论文标题
短时傅立叶变换和Gabor乘数的分形不确定性原理
A Fractal Uncertainty Principle for the Short-Time Fourier Transform and Gabor multipliers
论文作者
论文摘要
我们研究了联合时频表示中的分形不确定性原理，并在调制空间上使用高斯窗口证明了短时傅立叶变换的版本。这可以等效地根据投影算子在整个功能的Bargmann-fock空间上进行配制。专门针对$ l^2（\ Mathbb {r}^d）$中的信号，我们获得了Daubechies的时间频率定位运算符的标准估算。该证明基于此类集合的最大奈奎斯特密度，对于多维cantor迭代，我们得出了明确的上限渐近线。最后，我们将分形的不确定性原理转化为离散的高斯Gabor乘数。
We study the fractal uncertainty principle in the joint time-frequency representation, and we prove a version for the Short-Time Fourier transform with Gaussian window on the modulation spaces. This can equivalently be formulated in terms of projection operators on the Bargmann-Fock spaces of entire functions. Specifically for signals in $L^2(\mathbb{R}^d)$, we obtain norm estimates of Daubechies' time-frequency localization operator localizing on porous sets. The proof is based on the maximal Nyquist density of such sets, and for multidimensional Cantor iterates we derive explicit upper bound asymptotes. Finally, we translate the fractal uncertainty principle to discrete Gaussian Gabor multipliers.
