Realization of 2-D linear-phase FIR filters by using the singular-value decomposition
Realization of 2-D linear-phase FIR filters by using the singular-value decomposition
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DOI：
10.1109/78.757222
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发表时间：
1999-05
期刊：
影响因子：
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通讯作者：
Weiping Zhu;M. Ahmad;M.N.S. Swamy
中科院分区：
文献类型：
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作者：
Weiping Zhu;M. Ahmad;M.N.S. Swamy
本文研究了用奇异值分解（SVD）技术实现具有任意幅值响应的二维线性相位FIR滤波器。通过对二维FIR滤波器的冲激响应进行奇异值分解，得到了一种由多个一维FIR子滤波器组成的并行实现结构。它表明，通过使用的2-D脉冲响应的对称性，并通过开发一个适当的酉变换，SVD产生线性相位成分的1-D滤波器总是可以得到，使1-D线性相位滤波器的有效结构，可以利用2-D实现。结果表明，当2-D滤波器实现具有一定的对称性在其幅度响应，建议SVD实现将产生一个幅度特性具有相同的对称性。进行了分析，以获得严格的上限的脉冲响应中的错误，以及在实现的滤波器的频率响应。它示出的平行部分的数量可以显着减少，而不会引入大的误差，即使在2-D滤波器的情况下，与非对称的幅度响应。
The singular-value decomposition (SVD) technique is investigated for the realization of a general two-dimensional (2-D) linear-phase FIR filter with an arbitrary magnitude response. A parallel realization structure consisting of a number of one-dimensional (1-D) FIR subfilters is obtained by applying the SVD to the impulse response of a 2-D filter. It is shown that by using the symmetry property of the 2-D impulse response and by developing an appropriate unitary transformation, an SVD yielding linear-phase constituent 1-D filters can always be obtained so that the efficient structures of the 1-D linear-phase filters can be exploited for 2-D realization. It is shown that when the 2-D filter to be realized has some specified symmetry in its magnitude response, the proposed SVD realization would yield a magnitude characteristic with the same symmetry. An analysis is carried out to obtain tight upper bounds for the errors in the impulse response as well as in the frequency response of the realized filter. It is shown that the number of parallel sections can be reduced significantly without introducing large errors, even in the case of 2-D filters with nonsymmetric magnitude response.