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Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: A generalization of the space-bandwidth product

机译：线性规范变换域与分数阶傅立叶域和双规范宽度乘积的等价关系：空间带宽乘积的一般化

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Linear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and ordered by the corresponding fractional order parameter and provides insight into the evolution of light through an optical system modeled by LCTs. If a set of signals is highly confined to finite intervals in two arbitrary LCT domains, the space-frequency (phase space) support is a parallelogram. The number of degrees of freedom of this set of signals is given by the area of this parallelogram, which is equal to the bicanonical width product but usually smaller than the conventional space-bandwidth product. The bicanonical width product, which is a generalization of the space-bandwidth product, can provide a tighter measure of the actual number of degrees of freedom, and allows us to represent and process signals with fewer samples. © 2010 Optical Society of America.

机译：线性规范变换（LCT）形成了三参数积分变换系列，在光学领域得到了广泛的应用。我们显示，LCT域对应于比例分数阶傅立叶域，因此对应于空频平面中的比例斜轴。这使LCT域可以通过相应的分数阶参数进行标记和排序，并通过LCT建模的光学系统深入了解光的演化。如果将一组信号高度限制在两个任意LCT域中的有限间隔内，则空间频率（相空间）支持为平行四边形。该组信号的自由度数由该平行四边形的面积给出，该面积等于双规范宽度乘积，但通常小于常规的空间带宽积。双规范宽度乘积是空间带宽乘积的一种概括，可以提供对实际自由度数的更严格的度量，并允许我们用更少的样本表示和处理信号。 ©2010美国眼镜学会。

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Oktem F.S.; Ozaktas, H., M.;
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1. Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space-bandwidth product [J] . Figen S. Oktem, Haldun M. Ozaktas Journal of the Optical Society of America, A. Optics, image science, and vision . 2010,第8期

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2. Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space–bandwidth product [J] . Figen S. Oktem and Haldun M. Ozaktas Journal of the Optical Society of America A: Optics, Image Science & Vision . 2010,第8期

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3. Optimal Joint Design of Discrete Fractional Fourier Transform Matrices and Mask Coefficients for Multichannel Filtering in Fractional Fourier Domains [J] . Xiao-Zhi Zhang, Bingo Wing-Kuen Ling, Hai Huyen Dam, IEEE Transactions on Signal Processing . 2018,第22期

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Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: A generalization of the space-bandwidth product

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