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The application of a shift theorem analysis technique to multipoint measurements


Radiation integral is efficiently evaluated by taking advantages of the convolution property leading to use the Fast Fourier Transform and the related shift theorem.


The QWT's approximate shift theorem enables efficient and easytouse analysis of the phase behavior around edge regions.


This quantity is also determined in the frequency domain utilizing the Fourier Shift Theorem to modulate the phase of each time course.


In contrast, our algorithm is entirely based on the dualtree QWT and its shift theorem, without using any optical flow assumptions.

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 This paper describes the sum and difference patterns of monopulse linear arrays of equally spaced discrete inphase elements which are excited in such a way that the envelope of the excitation amplitudes is uniform, triangular, or V in shape. Analysis of the radiation patterns is carried out by using exact or truncated Ztransform, and then the compact form as S (z) = F(z)  G (z), i. e. Eq. ( 4 ), is obtained. This method was first developed by D. K. Cheng and M. T. Ma in 1960. With the aid of Eq. ( 8 ) or the... This paper describes the sum and difference patterns of monopulse linear arrays of equally spaced discrete inphase elements which are excited in such a way that the envelope of the excitation amplitudes is uniform, triangular, or V in shape. Analysis of the radiation patterns is carried out by using exact or truncated Ztransform, and then the compact form as S (z) = F(z)  G (z), i. e. Eq. ( 4 ), is obtained. This method was first developed by D. K. Cheng and M. T. Ma in 1960. With the aid of Eq. ( 8 ) or the formula of G (z) derived from the shifting theorem, S (z) can be found simply by the unilateral Ztransform without considering whether the envelope function is symmetrical or unsymmetrical. Also a numerical example is given, showing that the theoretically calculated sum pattern compares quite favorably with that obtained from experiments, especially in the major region the test data and the analytical results have been found in fairly satisfactory agreement. The difference pattern also has been checked by experiments. The method proposed here is simple and easy to carry out.  文中讨论了离散元等间距排列成单脉冲阵列的和差方向图函数。激励幅度的包络是等幅、三角形和倒三角形(V形)分布。人们利用Z变换法或有限Z变换法已获得了紧凑的阵因子表达式(4),S(z)=F(2)G(z)。这里利用G(z)简洁公式(8),有时兼用位移定理,只以单边Z变换求出S(z),而不管包络函数对称与否。给出了计算例子。对和方向图还进行了实验研究,在主波瓣范围内实测数据同计算结果吻合得较好。差方向图也被实验验证过。  This paper attempts to apply Walsh transforms to the statespace analysis of linear discretetime systems. A cyclic shifttheorem of Wal'sh transforms presented by Cheng and Liu is first extended, and with the aid of Walsh transforms of the discrete state equations, a simple numerical formula for solving the state equations in the sequence domain is derived, from which a group of cyclic solutions of zerostate,response of a system can be obtained. An illustrative example is given.  本文探讨了Walsh变换在时域离散系统状态空间分析中的应用。文中推广了Walsh变换的循环位移定理,并利用它对离散状态方程进行离散Walsh变换,导出了状态方程求解较为简便的公式,从而可以得到系统零状态响应的一组循环解。文末给出了数值计算实例。  A transform of 3~n samples is given in this paper,which is similar to the modified walshHadamard transform(MWHT).Physical interpretation of the power spectra and the cyclic shift theorem are discussed.On this basis,two families of ortho gonal transforms are produced by combining two classes of reeursive relation which generate higher order orthogonal matrixes.These two families have fast transforms' algorithm and consist of the MWHT and the Haar transform(H*T),respectively.It is convenient to chose two... A transform of 3~n samples is given in this paper,which is similar to the modified walshHadamard transform(MWHT).Physical interpretation of the power spectra and the cyclic shift theorem are discussed.On this basis,two families of ortho gonal transforms are produced by combining two classes of reeursive relation which generate higher order orthogonal matrixes.These two families have fast transforms' algorithm and consist of the MWHT and the Haar transform(H*T),respectively.It is convenient to chose two transforms from these two families which can operate faster than the MWHT and H*T respectively when the number of sampling points is larger than 2~n but smaller than or equal to 3·2~(n1).  本文给出了取样周期为 N=3~n 序列的类似于修改的沃尔什阿达玛变换的变换。讨论了其功率谱的物理意义及循环移位定理。在此基础上,用两种递推生成高阶正交矩阵的关系组合的思想,生成二族正交变换,它们都具有快速算法;MWHT 和 HT 分别在这两族变换中,当取样点为 N(2~n   << 更多相关文摘 
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