In classical information processing, the windowed Fourier transform (WFT), or short-time Fourier transform, which is a variant of the Fourier transform by dividing a longer time signal into shorter segments of equal length and then computing the Fourier transform separately on each shorter segment, is proposed to provide a method of signal processing. Up to now the discrete Fourier transform has been successfully applied to the field of quantum information, but the related short-time discrete Fourier transform of this field has not been developed accordingly. To address this problem, we first introduce the concept of quantum window state, and further prove that the quantum Fourier transform of a quantum window state is also a quantum window state. Based on the definition of the quantum window state the local information of a quantum signal is extracted and the corresponding quantum circuits are also given. And then, by applying the quantum Fourier transform to the windowed quantum superposition states, we propose a novel concept called quantum windowed Fourier transform (QWFT). Finally, an application of quantum signal processing is given where QWFT is employed.

在经典信息处理中，加窗傅里叶变换 (WFT) 或短时傅里叶变换是傅里叶变换的一种变体，它通过将较长时间的信号分成相等长度的较短段，然后分别对每个较短的段进行傅里叶变换计算段，被提议提供一种信号处理方法。迄今为止，离散傅里叶变换已经成功地应用于量子信息领域，但该领域相关的短时离散傅里叶变换还没有得到相应的发展。为了解决这个问题，我们首先引入量子窗态的概念，进一步证明量子窗态的量子傅立叶变换也是量子窗态。根据量子窗态的定义，提取了量子信号的局部信息，并给出了相应的量子电路。然后，通过将量子傅里叶变换应用于加窗量子叠加态，我们提出了一个称为量子加窗傅里叶变换 (QWFT) 的新概念。最后，给出了采用 QWFT 的量子信号处理的应用。