Discrete multi-Gabor expansions
Discrete multi-Gabor expansions
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DOI：
10.1109/18.782117
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发表时间：
1999-09
期刊：
影响因子：
--
通讯作者：
Shidong Li
中科院分区：
文献类型：
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作者：
Shidong Li
为了满足信号时频表示的局域化和精细化要求，提出了一种离散多gabor展开（DMGE）。DMGE使用多个窗口及其平移和复杂调制作为合成（或分析）波形。它包括并推广了在信号分析中有用的元表象（平移、调制和扩张）。分析了均匀、非均匀和比例时间采样方案。讨论了DMGE的基本特点和重要性。重点研究了DMGE的构造和相关多分析序列的快速计算算法。利用矩阵代数，导出的算法既适用于多Gabor展开式，也适用于单窗口Gabor展开式。DMGE的另一个有用的特点是，多gabor变换可以在基于并行fft的实现结构中实现。文中还讨论了DMGE的实例及其在TF分析中的应用。
A discrete multi-Gabor expansion (DMGE) is developed to meet the requirements of localized and refined time-frequency (TF) representation of signals. The DMGE uses multiple windows and their translations and complex modulations as synthesis (or analysis) waveforms. It includes and generalizes the metaplectic (translation, modulation, and dilation) representations which are useful in signal analysis. Uniform, nonuniform, and proportional time sampling schemes are analyzed. The fundamental features and the importance of the DMGE are discussed. We focus on the construction of DMGE and deriving fast algorithms for the computation of related multi-analysis sequences. With matrix algebra, the algorithms derived apply to both multi-Gabor expansions and uni-(window) Gabor expansions. Another useful feature of the DMGE lies in the fact that the multi-Gabor transform can be realized in a parallel FFT-based implementation structure. Examples of DMGE and their applications to TF analysis are also discussed.