In this paper, the following important problem is answered: Under what condition can the Hilbert transform be put in the simple form. Then, using the Hilbert technique, it is demonstrated that, with some relative weak...In this paper, the following important problem is answered: Under what condition can the Hilbert transform be put in the simple form. Then, using the Hilbert technique, it is demonstrated that, with some relative weak restrictions, the particle motion at the sea surface and energy transmission may be obtained from a wave record. The analysis show that for the two-dimensional and narrow-band mo- tion (or a physical phenomena, such as capillary waves breaking, which satisfy the narrow-band approx- imation) the local kinetic energy fluctuates in time as the envelope equared multiplied by a constant factor and can be obtained directly from a wave record. It is pointed that the local fluctuatiom of the potential energy as well as the local fluctuations of the total energy can be separated into a slowly varying part and a more rapid oscillating Part. Both Parts can be evaluated by meaas of the Hilbert transform. Finally, a physical interpretation of the envelope of the two-dimensional capillary waves as well as the method for wave group analysis is presented.展开更多
In this paper, a new signal separation method mainly for AM-FM components blended in noises is revisited based on the new derived time-varying bandpass filter (TVBF), which can separate the AM-FM components whose freq...In this paper, a new signal separation method mainly for AM-FM components blended in noises is revisited based on the new derived time-varying bandpass filter (TVBF), which can separate the AM-FM components whose frequencies have overlapped regions in Fourier transform domain and even have crossed points in time-frequency distribution (TFD) so that the proposed TVBF seems like a “soft-cutter” that cuts the frequency domain to snaky slices with rational physical sense. First, the Hilbert transform based decomposition is analyzed for the analysis of nonstationary signals. Based on the above analysis, a hypothesis under a certain condition that AM-FM components can be separated successfully based on Hilbert transform and the assisted signal is developed, which is supported by representative experiments and theoretical performance analyses on a error bound that is shown to be proportional to the product of frequency width and noise variance. The assisted signals are derived from the refined time-frequency distributions via image fusion and least squares optimization. Experiments on man-made and real-life data verify the efficiency of the proposed method and demonstrate the advantages over the other main methods.展开更多
文摘In this paper, the following important problem is answered: Under what condition can the Hilbert transform be put in the simple form. Then, using the Hilbert technique, it is demonstrated that, with some relative weak restrictions, the particle motion at the sea surface and energy transmission may be obtained from a wave record. The analysis show that for the two-dimensional and narrow-band mo- tion (or a physical phenomena, such as capillary waves breaking, which satisfy the narrow-band approx- imation) the local kinetic energy fluctuates in time as the envelope equared multiplied by a constant factor and can be obtained directly from a wave record. It is pointed that the local fluctuatiom of the potential energy as well as the local fluctuations of the total energy can be separated into a slowly varying part and a more rapid oscillating Part. Both Parts can be evaluated by meaas of the Hilbert transform. Finally, a physical interpretation of the envelope of the two-dimensional capillary waves as well as the method for wave group analysis is presented.
文摘In this paper, a new signal separation method mainly for AM-FM components blended in noises is revisited based on the new derived time-varying bandpass filter (TVBF), which can separate the AM-FM components whose frequencies have overlapped regions in Fourier transform domain and even have crossed points in time-frequency distribution (TFD) so that the proposed TVBF seems like a “soft-cutter” that cuts the frequency domain to snaky slices with rational physical sense. First, the Hilbert transform based decomposition is analyzed for the analysis of nonstationary signals. Based on the above analysis, a hypothesis under a certain condition that AM-FM components can be separated successfully based on Hilbert transform and the assisted signal is developed, which is supported by representative experiments and theoretical performance analyses on a error bound that is shown to be proportional to the product of frequency width and noise variance. The assisted signals are derived from the refined time-frequency distributions via image fusion and least squares optimization. Experiments on man-made and real-life data verify the efficiency of the proposed method and demonstrate the advantages over the other main methods.
