In this paper, we give necessary and sufficient conditions for two families of Gabor functions of a certain type to yield a reproducing identity on L^2（R^n）. As applications, we characterize when such families yield...In this paper, we give necessary and sufficient conditions for two families of Gabor functions of a certain type to yield a reproducing identity on L^2（R^n）. As applications, we characterize when such families yield orthonormal or bi-orthogonal expansions. We also obtain a generalization of the Balian-Low theorem for general reprodueing identities （not necessary coming from a frame）.展开更多
A new method of parameter identification based on linear time-frequencyrepresentation and Hubert transform is proposed to identity modal parameters of linear time-varyingsystems from measured vibration responses. Usin...A new method of parameter identification based on linear time-frequencyrepresentation and Hubert transform is proposed to identity modal parameters of linear time-varyingsystems from measured vibration responses. Using Gabor expansion and synthesis theory, measuredresponses are represented in the time-frequency domain and modal components are reconstructed bytime-frequency filtering. The Hilbert transform is applied to obtain time histories of the amplitudeand phase angle of each modal component, from which time-varying frequencies and damping ratios areidentified. The proposed method has been demonstrated with a numerical example in which a lineartime-varying system of two degrees of freedom is used to validate the identification scheme based ontime-frequency representation. Simulation results have indicated that time-frequency representationpresents an effective tool for modal parameter identification of time-varying systems.展开更多
We consider expansions of the type arising from Wilson bases. We characterize such expansions for L^2（R）. As an application, we see that such an expansion must be orthonormal, in contrast to the case of wavelet expa...We consider expansions of the type arising from Wilson bases. We characterize such expansions for L^2（R）. As an application, we see that such an expansion must be orthonormal, in contrast to the case of wavelet expansions generated by translations and dilation.展开更多
基金This work is partially financed by NSC under 87-2115-M277-001.
文摘In this paper, we give necessary and sufficient conditions for two families of Gabor functions of a certain type to yield a reproducing identity on L^2（R^n）. As applications, we characterize when such families yield orthonormal or bi-orthogonal expansions. We also obtain a generalization of the Balian-Low theorem for general reprodueing identities （not necessary coming from a frame）.
基金Automobile Industrial Science Foundation of Shanghai (No.2000187)
文摘A new method of parameter identification based on linear time-frequencyrepresentation and Hubert transform is proposed to identity modal parameters of linear time-varyingsystems from measured vibration responses. Using Gabor expansion and synthesis theory, measuredresponses are represented in the time-frequency domain and modal components are reconstructed bytime-frequency filtering. The Hilbert transform is applied to obtain time histories of the amplitudeand phase angle of each modal component, from which time-varying frequencies and damping ratios areidentified. The proposed method has been demonstrated with a numerical example in which a lineartime-varying system of two degrees of freedom is used to validate the identification scheme based ontime-frequency representation. Simulation results have indicated that time-frequency representationpresents an effective tool for modal parameter identification of time-varying systems.
文摘We consider expansions of the type arising from Wilson bases. We characterize such expansions for L^2（R）. As an application, we see that such an expansion must be orthonormal, in contrast to the case of wavelet expansions generated by translations and dilation.
