The generalized evolutionary spectrum

Detka, C.S.; El-Jaroudi, A.

doi:10.1109/78.542447

Cited by 8 publications

(5 citation statements)

References 11 publications

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“…This study adopts a generalized Fourier transform to complete the aforementioned process. The GFT of a signal s(t) is expressed as follows (Detka and El-Jaroudi, 1996):…”

Section: Brief Recap Of the Sst And Gftmentioning

confidence: 99%

Application of high-resolution processing in seismic data based on an improved synchrosqueezing transform

Wang

Cheng

2022

Front. Earth Sci.

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This study proposes a high-resolution processing technique for seismic data based on the improved synchrosqueezing transform (SST). The SST rearranges the complex spectrum of the wavelet transform along the frequency axis. However, the energy is not concentrated in the position with the faster frequency change rate. To overcome these problems, the proposed method first transformed the seismic signal into an analytical one via Hilbert transformation and then determined the phase correction value (x0(t)) before and after the transformation. This was achieved using the instantaneous frequency attribute (ω(t)) of the analytical signal and a specific frequency (ω0) selected as the dominant frequency of the input data to adjust the change rate of the signal frequency before the SST falls close to zero, which can improve the time–frequency resolution after compression transformation. The essence of this method only adjusts the phase of the signal before and after transformation, without affecting the inverse expression of the SST. The one- and two-dimensional model data results show that the proposed method can better identify the time–frequency distribution characteristics of seismic signals and improve their resolution and the focusing effect in the time–frequency domain. The proposed method shows good prospects for application in gas reservoir detection and identification.

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“…This study adopts a generalized Fourier transform to complete the aforementioned process. The GFT of a signal s(t) is expressed as follows (Detka and El-Jaroudi, 1996):…”

Section: Brief Recap Of the Sst And Gftmentioning

confidence: 99%

Application of high-resolution processing in seismic data based on an improved synchrosqueezing transform

Wang

Cheng

2022

Front. Earth Sci.

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“…where M t -A2(t + r)h2(r)rdr n( ) -A2(t + r)h2(r)dr (9) and (n+i) (t) is the (m + 1) derivative of the phase of the signal, with…”

Section: Convergencementioning

confidence: 99%

Iterative estimation of instantaneous frequency and adaptive spectrogram

Emresoy

El-Jaroudi

1997

SPIE Proceedings

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In this paper, we present an iterative algorithm to estimate the instantaneous frequency (IF) and matched spectrogram of nonstationary signals. The matched spectrogram obtained by this method is concentrated along the IF for monocomponent signals. The convergence analysis and the properties of the IF estimation algorithm are presented. Finally examples showing the performance of the proposed algorithm is given.

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“…In addition to Priestley, estimation of the ES has been condidered by many others [12], [17], [18], [22], [30], [31], [32]. (There have also been generalizations and modifications of the ES [1], [11], [34] directed to the analysis of deterministic signals and involving instantaneous frequency. )…”

Section: Introductionmentioning

confidence: 99%

Statistical Properties for Coherence Estimators From Evolutionary Spectra

Walden

Cohen

2012

IEEE Trans. Signal Process.

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Abstract-Evolutionary spectra were developed by Priestley to extend spectral analysis to some nonstationary time series, in particularly semistationary processes, of which the ubiquitous uniformly modulated processes are a subclass. Coherence is well-defined for bivariate semistationary processes and can be estimated from such processes. We consider Priestley's estimator for the evolutionary spectral density matrix, and show that its elements can be written as weighted multitaper estimators with calculable weights and tapers. Under Gaussianity an approximating Wishartdistribution model follows for the spectral matrix, valid for all frequencies except small computable intervals near zero and Nyquist. Moreover, the critically important degrees of freedom are known. Consequently the statistical distribution of the coherence is given by Goodman's distribution and the raw coherence estimate can be accurately debiased. Theoretical results are verified using a model for wind fluctuations: simulations give excellent agreement between the mean debiased coherence estimates and true coherence, and between the proposed and empirical distributions of coherence.

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The generalized evolutionary spectrum

Cited by 8 publications

References 11 publications

Application of high-resolution processing in seismic data based on an improved synchrosqueezing transform

Application of high-resolution processing in seismic data based on an improved synchrosqueezing transform

Iterative estimation of instantaneous frequency and adaptive spectrogram

Statistical Properties for Coherence Estimators From Evolutionary Spectra

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