Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 58, Issue 5, Pages 2568-2580Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2009.2028095
Keywords
Fractional Fourier transform (FRFT); optimal window; short-time fractional Fourier transform (STFRFT); time-FRFD-bandwidth product (TFBP)
Categories
Funding
- National Key Basic Research Program [2009CB724003]
- National Science Foundation of China for Distinguished Young Scholars [60625104]
- National Science Foundation of China [60890072]
- Advanced Research Project of the Eleventh Five-year Plan of China [41101030403]
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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.
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