Time Frequency Split Zak Transform for Finite Gabor Expansion

S. Pei, M. Yeh
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引用次数: 6

Abstract

The relationship between the finite discrete Zak transform and the finite Gabor expansion are discussed in this paper. We present two DFT-based algorithms for computing Gabor coefficients. One is based upon the time-split Zak transform, the other upon the frequency-split Zak transform. These two methods are time and frequency dual pairs. Furthermore, we extend the relationship between the finite discrete Zak transform and the Gabor expansion to the 2-D case and compute 2-D Gabor expansion coefficients through the 2-D discrete Zak transform and 4-D DFT. Four methods can be applied in the 2-D case. They are time-time-split, time-frequency-split, frequency-time-split and frequency-frequency-split.
有限Gabor展开的时频分裂Zak变换
本文讨论了有限离散Zak变换与有限Gabor展开之间的关系。我们提出了两种基于dft的计算Gabor系数的算法。一种是基于时分Zak变换,另一种是基于频分Zak变换。这两种方法是时间和频率对偶。进一步将有限离散Zak变换与Gabor展开之间的关系推广到二维情况,并通过二维离散Zak变换和四维DFT计算二维Gabor展开系数。在二维情况下,有四种方法可以应用。它们是时-时-分,时-频-分,频-时-分和频-频-分。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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