Short-time fractional fourier transform and its applications

  • Authors:

  • Ran Tao;Yan-Lei Li;Yue Wang

  • Affiliations:

  • Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China;Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China;Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 2010

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Abstract

The fractional Fourier transform (FRFT) is a potent tool to analyze the chirp signal. However, it fails in locating the fractional Fourier domain (FRFD)-frequency contents which is required in some applications. The short-time fractional Fourier transform (STFRFT) is proposed to solve this problem. It displays the time and FRFD-frequency information jointly in the short-time fractional Fourier domain (STFRFD). Two aspects of its performance are considered: the 2-D resolution and the STFRFD support. The time-FRFD-bandwidth product (TFBP) is defined to measure the resolvable area and the STFRFD support. The optimal STFRFT is obtained with the criteria that maximize the 2-D resolution and minimize the STFRFD support. Its inverse transform, properties and computational complexity are presented. Two applications are discussed: the estimations of the time-of-arrival (TOA) and pulsewidth (PW) of chirp signals, and the STFRFD filtering. Simulations verify the validity of the proposed algorithms.