The short-time fractional Fourier transform (STFRFT) has been shown to be a powerful tool for processing signals whose fractional frequencies vary with time. However, for real-time applications that require recalculating the STFRFT at each or several samples, the existing discrete algorithms are not suitable. To solve this problem, a new sliding algorithm is proposed, termed as the sliding STFRFT. First, the sliding STFRFT algorithm with the sliding step 1 is proposed. Then, it is derived to the circumstance when the sliding step turns to p(p>1)\boldsymbol{p}\;(\boldsymbol{p} > \boldsymbol{1}). The proposed sliding STFRFT algorithm directly computes the STFRFT at the time m+1m+1\bm{m+1} or m+pm+p\bm{m+p} using the STFRFT output result at the time m\boldsymbol{m}, which greatly reduces the computation complexity. The theoretical analysis demonstrates that the proposed algorithm has the lowest computational cost among existing STFRFT algorithms.

中文翻译：

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滑动短时分数阶傅里叶变换


短时分数傅里叶变换 (STFRFT) 已被证明是处理分数频率随时间变化的信号的强大工具。然而，对于需要在每个或多个样本处重新计算 STFRFT 的实时应用，现有的离散算法并不适合。为了解决这个问题，提出了一种新的滑动算法，称为滑动STFRFT。首先，提出了滑动步长为1的滑动STFRFT算法。然后推导出滑动步长为p(p>1)\boldsymbol{p}\;(\boldsymbol{p} > \boldsymbol{1})时的情况。所提出的滑动 STFRFT 算法使用 m\boldsymbol{m 时刻的 STFRFT 输出结果直接计算 m+1m+1\bm{m+1} 或 m+pm+p\bm{m+p} 时刻的 STFRFT }，大大降低了计算复杂度。理论分析表明，该算法是现有STFRFT算法中计算成本最低的。