Unified study on characteristic spectrum representation of signals and spectral decomposition for stationary random signals |
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| Authors: | Hongyu WANG Tianshuang QIU |
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| Affiliation: | Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China |
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| Abstract: | The unified relationship between the signal characteristic spectrum representation and the spectral decomposition for the stationary random signal was deeply studied. By using the relations among the differential operators, the integral operator and the Green's function of the characteristic differential equation, the inverse relationship between the Hermitian differential operator and the Hermitian integral operator were given, the characteristic differential equation and corresponding characteristic integral equation were demonstrated, and the spectral representations of both Hermitian differential and integral operators and the general spectral representations for both operators were provided. Based on the superposition method of the stochastic simple harmonic vibration and the Hilbert space unitary operator method for the stationary random signal spectral decomposition, the connection and unification on mathematics of the signal characteristic spectral representation and the stationary random signal spectral decomposition are revealed. |
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| Keywords: | Green function Hermitian operator differential operator integral operator orthogonal projection operator spectral representation unitary operator spectral decomposition |
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