ABSTRACT
Windowed Fourier transform (WFT) is another excellent spatial frequency analysis method for nonstationary signal analysis. To overcome the deficiency of FT with poor spatial localization, Dennis Gabor adapted the FT to analyze only a small section of the signal at a time and proposed a technique called WFT or Gabor transform in 1946 [16]. The main idea of this technique involves introducing a window to the FT in the spatial domain to achieve spatial localization analysis. In recent years, WFT has been applied to the analysis of fringe signals. Jiawen Weng and Jingang Zhong have presented an approach for the analysis of fringe patterns using the WFT for 3-D profilometry [17]. Based on the WFT, windowed Fourier ridges (WFR) and windowed Fourier filtering (WFF) algorithms have been proposed by Qian Kemao et al. for fringe pattern analysis [18-22]. Hlubina et al. [23] proposed processing spectral interference signals using a method based on WFT applied in the wavelength
domain. A two-dimensional WFT has been developed for fringe pattern analysis [24,25]. For the WFT method, an essential factor is the determination of an appropriate window size for the localization analysis. Qian Kemao [26] proposed that the window size should be determined according to the balance between the linear phase approximation error and the noise level. However, the WFT method with an invariable window size is not suitable for analyzing the fringe signal with widely spectral parameters because of the invariable resolution in the spatial and frequency domains.
