H. L. Gray, C. C. Vijverberg and W. A. Woodward, “Non-stationary Data Analysis by Time Deformation,” Communication in Statistics-Theory and Methods, Vol. 34, No. 1, 2005, pp. 163-192. doi:10.1081/STA-200045869

has been cited by the following article:

• TITLE: Comparing the Time-Deformation Method with the Fractional Fourier Transform in Filtering Non-Stationary Processes

  AUTHORS: Mengyuan Xu, Wayne A. Woodward, Henry L. Gray

  KEYWORDS: Filtering; Time-Frequency; Time-Deformation; Fractional Fourier Transform

  JOURNAL NAME: Journal of Signal and Information Processing, Vol.3 No.4, November 29, 2012

  ABSTRACT: The classical linear filter is able to extract components from multi-component stochastic processes where the frequencies of components do not overlap over time, but fail for those processes where the frequencies overlap over time. In this paper, we discuss two filtering methods for non-stationary processes: the G-filtering method and the Fractional Fourier transform (FrFT) method. The FrFT method is mainly designed for linear chirp signals where the frequency is linearly changing with time. The G-filter can be used to filter signals with wide range of frequency behaviors such as linear chirps, quadratic chirps and other type of chirp signals with strong time-varying frequency behavior. If frequencies of the components can be approximated or separated by a straight line or a polynomial curve, the G-filter can successfully extract components from the original series. We show that the G-filter is applicable to a wider variety of filtering applications than methods such as the FrFT which require data of a specified frequency behavior.