The fractional Fourier transform （FRFT） has multiplicity, which is intrinsic in fractional operator. A new source for the multiplicity of the weight-type fractional Fourier transform （WFRFT） is proposed, which can...The fractional Fourier transform （FRFT） has multiplicity, which is intrinsic in fractional operator. A new source for the multiplicity of the weight-type fractional Fourier transform （WFRFT） is proposed, which can generalize the weight coefficients of WFRFT to contain two vector parameters m,n ∈ Z^M . Therefore a generalized fractional Fourier transform can be defined, which is denoted by the multiple-parameter fractional Fourier transform （MPFRFT）. It enlarges the multiplicity of the FRFT, which not only includes the conventional FRFT and general multi-fractional Fourier transform as special cases, but also introduces new fractional Fourier transforms. It provides a unified framework for the FRFT, and the method is also available for fractionalizing other linear operators. In addition, numerical simulations of the MPFRFT on the Hermite-Gaussian and rectangular functions have been performed as a simple application of MPFRFT to signal processing.展开更多
In this paper, we study an application of deep learning to the advanced laser interferometer gravitational wave observatory(LIGO)and advanced Virgo coincident detection of gravitational waves(GWs) from compact binary ...In this paper, we study an application of deep learning to the advanced laser interferometer gravitational wave observatory(LIGO)and advanced Virgo coincident detection of gravitational waves(GWs) from compact binary star mergers. This deep learning method is an extension of the Deep Filtering method used by George and Huerta(2017) for multi-inputs of network detectors.Simulated coincident time series data sets in advanced LIGO and advanced Virgo detectors are analyzed for estimating source luminosity distance and sky location. As a classifier, our deep neural network(DNN) can effectively recognize the presence of GW signals when the optimal signal-to-noise ratio(SNR) of network detectors ≥ 9. As a predictor, it can also effectively estimate the corresponding source space parameters, including the luminosity distance D, right ascension α, and declination δ of the compact binary star mergers. When the SNR of the network detectors is greater than 8, their relative errors are all less than 23%.Our results demonstrate that Deep Filtering can process coincident GW time series inputs and perform effective classification and multiple space parameter estimation. Furthermore, we compare the results obtained from one, two, and three network detectors;these results reveal that a larger number of network detectors results in a better source location.展开更多
基金the National Natural Science Foundation of China(Grant No.60572094)the Doctorship Foundation of China Educational Depart-ment(Grant No.1010036620602)the National Natural Science Foundation of China for Distinguished Young Scholars(Grant No.60625104)
文摘The fractional Fourier transform （FRFT） has multiplicity, which is intrinsic in fractional operator. A new source for the multiplicity of the weight-type fractional Fourier transform （WFRFT） is proposed, which can generalize the weight coefficients of WFRFT to contain two vector parameters m,n ∈ Z^M . Therefore a generalized fractional Fourier transform can be defined, which is denoted by the multiple-parameter fractional Fourier transform （MPFRFT）. It enlarges the multiplicity of the FRFT, which not only includes the conventional FRFT and general multi-fractional Fourier transform as special cases, but also introduces new fractional Fourier transforms. It provides a unified framework for the FRFT, and the method is also available for fractionalizing other linear operators. In addition, numerical simulations of the MPFRFT on the Hermite-Gaussian and rectangular functions have been performed as a simple application of MPFRFT to signal processing.
基金supported by the National Natural Science Foundation of China(Grant Nos.11873001,11633001,11673008,and 61501069)the Natural Science Foundation of Chongqing(Grant No.cstc2018jcyjAX0767)+4 种基金the Strategic Priority Program of the Chinese Academy of Sciences(Grant No.XDB23040100)Newton International Fellowship Alumni Followon Fundingthe Fundamental Research Funds for the Central Universities Project(Grant Nos.106112017CDJXFLX0014,and 106112016CDJXY300002)Chinese State Scholarship FundNewton International Fellowship Alumni Follow on Funding
文摘In this paper, we study an application of deep learning to the advanced laser interferometer gravitational wave observatory(LIGO)and advanced Virgo coincident detection of gravitational waves(GWs) from compact binary star mergers. This deep learning method is an extension of the Deep Filtering method used by George and Huerta(2017) for multi-inputs of network detectors.Simulated coincident time series data sets in advanced LIGO and advanced Virgo detectors are analyzed for estimating source luminosity distance and sky location. As a classifier, our deep neural network(DNN) can effectively recognize the presence of GW signals when the optimal signal-to-noise ratio(SNR) of network detectors ≥ 9. As a predictor, it can also effectively estimate the corresponding source space parameters, including the luminosity distance D, right ascension α, and declination δ of the compact binary star mergers. When the SNR of the network detectors is greater than 8, their relative errors are all less than 23%.Our results demonstrate that Deep Filtering can process coincident GW time series inputs and perform effective classification and multiple space parameter estimation. Furthermore, we compare the results obtained from one, two, and three network detectors;these results reveal that a larger number of network detectors results in a better source location.
