Localization of the complex spectrum: the S transform
Citations
646 citations
Cites background from "Localization of the complex spectru..."
...Research activities reported in the literature can be summarized in the following four aspects: The first two deal with the development of new TFRs based on either signal decomposition or Cohen’s idea....
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...The Fourier transform of the signal cannot depict how the spectral content of the signal changes with time, which is critical in many nonstationary signals in practice....
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452 citations
Cites background or methods from "Localization of the complex spectru..."
...The expression of the S-transform given by Stockwell et al. (1996) is...
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...The S-transform ( Stockwell et al., 1996 ) is a time-frequency spectral localization method, similar to the short-time Fourier transform (STFT), but with a Gaussian window whose width scales inversely, and whose height scales linearly, with the frequency....
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...S-transform of Stockwell et al. (1996) and its relation to the Fourier spectrum....
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...Specific cases of the generalized S-transform are the Gaussian S-transform of Stockwell et al. (1996) and the newly introduced hyperbolic S-transform, which is designed to improve the resolution of wave train initiation time over the Gaussian S-transform....
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444 citations
Cites background from "Localization of the complex spectru..."
...This paper presents a probabilistic neural network (PNN) classifier based on S-Transform[9]where less numberof features i....
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...In the discrete case, the S-Transform is the projection of the vector defined by the time series , onto a spanning set of vectors [9]....
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...The S-Transform of a discrete time series , is given by [9]...
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441 citations
363 citations
Cites background or methods from "Localization of the complex spectru..."
...The use of instantaneous frequency in a local spectral representation was introduced for the S-transform [19], and independently was employed by Nelson [47] to study nonstationary multicomponent FM signals....
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...The continuous S-transform [19] of a function h(t) is...
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...This is called “voice windowing” and is analogous to the “voice Gaussian” of the S-transform [19]....
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...A more recent time-frequency representation, the S-transform [19], has found application in a range of fields....
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...(11) of [19], the “n” voice S[jT ,n/NT ] has the same frequency translation applied by the shift of the spectrum H [(m + n)/NT ] by “n” which centers the spectrum around the n frequency....
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References
6,180 citations
"Localization of the complex spectru..." refers background in this paper
...Along with (1), there exists an admissibility condition on the mother wavelet w(t, d) [5] that w(t, d) must have zero mean....
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5,910 citations
"Localization of the complex spectru..." refers methods in this paper
...Several techniques of examining the time-varying nature of the spectrum have been proposed in the past; among them are the Gabor transform [7], the related short time Fourier transforms, the continuous wavelet transform [8] and the bilinear class of time-frequency distributions known as Cohen’s class [4], of which the Wigner distribution [9] is a member....
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5,714 citations
3,568 citations
"Localization of the complex spectru..." refers background or methods in this paper
...Several techniques of examining the time-varying nature of the spectrum have been proposed in the past; among them are the Gabor transform [7], the related short time Fourier transforms, the continuous wavelet transform [8] and the bilinear class of time-frequency distributions known as Cohen’s class [4], of which the Wigner distribution [9] is a member....
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...This is an advantage over the bilinear class of TFRs (see “propagation of noise” in [4] ), where one £nds TFR{data} = TFR{signal} + TFR{noise} +2 ∗ TFR{signal} ∗ TFR{noise}....
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2,945 citations
"Localization of the complex spectru..." refers background in this paper
...The reader is referred to Rioul and Vetterli [10] and Young [11] for reviews of the literature....
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