New correlation analysis method for nonstationary signal

Authors:
Zuojin Li;Weiren Shi;Kai Wang;Xiaowei Sun;Zhi Zhong
Affiliations:
College of Automation, Chongqing University, Shapingba District, Chongqing, People's Republic of China;College of Automation, Chongqing University, Shapingba District, Chongqing, People's Republic of China;College of Automation, Chongqing University, Shapingba District, Chongqing, People's Republic of China;College of Automation, Chongqing University, Shapingba District, Chongqing, People's Republic of China;The Smartech Institute, Futian District, Shenzhen
Venue:
WSEAS Transactions on Information Science and Applications
Year:
2008

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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, ƒ, meets a certain condition, its auto-correlation property of Fourier transform can be presented by Fourier transform of its energy function, |ƒ(t)|2, 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 ω=0. The above conclusion explains the theory of image compressing and noise removing through wavelet transform.