A time series x(t), t≥1, is said to be an unstable ARMA process if x(t) satisfies an unstableARMA model such asx(t)=a_1x(t-1)+a_2x(t-2)+…+a_8x(t-s)+w(t)where w(t) is a stationary ARMA process; and the characteristic...A time series x(t), t≥1, is said to be an unstable ARMA process if x(t) satisfies an unstableARMA model such asx(t)=a_1x(t-1)+a_2x(t-2)+…+a_8x(t-s)+w(t)where w(t) is a stationary ARMA process; and the characteristic polynomial A(z)=1-a_1z-a_2z^2-…-a_3z^3 has all roots on the unit circle. Asymptotic behavior of sum form 1 to n (x^2(t)) will be studied by showing somerates of divergence of sum form 1 to n (x^2(t)). This kind of properties Will be used for getting the rates of convergenceof least squares estimates of parameters a_1, a_2,…, a_?展开更多
A concise fractional Fourier transform （CFRFT） is proposed to detect the linear frequency-modulated （LFM） signal with low signal to noise ratio （SNR）. The frequency axis in time-frequency plane of the CFRFT is r...A concise fractional Fourier transform （CFRFT） is proposed to detect the linear frequency-modulated （LFM） signal with low signal to noise ratio （SNR）. The frequency axis in time-frequency plane of the CFRFT is rotated to get the spectrum of the signal in different an- gles using chirp multiplication and Fourier transform （FT）. For LFM signal which distributes as a straight line in time-frequency plane, the CFRFT can gather the energy in the corresponding angle as a peak and improve the detection SNR, thus the LFM signal of low SNR can be de- tected. Meanwhile, the location of the peak value relates to the parameters of the LFM signal. Numerical simulations and experimental results show that, the proposed method can be used to efficiently detect the LFM signal masked by noise and to estimate the signal＇s parameters accurately. Compared with the conventional fractional Fourier transform （FRFT）, the CFRFT reduces the transform complexity and improves the real-time detection performance of LFM signal.展开更多
文摘A time series x(t), t≥1, is said to be an unstable ARMA process if x(t) satisfies an unstableARMA model such asx(t)=a_1x(t-1)+a_2x(t-2)+…+a_8x(t-s)+w(t)where w(t) is a stationary ARMA process; and the characteristic polynomial A(z)=1-a_1z-a_2z^2-…-a_3z^3 has all roots on the unit circle. Asymptotic behavior of sum form 1 to n (x^2(t)) will be studied by showing somerates of divergence of sum form 1 to n (x^2(t)). This kind of properties Will be used for getting the rates of convergenceof least squares estimates of parameters a_1, a_2,…, a_?
基金supported by the National Natural Science Foundation of China(11434012)
文摘A concise fractional Fourier transform （CFRFT） is proposed to detect the linear frequency-modulated （LFM） signal with low signal to noise ratio （SNR）. The frequency axis in time-frequency plane of the CFRFT is rotated to get the spectrum of the signal in different an- gles using chirp multiplication and Fourier transform （FT）. For LFM signal which distributes as a straight line in time-frequency plane, the CFRFT can gather the energy in the corresponding angle as a peak and improve the detection SNR, thus the LFM signal of low SNR can be de- tected. Meanwhile, the location of the peak value relates to the parameters of the LFM signal. Numerical simulations and experimental results show that, the proposed method can be used to efficiently detect the LFM signal masked by noise and to estimate the signal＇s parameters accurately. Compared with the conventional fractional Fourier transform （FRFT）, the CFRFT reduces the transform complexity and improves the real-time detection performance of LFM signal.
