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

Automated summary

The short-time fractional Fourier transform (STFRFT) is a powerful tool for processing signals with fractional frequencies that vary over time. However, the existing discrete algorithms are not suitable for real-time applications that require recalculating the STFRFT at each or several samples. To solve this problem, a new sliding algorithm, called the sliding STFRFT, is proposed. It directly computes the STFRFT at the given time using the output result of the previous time step, significantly reducing computation complexity. The proposed algorithm has been shown to have the lowest computational cost among existing STFRFT algorithms.