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System identification based on distribution theory and wavelet transform |
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| Authors: | Ryuichi Ashino Takeshi Mandai † Akira Morimoto ‡ |
| Institution: | 1. Mathematical Sciences , Osaka Kyoiku University , Kashiwara, Osaka 582-8582, Japan ashino@cc.osaka-kyoiku.ac.jp;3. Research Center for Physics and Mathematics , Osaka Electro-Communication University , Neyagawa, Osaka 572-8530, Japan;4. Information Science , Osaka Kyoiku University , Kashiwara, Osaka 582-8582, Japan |
| Abstract: | A review of system identification based on distribution theory is given. By the Schwartz kernel theorem, to every continuous linear system there corresponds a unique distribution, called kernel distribution. Formulae using wavelet transform to access time--frequency information of kernel distributions are deduced. A new wavelet-based system identification method for health monitoring systems is proposed as an application of a discretized formula using stationary wavelet transform. |
| Keywords: | System identification Distribution Wavelet transform Stationary wavelet 2000 Mathematics Subject Classifications: Primary 42C40 Secondary 93B30 46F12 65T60 |