Sliding Short-Time Fractional Fourier Transform

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
$\boldsymbol{p}\;(\boldsymbol{p} > \boldsymbol{1})$
. The proposed sliding STFRFT algorithm directly computes the STFRFT at the time
$\bm{m+1}$
or
$\bm{m+p}$
using the STFRFT output result at the time
$\boldsymbol{m}$
, which greatly reduces the computation complexity. The theoretical analysis demonstrates that the proposed algorithm has the lowest computational cost among existing STFRFT algorithms.