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A CLOSED-FORM DISCRETE FRACTIONAL GABOR EXPANSION

Journal Name:

  • Istanbul University Journal of Electrical & Electronics Engineering

Publication Year:

  • 2004

Key Words:

Author NameUniversity of Author
Abstract (2. Language): 
We present a discrete fractional Gabor expansion based on the closed form discrete fractional Fourier transform. The traditional Gabor expansion represents a signal as a linear combination of time and frequency shifted basis functions. This constant-bandwidth analysis generates a rectangular time-frequency lattice which might lead to poor time-frequency localization for many signals. Proposed expansion uses a set of basis functions related to the fractional Fourier basis and generate a parallelogram-shaped tiling. Completeness and biorthogonality conditions of the new expansion are given.
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  • 1
1105-1111
  • English

REFERENCES

References: 

[1] Cohen, L., Time-Frequency Analysis. Prentice Hall, Englewood Cliffs, NJ, 1995.
[2] Qian, S., and Chen, D., Joint Time-Frequency Analysis:Methods and Applications. Prentice Hall, Upper Saddle River, NJ, 1996.
[3] Gabor, D., “Theory of Communication,” J. IEE, Vol. 93, pp. 429-459, 1946.
[4] Jones, D.L., and Parks, T.W., “A High Resolution Data-Adaptive Time-Frequency Representation,” IEEE Trans. on Signal Proc., Vol. 38, No. 12, pp. 2127-2135, Dec. 1990.
[5] Jones, D.L., and Baraniuk, R.G., “A Simple Scheme For Adapting Time-Frequency Representations,” IEEE Trans. on Signal Proc., Vol. 42, No. 12, pp. 3530-3535, Dec. 1994.
[6] Mallat, S., and, Zhang, Z., “Matching Pursuit with Time-Frequency Dictionaries,” IEEE Trans. on Signal Proc., Vol. 41, pp. 3397-3415, Dec. 1993.
[7] Baraniuk, R.G., and Jones, D.L., “Shear Madness: New Orthonormal Bases and Frames Using Chirp Functions,” IEEE Trans. on Signal Proc., Vol. 41, No. 12, pp. 3543-3549, Dec. 1993.
[8] Akan, A., and Chaparro, L.F., “Multi-window Gabor Expansion for Evolutionary Spectral Analysis,” Signal Processing, Vol. 63, pp. 249-262, Dec. 1997.
[9] Bultan, A, “A Four-Parameter Atomic Decomposition of Chirplets,” IEEE Tans. on Signal Proc., Vol. 47 pp. 731-745, 1999.
[10] Akan, A., and Chaparro, L.F., “Evolutionary Chirp Representation of Non-stationary Signals via Gabor Transform,” Signal Processing, Vol. 81, No. 11, pp. 2429-2436, Nov. 2001.
[11] Akan, A., and Chaparro, L.F., “Signal-Adaptive Evolutionary Spectral Analysis Using Instantaneous Frequency Estimation,” IEEE-SP Proceedings of International Symposium on Time-Frequency and Time-Scale Analysis - TFTS'98, pp. 661-664, Pittsburgh, PA, Oct. 6-9, 1998.
[12] Bastiaans, M.J., and van Leest, A.J., “From the Rectangular to the Quincunx Gabor Lattice via Fractional Fourier Trasformation,” IEEE Signal Proc. Letters, Vol. 5, No. 8, pp. 203-205, 1998.
[13] van Leest, A.J., and Bastiaans, M.J., “Gabor's Signal Expansion and the Gabor Transform on a Non-separable Time-Frequency Lattice,” J. Franklin Institute, Vol. 337, No. 4, pp. 291-301, Jul. 2000.
[14] Pei, S.C., ve Ding, J.J., “Closed-Form Discrete Fractional and Affine Fourier Transform,” IEEE Trans. on Signal Proc., Vol. 48, No. 5, pp. 1338-1353, May 2000.
[15] Wexler, J., and Raz, S., “Discrete Gabor Expansions,” Signal Processing, Vol. 21, No. 3, pp. 207-220, Nov. 1990.
[16] Bastiaans, M.J., “Gabor's Expansion of a Signal into Gaussian Elementary Signals,” Proc. IEEE Vol. 68, No. 4, pp. 538-539, Apr. 1980.
[17] Akan, A., and Cekic, Y., “A Fractional Gabor Expansion,” to appear in Journal of The Franklin Institute, Aug. 2003.
[18] Almeida, L.B., “The Fractional Fourier Transform and Time-Frequency Representations,” IEEE Trans. on Signal Proc., Vol. 42, No. 11, pp. 3084-3091, Nov. 1994.
[19] Pei S.C., Yeh, M.H. and Tseng, C.C., “Discrete Fractional Fourier TransformBased on Orthogonal Projections,” IEEE Trans. on Signal Proc., Vol. 47, No. 5, pp. 1335-1348, May 1999.

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