Optimal Window Width Selection For Real-valued Discrete Gabor Transform Based On DCT Kernel

In the process of time-frequency analysis of signal, as a forceful analysis tool, Gabor transform has overcome the disadvantage that Fourier transform cannot exactly describe signal time-frequency changes as time changes. However, the calculation of traditional complex transform that Dennis Gabor put forward is too detailed, its real-time application is limited to a certain extent. To overcome the disadvantage of traditional Gabor transform, Tao Liang and his teammates have put forward real-valued discrete Gabor transform on the basis of discrete cosine transform. The idea of real-valued discrete Gabor transform only involves real arithmetic in respects of module calculation, signal reconstruction and the solution of bi-orthogonal analysis window functions, it reduces the calculation of Gabor transform to a great extent, which facilitates its application.In the process of Gabor transform, to gain Gabor expression of good aggregation and high time-frequency resolution, the choice of applicable type and width of window function. Research has revealed that the choice of applicable width of window function is more important than choice of type for time-frequency signal. Therefore, Du Xiuli and her teammates have put forward the choice adaptive algorithm of entropy-based Gabor transform window function. The algorithm chooses the optimal width of window function in the use of Shannon entropy, which resolves the problem of choosing the width of window function to a certain extent.The article first introduces the theory and common methods of time-frequency analysis, reviews the development process of Gabor transform theory, and mainly introduces real-valued discrete Gabor transform and its rapid calculation on the basis of DCT. Then it applies the choice of window function algorithm in the utilization of Shannon entropy to real-valued discrete Gabor transform which is based on DCT and proposes the optimal selection algorithm of window function of real-valued discrete Gabor transform based on DCT core. The article also verifies the effectiveness of algorithm through simulation experiment of cosine signal, frequency modulation signal and Gaussian envelope signal and applies the algorithm to the processing of radar signal through simulation experiment of selecting radar signal in different circumstances to verify the effectiveness of the algorithm in real application. Experiment results reveal that transient signal of cosine modulation can gain optimal width of window function in the process of Gabor transform and possesses the ability of anti-noise to a certain extent.Moreover, real-valued discrete Gabor transform based on DCT core only involves real arithmetic which reduces calculation, facilitates its application and improves the analysis, processing rate and efficiency of non-stationary signal effectively.