This paper proposes a new amplitude and phase demodulation scheme different from the traditional method for AM-FM signals. The traditional amplitude demodulation assumes that the amplitude should be non-negative, and ...This paper proposes a new amplitude and phase demodulation scheme different from the traditional method for AM-FM signals. The traditional amplitude demodulation assumes that the amplitude should be non-negative, and the phase is obtained under the case of non-negative amplitude, which approximates the true amplitude and phase but distorts the true amplitude and phase in some cases. In this paper we assume that the amplitude is signed (zero, positive or negative), and the phase is obtained under the case of signed amplitude by optimization, as is called signed demodulation. The main merit of the signed demodulation lies in the revelation of senseful physi- cal meaning on phase and frequency. Experiments on the real-world data show the efficiency of the method.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
Based on the definition and properties of discrete fractional Fourier transform (DFRFT), we introduced the discrete Hausdorff-Young inequality. Furthermore, the discrete Shannon entropic uncertainty relation and discr...Based on the definition and properties of discrete fractional Fourier transform (DFRFT), we introduced the discrete Hausdorff-Young inequality. Furthermore, the discrete Shannon entropic uncertainty relation and discrete Rényi entropic uncertainty relation were explored. Also, the condition of equality via Lagrange optimization was developed, as shows that if the two conjugate variables have constant amplitudes that are the inverse of the square root of numbers of non-zero elements, then the uncertainty relations reach their lowest bounds. In addition, the resolution analysis via the uncertainty is discussed as well.展开更多
文摘This paper proposes a new amplitude and phase demodulation scheme different from the traditional method for AM-FM signals. The traditional amplitude demodulation assumes that the amplitude should be non-negative, and the phase is obtained under the case of non-negative amplitude, which approximates the true amplitude and phase but distorts the true amplitude and phase in some cases. In this paper we assume that the amplitude is signed (zero, positive or negative), and the phase is obtained under the case of signed amplitude by optimization, as is called signed demodulation. The main merit of the signed demodulation lies in the revelation of senseful physi- cal meaning on phase and frequency. Experiments on the real-world data show the efficiency of the method.
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.
文摘Based on the definition and properties of discrete fractional Fourier transform (DFRFT), we introduced the discrete Hausdorff-Young inequality. Furthermore, the discrete Shannon entropic uncertainty relation and discrete Rényi entropic uncertainty relation were explored. Also, the condition of equality via Lagrange optimization was developed, as shows that if the two conjugate variables have constant amplitudes that are the inverse of the square root of numbers of non-zero elements, then the uncertainty relations reach their lowest bounds. In addition, the resolution analysis via the uncertainty is discussed as well.
