratic time-frequency representations. Examples of the application of these representations to typical problems encountered in time-varying signal processing are provided. >

1,587 citations

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23 Mar 1999TL;DR: This paper proposes to use Haar Wavelet Transform for time series indexing and shows that Haar transform can outperform DFT through experiments, and proposes a two-phase method for efficient n-nearest neighbor query in time series databases.

Abstract: Time series stored as feature vectors can be indexed by multidimensional index trees like R-Trees for fast retrieval. Due to the dimensionality curse problem, transformations are applied to time series to reduce the number of dimensions of the feature vectors. Different transformations like Discrete Fourier Transform (DFT) Discrete Wavelet Transform (DWT), Karhunen-Loeve (KL) transform or Singular Value Decomposition (SVD) can be applied. While the use of DFT and K-L transform or SVD have been studied on the literature, to our knowledge, there is no in-depth study on the application of DWT. In this paper we propose to use Haar Wavelet Transform for time series indexing. The major contributions are: (1) we show that Euclidean distance is preserved in the Haar transformed domain and no false dismissal will occur, (2) we show that Haar transform can outperform DFT through experiments, (3) a new similarity model is suggested to accommodate vertical shift of time series, and (4) a two-phase method is proposed for efficient n-nearest neighbor query in time series databases.

1,160 citations