GENERALIZED INVERSE GROUP OF SIGNAL AND ITS IMPLEMENTATION WITH NEURAL NETWORKS
信号的广义逆群及其神经网络实现

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 perceptron 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(N~2). And the less leaking coefficient is, the more reliable the deconvolution will be.