中文摘要：

采用传统的窗口Fourier变换的加窗方法,对L2（R）空间中的加权Fourier变换进行加窗,通过图示的方法说明构造的规范加权窗口Fourier变换的实质是把一个信号划分成许多小的时间间隔,用加权Fourier变换分析每个时间间隔,并推出了此规范加权窗口Fourier变换在算子弱收敛与强收敛意义下的重构公式.

英文摘要：

By using the method of constructing the windowed Fourier transform on the basis of the traditional Fourier transform, this paper adds a window function to the weighted Fourier transform, and through a figure, illustrates the essence of the windowed Fourier transform with a normalized weight, that is, that dividing a signal into many intervals and analyzing every interval by using the weighted Fourier transform, and offers two inverse formulas in the sense of weak and strong convergence.