L.Durak, "On the Applications of Fractional...", Nov. 19, 13:40, G032
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  • L.Durak, "On the Applications of Fractional...", Nov. 19, 13:40, G032

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Faculty of Engineering and Natural Sciences


EE 551 Seminar



On the Applications of Fractional Fourier Transform in Time-Frequency Signal Processing

Lütfiye Durak, Yıldız Technical University, Istanbul


The fractional Fourier transform (FrFT) is a generalization of the ordinary  Fourier transform with an order -or power- parameter of a. The first-order FrFT is the ordinary Fourier transform and the zeroth-order FrFT is the function itself. Fractional Fourier domains are the set of all domains which interpolate between time and frequency. The FrFT has found many applications in the field of signal processing, time-frequency analysis, communications, optics, and image processing. This talk provides an introduction to the FrFT and discusses some of its properties, including its effects on the time-frequency representations of signals as a special case of the linear canonical transforms. The time-frequency domain localization of signals by short-time Fourier transform (STFT) is characterized by introducing a novel generalized time-bandwidth product (GTBP) definition which is an extension of the time-bandwidth product on the fractional Fourier domains. The GTBP optimal STFT, which is a well-localized and high resolution time-frequency representation is introduced and its computationally efficient form is presented. It provides optimal results for chirp-like signals which can be encountered in a variety of application areas including radar, sonar, seismic, biological signal processing and communications. Furthermore, for signals with non-convex time-frequency support, an improved time-frequency domain analysis is obtained through chirp multiplication.

BIO:  Lutfiye Durak received the B.Sc., M.Sc. and PhD. degrees in Electrical Engineering Department of Bilkent University, Ankara, Turkey, in 1996, 1999 and 2003, respectively. She worked in the Statistical Signal Processing Laboratory of Korean Advanced Institute of Science and Technology, KAIST until 2005. She was a visiting research scholar in the Department of Electrical and Computer Engineering of University of Pittsburgh for the summer of 2008. She is currently an assistant professor in the Electronics and Communications Engineering Department of Yildiz Technical University, Istanbul, Turkey. Her research interests are in time-frequency signal processing, adaptive signal processing, statistical signal processing and communications theory.


Nov. 19, 2008, 13:40, FENS G032