A Sparse Analysis Window for Discrete Gabor Transform

作者：Zhou, Jian^*; Fang, Xianyong; Tao, Liang

来源：Circuits, Systems, and Signal Processing, 2017, 36(10): 4161-4180.

DOI：10.1007/s00034-017-0510-0

• Gabor time-frequency analysis
• Sparse analysis window
• Synthesis window

Here, we analyze sparse analysis windows for complex-valued and real-valued discrete Gabor transforms. A number of theories presented in this study indicate that the existence and uniqueness of a sparse analysis window for a given synthesis window depend to a great extent on the sparsity of the synthesis Specifically, the upper and lower bounds on the analysis window sparsity are obtained for synthesis windows of different sparsities and analyzed in detail. Particularly, if the sparsity of a given synthesis window with connected support is equal to the discrete Gabor transform time-shift parameter, the sparsest analysis window is unique. In addition, we propose an algorithm that searches for a sparse analysis Compared with existing algorithms, a sparse analysis window with fewer nonzero elements and/or smaller reconstruction errors can be obtained with the proposed algorithm. A sequence of experimental results reveals its superior effectiveness. In addition, a better Gabor representation with high concentration and time-frequency resolution is obtained with the sparse analysis

• 出版日期2017-10
• 单位安徽大学