信號的廣義逆群及其神經(jīng)網(wǎng)絡(luò)實(shí)現(xiàn)
GENERALIZED INVERSE GROUP OF SIGNAL AND ITS IMPLEMENTATION WITH NEURAL NETWORKS
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摘要: 本文首次提出了信號的廣義逆群這一新概念,并討論了它的性質(zhì)、泄漏系數(shù)和神經(jīng)網(wǎng)絡(luò)實(shí)現(xiàn)技術(shù)。研究表明,有限長信號存在多組有限長廣義逆信號,它們構(gòu)成原信號的廣義逆群;各廣義逆群的泄漏系數(shù)一般不相同,因而其病態(tài)程度不同;廣義逆群可以用一個(gè)特殊的神經(jīng)網(wǎng)絡(luò)并行實(shí)現(xiàn)且收斂快.最后指出,廣義逆群用于反卷積時(shí)可形成一種新的并行有限長濾波反卷積方法,對于離線處理,計(jì)算時(shí)間可從N2階次降到N階次;最低泄漏系數(shù)廣義逆群對應(yīng)的反卷積最可信。
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關(guān)鍵詞:
- 信號處理; 神經(jīng)網(wǎng)絡(luò); 廣義逆群; 反卷積
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. -
S.M. Riad, Proc. IEEE, 74(1986)1, 82-85.[2]C. A. Berenstein, E.V. Patrick, Proc. IEEE, 78(1990)4, 723-734.[3]Special Issue on inverse methods in electromagnetics, IEEE Trans on AP, AP-29 (1981)3.[4]M.G.M. Hussain, M. Jarach, IEEE. Trans. on CAS, CAS-36(1989)4, 622-628.[5]何明一,基于神經(jīng)網(wǎng)絡(luò)的高可信度并行反卷積器基本原理.第二屆全國神經(jīng)網(wǎng)絡(luò)信號處理學(xué)術(shù)會議論文集,南京,1991年,12月2-6日,第129-133頁.[6]何明一,神經(jīng)計(jì)算原理語言設(shè)計(jì)應(yīng)用,西安電子科技大學(xué)出版社,西安,1992年,第14章.[7]R.E. Blahut, Fast Algorithms for Digital Signal Processing, Addison-Wesley Publishing Company, (1985), Chapter 11. -
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