On the construction and frequency localization of finite orthogonal quadrature filters
On the construction and frequency localization of finite orthogonal quadrature filters
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DOI：
10.1006/jath.2000.3514
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发表时间：
2001-01-01
影响因子：
0.9
通讯作者：
Nielsen, M
中科院分区：
文献类型：
--
作者：
Nielsen, M
介绍了一种利用卷积核构造有限正交正交滤波器的新方法，并证明了每一个原点值为1的滤波器都可以由偶非负核得到。我们将该方法应用于有限滤波器的频率局部化估计。有限滤波器m(0)的频率局部化γ (p)由l -p范数中/m(0)/(2)与Shannon低通滤波器之间的距离给出。对于每个N > 0，存在一个长度为2N的滤波器m(0)(N)，使值gamma (p)最小化。我们证明了对于这样一个最小化序列，我们有(p)(p)(m(0)(N)) = O(1n)， 1小于等于p小于等于2，并且这个估计是最优的。我们构造了几个新的具有最优渐近频率定位的MRA和非MRA滤波器族。(C) 2000年学术出版社。
We introduce a new method to construct finite orthogonal quadrature filters using convolution kernels and show that every filter with value 1 at the origin can be obtained from an even nonnegative kernel.We apply the method to estimate the frequency localization of finite filters. The frequency localization gamma (p) of a finite filter m(0) is given by the distance in L-P-norm between /m(0)/(2) and the Shannon low-pass filter. For each N > 0 there is a filter m(0)(N) of length 2N minimizing the value gamma (p). We prove that for such a minimizing sequence we have gamma (p)(p)(m(0)(N)) = O(1 N), 1 less than or equal to p less than or equal to 2, and this estimate is optimal. We construct several new families of both MRA and non-MRA filters with optimal asymptotic frequency localization. (C) 2000 Academic Press.