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当一个函数由乘数因子 expja(t)变形时(其中 a 代表平稳的随机过程),它所涉及的数学问题包括确定该函数的傅利叶交换的展开式。设 F(ω)表示 f(t)的傅利叶变换,F_m(ω)表示 f(t)expja(t)的傅利叶变换。例如,f 表示线性天线的照射函数,a 用以计算该天线的不完善相位关系。傅利叶变换的主要结果包括天线方向图|F_m|~2的均方根偏差简单公式及均方根旋转半径(或波束宽度)。这些位置误差及分辨力的降低是根据没有相位误差的天线方向图项与功率密度谱 a′而确定的。为了算出所有照射函数可能的最佳分辨力即,具有最小均方误差的分辨力,需要数值解法。但是,往往能得到均方根误差比 rmsa′及(rmsa″)~(1/2)二者中较小者还要小的分辨力。实际的数值解是与此正弦相位误差的简单近似值进行比较。傅利叶变换的一般结果应用很广;本文着重说明线性调频脉冲具有时相误差及色散(频相误差)的时问及频率模糊度函数展开式。还检查了有关平方相位误差、信/噪性能,以及点目标响应特性的均方误差问题。
When a function is deformed by the multiplier factor expja (t) (where a represents a stationary stochastic process), its mathematical problems include determining the expansion of the Fourier exchange of the function. Let F (ω) denote the Fourier transform of f (t) and F_m (ω) denote the Fourier transform of f (t) expja (t). For example, f represents the illumination function of the linear antenna and a is used to calculate the imperfect phase relationship of the antenna. The main results of the Fourier transform include the simple root mean square deviation equation and the root mean square radius of gyration (or beam width) of the antenna pattern | F_m | ~ 2. The reduction of these position errors and resolution is based on the antenna pattern term and power density spectrum a ’without phase error. In order to calculate the best possible resolution of all the illumination functions, the resolution with the smallest mean square error requires a numerical solution. However, resolution of less than the smaller of rmsa ’and (rmsa ") ~ (1/2) can often be obtained. The actual numerical solution is in agreement with a simple approximation of this sinusoidal phase error The general results of the Fourier transform are widely used. This paper focuses on the chronological and chromatic dispersion (frequency-phase error) chirp and the expansion of the frequency ambiguity function of the chirp. The quadratic phase error, signal / noise Performance, and point-target response characteristics of the mean square error.