Sliding Short-Time Fractional Fourier Transform
Gaowa Huang, Feng Zhang, Ran Tao
Abstract
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 <inline-formula><tex-math notation="LaTeX">$\bm {p\;(p > 1)}$</tex-math></inline-formula>. The proposed sliding STFRFT algorithm directly computes the STFRFT at the time <inline-formula><tex-math notation="LaTeX">$\bm {m+1}$</tex-math></inline-formula> or <inline-formula><tex-math notation="LaTeX">$\bm {m+p}$</tex-math></inline-formula> using the STFRFT output result at the time <inline-formula><tex-math notation="LaTeX">$\bm {m}$</tex-math></inline-formula>, which greatly reduces the computation complexity. The theoretical analysis demonstrates that the proposed algorithm has the lowest computational cost among existing STFRFT algorithms.