连续Gabor展开离散化后的混叠问题

Aliasing Problem after Continuous Gabor Expansion be Made Discrete

为能进行数值计算，需对连续Ｇａｂｏｒ展开离散化有限化。本文就时域与频域两种情况，给出了在过采样率的一般情况下，有限离散化后的Ｇａｂｏｒ展开系数与原连续Ｇａｂｏｒ展开系数之间的关系，并由此推出了离散Ｇａｂｏｒ展开系数不产生混叠的条件——连续Ｇａｂｏｒ展开离散化的采样定理。

The continuous Gabor expansion must be made discrete and finite in numerical implementation.This paper presents the relation between finite discrete Gabor expansion coefficients and original continuous Gabor expansion coefficients in oversampling case.The Gabor expansion in time domain and in frequency domain are respectively considered.According to the relation,the paper gives the conditions in which finite discrete Gabor expansion coefficients are no aliasing.These conditions can be called as sampling theorem of Gabor expansion.A numerical example is given.