TIME FREQUENCY LOCALIZATION OPERATORS - A GEOMETRIC PHASE-SPACE APPROACH
TIME FREQUENCY LOCALIZATION OPERATORS - A GEOMETRIC PHASE-SPACE APPROACH
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DOI：
10.1109/18.9761
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发表时间：
1988-07-01
影响因子：
2.5
通讯作者：
DAUBECHIES, I
中科院分区：
文献类型：
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作者：
DAUBECHIES, I
作者定义了一组在时间和频率上都本地化的算子。这些算子与低通时限算子相似但又不同，低通时限算子的奇异函数是长椭球波函数。作者的构造与通常的方法不同，她将时频平面视为一个几何整体（相空间），而不是两个独立的空间。对于时频平面中的盘形或椭圆形域，相关的定位算子非常简单。它们的特征函数是埃尔米特函数，相应的特征值由涉及不完全伽玛函数的简单显式公式给出。< >
The author defines a set of operators which localize in both time and frequency. These operators are similar to but different from the low-pass time-limiting operator, the singular functions of which are the prolate spheroidal wave functions. The author's construction differs from the usual approach in that she treats the time-frequency plane as one geometric whole (phase space) rather than as two separate spaces. For disk-shaped or ellipse-shaped domains in time-frequency plane, the associated localization operators are remarkably simple. Their eigenfunctions are Hermite functions, and the corresponding eigenvalues are given by simple explicit formulas involving the incomplete gamma functions.< >