论文标题
短期傅立叶变换的不确定性原理
Uncertainty principles for the short-time Fourier transform on the lattice
论文作者
论文摘要
在本文中，我们研究了晶格$ \ mathbb z^n \ times \ mathbb t^n $的短时傅立叶变换的不确定性原理的几个版本。特别是，我们确定了正顺序序列的不确定性原理，Donoho- Stark的不确定性原理，Benedicks-type不确定性原理，Heisenberg-type不确定性原理和局部不确定性不平等，用于这种转变的$ \ Mathbb z^n \ times \ Mathbb times \ Mathbb t^n $。此外，我们使用$ \ mathbb z^n \ times \ times \ mathbb t^n $的短期傅立叶变换的$ k $ entropy获得了海森伯格型不确定性不平等。
In this paper, we study a few versions of the uncertainty principle for the short-time Fourier transform on the lattice $\mathbb Z^n \times \mathbb T^n$. In particular, we establish the uncertainty principle for orthonormal sequences, Donoho--Stark's uncertainty principle, Benedicks-type uncertainty principle, Heisenberg-type uncertainty principle and local uncertainty inequality for this transform on $\mathbb Z^n \times \mathbb T^n$. Also, we obtain the Heisenberg-type uncertainty inequality using the $k$-entropy of the short-time Fourier transform on $\mathbb Z^n \times \mathbb T^n$.
