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请稍等！！ zhidao/question/100602655.htmlTaking above into account, we have proposed two efficient techniques for the design of 1-D and 2-D variable filters, which are based on the decomposition of the given 1-D and 2-D variable magnitude specifications [3, 4].请考虑一下，我们假设用两种有效的方法来设计线形（1－D）的和平面（2－D）可变滤波器，这是根据给定的1－D与2－D可变幅度技术条件[3, 4]分解的。The techniques are very computationally efficient because they solely need designing a set of 1-D constant filters and approximating several 1-D polynomials. 由于完全依赖设计一套1－D常量滤波器以及近似于数个1－D多项式，本技术是很有计算效率的。In particular, the techniques can always guarantee the stability of the resulting variable filters. 特别是，本技术始终能够保证可变滤波器结果稳定性。However, in the 2-D case, the variable filters designed by such a technique are constrained to only have quadrantally symmetrical magnitude characteristics. 然而，在平面条件下，用该技术设计的可变滤波器受到约束，仅仅只有象限幅度对称性。That is to say, assume that is the given 2-D variable magnitude specification, where and are the normalized frequencies, and is a real valued vector whose elements are spectral parameters. 也就是说，设：
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为给定的2－D可变技术条件，式中 与 为标准化的频率，并且为值实向量，其要素为光谱参数。The technique [4] can only approximate the given 2-D variable magnitude specification in the case.本技术[4]仅在这种情况下能够近似算出给定的2－D可变滤波器技术条件 。 = (1) To circumvent this difficulty, this paper proposes a new method for designing 2-D variable digital filters with arbitrary magnitude characteristics. 围绕这一难题，本文提出了一项新方法，用于设计2－D可变数字滤波器，带有任意幅度性能。In other words, the technique can approximate 2-D variable magnitude specifications even though换言之，虽然 ≠ (2)，本技术能够近似计算出2－D可变幅度滤波器。 The technique is based on the decomposition of the given 2-D variable magnitude specifications, which is different from the one proposed in [4], and it only requires the normal 2-D constant filter designs and 1-D polynomial approximations. 本技术根据给定的1－D与2－D可变幅度技术条件分解的，但不同于[4]中提出技术方法，并且只需要公称2－D常量滤波器结构以及1－D多项式近似法。Since 2-D constant filters are relatively easy to design by applying the existing design techniques and 1-D polynomials can be easily approximated by solving simultaneous linear equations, the technique significantly simplifies the original 2-D variable filter design problem. 由于，2－D常量滤波器用现有的设计技术以及1－D多项式也可用求出同步线形方程而相对简单，所以本技术相当地简化了原有的2－D可变滤波器设计的难题。In particular, it should be emphasized that this technique can guarantee the stability of the resulting 2-D variable filters so long as the 2-D constant filters are designed to be stable. An example is given to illustrate the effectiveness of the proposed technique. 特别应当提出的是，本技术能够只要在2－D常量滤波器设计得稳定的话，就能保证取得的2－D可变滤波器结果的稳定性。文中详细说明了所提出的技术的效力。2. Design problem formulation2．设计问题的说明 In this section, we formulate the problem of designing 2-D variable digital filters with arbitrary magnitude responses based on the newly proposed outer product expansion of the given 2-D variable magnitude specifications. 在本节中，根据给定2－D可变幅度技术条件提出的外围设备，我们阐述了任意幅度反应2－D可变数字滤波器的设计。Below, we first define an outer product expansion, then relate it with the 2-D variable filter design problem.下面，我们首次对外围设备做了定义，然后将其同2－D可变滤波器考虑到以上因素，我们提出了基于给定1-D和2-D变量幅度规格[3, 4]的分解而设计1-D和2-D过滤器的两种高效技术。这两种技术在计算方面非常高效，因为它们只需要设计一组1-D常数过滤器和大约几个1-D多项式。特别的是，这些技术能保证生成变量过滤器的稳定性。但是，在2-D的情况下，这种技术设计的变量过滤器只有象限对称幅度特征。也就是说，假设【看不清的图片】是给定的2-D变量幅度规格，【看不清的图片】和【看不清的图片】是标准化的频率，【看不清的图片】是一个要素为光谱参数的有真实值的矢量。技术[4]只能在下列情况下大致估算给定的2-D变量幅度规格。【看不清的图片】=【看不清的图片】(1) 为了避开这个难点，本论文提出一种设计带有任意幅度特征的2-D变量数码过滤器的新方法。换句话说，即使在下列情况下该技术也能大致估算出2-D变量的幅度规格。【看不清的图片】≠【看不清的图片】(2)该技术基于给定的2-D变量幅度规格的分解，与[4]中建议的技术不同，它只需要常规2-D常量过滤器设计和1-D多项式近似值。由于采取现有设计技术2-D常量过滤器相对容易设计，1-D多项式也能通过解同步线性方程很容易地估算，该技术大大简化了原来的2-D变量过滤器设计问题。特别地，应当强调指出的是，只要2-D常量过滤器设计得很稳定，这个技术就能保证生成2-D变量过滤器的稳定性。本文给出了一个例子来说明所提出技术的有效性。
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