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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N~2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。
For the first time, this paper proposes a new concept of generalized inverse group of signals, and discusses its properties, leakage coefficient and neural network technology. The results show that there exists finite sets of generalized inverse signals of finite length, which form the generalized inverses of the original signal. The leak coefficients of generalized inverses are generally not the same, so their “pathological” degrees are different. The generalized inverse groups can be represented by a special And finally converges quickly.Finally, a new parallel limited-length filter deconvolution method can be formed when the generalized inverse groups are used in deconvolution. For offline processing, the computation time can be decreased from N ~ 2 orders To N order; the lowest leakage coefficient generalized inverse group corresponding to the most credible deconvolution.