New correlation analysis method for nonstationary signal
Zuojin Li, Weiren Shi, Kai Wang, Xiaowei Sun, Zhi Zhong · 2008
Abstract:- This paper proposes a new correlation analysis method for nonstationary and energy-limited continual signals, which works out a formula similar to time correlation theory; that is to say when the operator,, meets a certain condition, its auto-correlation property of Fourier transform can be presented by Fourier transform of its energy function, f 2) ( tf, revealing its correlation of the Fourier transform coefficients of frequency interval, ω. It proves that the Parseval identical equation is the special case happening when 0=ω. The above conclusion explains the theory of image compressing and noise removing through wavelet transform. Key-Words:- operator, energy function, wavelet transform, correlation function, image process a correlation analysis to nonstationary, energy-limited and power-limited signals, revealing their relations with time correlation theory. Literature [12] [13] prove that wavelet transform can reduce correlation and enhance the convergence speed of noise-removing algorithm, but theoretical explanations are not given. This paper conducts mathematic deduction to reach a conclusion similar 1.