Scheme for Designing the 1-D Convolution Window of Gabor Filter

A scheme for designing one-dimensional (1-D) convolution window of the circularly symmetric Gabor filter which is directly obtained from frequency domain is proposed. This scheme avoids the problem of choosing the sampling frequency in the spatial domain, or the sampling frequency must be determined when the window data is obtained by means of sampling the Gabor function, the impulse response of the Gabor filter. In this scheme, the discrete Fourier transform of the Gabor function is obtained by discretizing its Fourier transform. The window data can be derived by minimizing the sums of the squares of the complex magnitudes of difference between its discrete Fourier transform and the Gabor function's discrete Fourier transform. Not only the full description of this scheme but also its application to fabric defect detection are given in this paper. Experimental results show that the 1-D convolution windows can be used to significantly reduce computational cost and greatly ensure the quality of the Gabor filters. So this scheme can be used in some real-time processing systems.

A new family of windows——convolution windows and their applications

A new family of windows is constructed by convolutions via a few rectangular windows with same time width and is thus referred to as convolution windows. The expressions of the second-order up to the eighth-order convolution windows in both the time and frequency domains are derived. Their applications in high accuracy harmonic analysis of periodic signals are investigated. Comparisons between the proposed windows and some known windows with the same width shows that, when the synchronous deviation of data sampling is slight, the proposed ones have the least effect of spectral leakage. Therefore, the new windows are well suited for high accuracy harmonic analysis and parameter estimation for periodic signals. The error analysis and computer simulations show that the estimation errors, corresponding to frequency, amplitude and phase of every harmonic component of a signal, are proportional to the pth power of the relative frequency deviation in case of the pth-order convolution window is applied to windowing signal of approximately p cycles. By introducing real time adjustment in sampling interval, the proposed algorithm can adaptively trace signal frequency and lead to less sampling synchronous deviation. The proposed approach has the advantages of easy implementation and high measure precision and can be used in harmonic analysis of quasi-periodic signals whose fundamental frequency drifts slowly with time.