一种最优集中Gabor变换用于局部化时间-频率组件
An optimally concentrated Gabor transform for localized time-frequency components
AI总结：
本文提出优化算法，为选定的时间-频率模式提供最优窗口，基于l^p范数衡量时间-频率分散，通过数值实例展示方法潜力。
摘要：
Gabor分析是时间-频率信号分析中最常见的实例之一。选择适合信号的Gabor变换窗口常是实际应用中的挑战，特别是在音频信号处理中。不同形状的时间-频率（TF）模式可能存在于信号中，它们不能在同一个频谱图中稀疏表示。我们提出几种算法，为用户选定的TF模式提供最优窗口，基于不同的集中标准。我们的优化算法基于l^p范数作为TF分散的度量。对于给定的TF平面采样点数，我们还提出了最佳用于获得窗口的最优格点。我们通过选定的数值实例展示了该方法的潜力。
英文摘要：
Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing. Many time-frequency (TF) patterns of different shapes may be present in a signal and they can not all be sparsely represented in the same spectrogram. We propose several algorithms, which provide optimal windows for a user-selected TF pattern with respect to different concentration criteria. We base our optimization algorithm on $l^p$-norms as measure of TF spreading. For a given number of sampling points in the TF plane we also propose optimal lattices to be used with the obtained windows. We illustrate the potentiality of the method on selected numerical examples.
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