关于小波空间的框架

On a Problem About Frames of Wavelet Spaces

无论是信号处理,还是图像处理,首先要把模拟信号转换成数字信号,如何转换就涉及到采样问题,而框架理论是研究非均匀采样问题的一个重要工具.文章讨论若{2j2ψ(2jx-λn),n∈Z}是Wj的框架,对与另一采样集{an,n∈Z}满足什么样的条件,使得{22jψ(2jx-an),n∈Z}也是Wj的框架.

The frame theory is an important tool to study non-uniform sampling problem. There of it is obtained, that if {2j/2ψ（2^jx-λn）,n∈Z} is a frame in Wj and the non-uniform sampling set {ann∈Z} A_ j satisfies some conditions,then {2^j/2ψ（2^jx-an）,n∈Z} is a frame in Wj.