A closed-form discrete fractional gabor expansion

Temel Bulgular & Veri:This constant-bandwidth analysis generates a rectangular time-frequency lattice which might lead to poor time-frequency localization for many signals.

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Sonuç & Katkı:Completeness and biorthogonality conditions of the new expansion are given.

🔬Tür:Araştırma Makalesi

📍Kapsam:Genişletilmiş Akademik Örneklem

⚙️Değişkenler:Alan Parametreleri

Abstract

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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Bu Makaleye Atıf Yap

AKAN, A., ÖNEN, E. (2022). A closed-form discrete fractional gabor expansion. Istanbul University Journal of Electrical and Electronics Engineering, Cilt: 4 - Sayı: 1, 1105–1111. https://ajindex.com/articles/543863

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Kaynakça (15)

Cohen, L., Time-Frequency Analysis. Prentice Hall, Englewood Cliffs, NJ, 1995
Qian, S., and Chen, D., Joint Time-Frequency Analysis:Methods and Applications. Prentice Hall, Upper Saddle River, NJ, 1996
Gabor, D., “Theory of Communication,” J. IEE, Vol. 93, pp. 429-459, 1946
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
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
Mallat, S., and, Zhang, Z., “Matching Pursuit with Time-Frequency Dictionaries,” IEEE Trans. on Signal Proc., Vol. 41, pp. 3397-3415, Dec. 1993
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
Akan, A., and Chaparro, L.F., “Multi-window Gabor Expansion for Evolutionary Spectral Analysis,” Signal Processing, Vol. 63, pp. 249-262, Dec. 1997
Bultan, A., “A Four-Parameter Atomic Decomposition of Chirplets,” IEEE Tans. on Signal Proc., Vol. 47 pp. 731-745, 1999
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
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
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
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
Wexler, J., and Raz, S., “Discrete Gabor Expansions,” Signal Processing, Vol. 21, No. 3, pp. 207-220, Nov. 1990
Bastiaans, M.J., “Gabor's Expansion of a Signal into Gaussian Elementary Signals,” Proc. IEEE Vol. 68, No. 4, pp. 538-539,