摘要:
本文首次提出了信号的广义逆群这一新概念,并讨论了它的性质、泄漏系数和神经网络实现技术。研究表明,有限长信号存在多组有限长广义逆信号,它们构成原信号的广义逆群;各广义逆群的泄漏系数一般不相同,因而其病态程度不同;广义逆群可以用一个特殊的神经网络并行实现且收敛快.最后指出,广义逆群用于反卷积时可形成一种新的并行有限长滤波反卷积方法,对于离线处理,计算时间可从N2阶次降到N阶次;最低泄漏系数广义逆群对应的反卷积最可信。
Abstract:
A new concept, the generalized inverse group (GIG) of signal, is firstly proposed and its properties, leaking coefficients and implementation with neural networks are discussed in this paper. Theoretical analysis and computational simulation show that (1) there are a group of finite length generalized inverse signals for any finite signal, which form the GIG; (2) each inverse group has different leaking coefficients, thus different abnormal states; (3) each GIG can be implemented by a grouped and improved single-layer percep-
tron which appears with fast convergence. When used in deconvolution, the proposed GIG can form a new parallel finite length filtering deconvolution method. On off-line processing, the computational time is reduced to O(N) from O(N2).And the less leaking coefficient is, the more reliable the deconvolution will be.
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