New Correlation Analysis Method for Nonstationary Signal

摘要

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, f, meets a certain condition, its auto-correlation property of Fourier transform can be presented by Fourier transform of its energy function, |f(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.