四元数值函数小波框架的稳定性

On the Stability of Wavelet Frames of Quaternionic-valued Functions

令L^(2)(R^(2),H)为定义在R^(2)上的四元数平方可积函数空间,研究了双边窗口四元数傅里叶变换的小波框架。得到了构成空间L^(2)(R^(2),H)小波框架的函数序列在采样序列和母小波发生摄动时,关于框架稳定性的相关性质。

Let L^(2)(R^(2),H)be a space of square integrable quaternion-valued functions defined on R^(2).We study the quaternionic wavelet frame based on the two-sided quaternionic windowed Fourier transform(QWFT).We obtain the properties of the sequence of functions that constitute the wavelet frame on the space L^(2)(R^(2),H)about the stability of the frame when the sampling and the mother wavelet have perturbation.