Short-time Fourier transform: Two fundamental properties and an optimal implementation

IEEE Transactions on Signal Processing

Volumn 51, Issue 5, 2003, Pages 1231-1242

  Durak, Lötfiye ^a   Arikan, Orhan ^a  

^a BILKENT UNIVERSITY   (Turkey)

Author keywords

Fractional Fourier transform; Generalized time bandwidth product; Linear time frequency representations; Rotation invariance; Short time Fourier transform

Indexed keywords

ALGORITHMS; BANDWIDTH; FOURIER TRANSFORMS; PROBABILITY DISTRIBUTIONS; RADAR TARGET RECOGNITION; SPECTROGRAPHS; SPECTRUM ANALYSIS;

FRACTIONAL FOURIER TRANSFORM; GENERALIZED TIM-BANDWIDTH PRODUCT; LINEAR TIME-FREQUENCY REPRESENTATIONS; ROTATION INVARIANCE; SHORT-TIME FOURIER TRANSFORM;

SIGNAL PROCESSING;

EID: 0037721742     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2003.810293     Document Type: Article

References (38)

1. F. Hlawatsch and G. F. Boudreaux-Bartels, "Linear and quadratic time-frequency signal representations," IEEE Signal Processing Mag., vol. 9, pp. 21-67, Apr. 1992.
2. L. Cohen, "Time-frequency distributions-A review," Proc. IEEE, vol. 77, pp. 941-981, July 1989.
3. ____, Time-Frequency Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1995.
4. R. A. Altes, "Detection, estimation and classification with spectrograms," J. Acoust. Soc. Amer., vol. 67, no. 4, pp. 1232-1246, Apr. 1980.
5. S. Cheung and J. S. Lim, "Combined multiresolution (wide-band/narrow-band) spectrogram," IEEE Trans. Signal Processing, vol. 40, pp. 975-977, Apr. 1992.
6. E. J. Rothwell, K. M. Chen, and D. P. Nyquist, "An adaptive-window-width short-time Fourier transform for visualization of radar target substructure resonances," IEEE Trans. Antennas Propagat., vol. 46, pp. 1393-1395, Sept. 1998.
7. H. K. Kwok and D. L. Jones, "Improved instantaneous frequency estimation using an adaptive short-time Fourier transform," IEEE Trans. Signal Processing, vol. 48, pp. 2964-2972, Oct. 2000.
8. LJ. Stankovic, "A method for time-frequency signal analysis," IEEE Trans. Signal Processing, vol. 42, pp. 225-229, Jan. 1994.
9. P. K. Kumar and K. M. M. Prabhu, "Simulation studies of moving-target detection: A new approach with Wigner-Ville distribution," Proc. Inst. Elect. Eng. Radar. Sonar Navig., vol. 144, pp. 259-265, Oct. 1997.
10. P. Flandrin, "Some features of time-frequency representations of multicomponent signals," in Proc. IEEE Int. Conf. Acoust. Speech Signal Process., vol. 8, 1984, pp. 266-269.
11. K. J. R. Liu, "Novel parallel architecture for short-time Fourier transform," IEEE Trans. Circuits Syst., vol. 40, pp. 786-789, Dec. 1993.
12. M. G. Amin and K. D. Feng, "Short-time Fourier transform using cascade filter structures," IEEE Trans. Circuits Syst., vol. 42, pp. 631-641, Oct. 1995.
13. W. Chen, N. Kehtarnavaz, and T. W. Spencer, "An efficient recursive algorithm for time-varying Fourier transform," IEEE Trans. Signal Processing, vol. 41, pp. 2488-2490, July 1993.
14. A. W. Lohmann and B. H. Soffer, "Relationships between the Radon-Wigner and fractional Fourier transforms," J. Opt. Soc. Amer. A, vol. 11, pp. 1798-1801, 1994.
15. J. C. Wood and D. T. Barry, "Radon transformation of time-frequency distributions for analysis of multicomponent signals," IEEE Trans. Signal Processing, vol. 42, pp. 3166-3177, Nov. 1994.
16. G. Jones and B. Boashash, "Generalized instantaneous parameters and window matching in the time-frequency plane," IEEE Trans. Signal Processing, vol. 45, pp. 1264-1275, May 1997.
17. L. L. Scharf and B. Friedlander, "Toeplitz and Hankel kernels for estimating time-varying spectra of discrete-time random processes," IEEE Trans. Signal Processing, vol. 49, pp. 179-189, Jan. 2001.
18. A. W. Naylor and G. R. Sell, Linear Operator Theory in Engineering and Science. New York: Springer-Verlag, 1982.
19. L. B. Almedia, "The fractional Fourier transform and time-frequency representations," IEEE Trans. Signal Processing, vol. 42, pp. 3084-3091, Nov. 1994.
20. V. Namias, "The fractional order Fourier transform and its application to quantum mechanics," J. Inst. Math. Appl., vol. 25, pp. 241-265, 1980.
21. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform With Applications in Optics and Signal Processing. New York: Wiley, 2000.
22. H. M. Ozaktas, N. Erkaya, and M. A. Kutay, "Effect of fractional Fourier transformation on time-frequency distributions belonging to Cohen class," IEEE Signal Processing Lett., vol. 3, pp. 40-41, Feb. 1996.
23. H. M. Ozaktas, O. Arikan, M. A. Kutay, and G. Bozdagi, "Digital computation of the fractional Fourier transform," IEEE Trans. Signal Processing, vol. 44, pp. 2141-2150, Sept. 1996.
24. J. C. Wood and D. T. Barry, "Tomographic time-frequency analysis and its application toward time-varying filtering and adaptive kernel desing for multicomponent linear-FM signals," IEEE Trans. Signal Processing, vol. 42, pp. 2094-2104, Aug. 1994.
25. ____, "Linear signal synthesis using the Radon-Wigner transform," IEEE Trans. Signal Processing, vol. 42, pp. 2105-2111, Aug. 1994.
26. Z. Bao, G. Wang, and L. Luo, "Inverse synthetic aperture radar imaging of maneuvering targets," Opt. Eng., vol. 37, no. 5, pp. 1582-1588, May 1998.
27. A. K. Özdemir and O. Arikan, "Efficient computation of the ambiguity function and the Wigner distribution on arbitrary line segments," IEEE Trans. Signal Processing, vol. 49, pp. 381-393, Feb. 2001.
28. H. Ozaktas and O. Aytür, "Fractional Fourier domains," Signal Process., vol. 46, pp. 119-124, 1995.
29. S. Shinde and V. M. Gadre, "An uncertainty principle for real signals in the fractional Fourier transform domain," IEEE Trans. Signal Processing, vol. 49, pp. 2545-2548, Nov. 2001.
30. A. Bultan, "A Four-Parameter Atomic Decomposition and the Related Time-Frequency Distribution," Ph.D. dissertation, Dept. Electr. Electron. Eng., Middle East Tech. Univ., Ankara, Turkey, 1995.
31. ____, "A four-parameter atomic decomposition of chirplets," IEEE Trans. Signal Processing, vol. 47, pp. 731-745, Mar. 1999.
32. S. Pei and M. Yeh, "A novel method for discrete fractional Fourier transform computation," in Proc. IEEE Int. Symp. Circuits Syst., vol. 2, 2001, pp. 585-588.
33. O. Akay and G. F. Boudreaux-Bartels, "Fractional autocorrelation and its application to detection and estimation of linear fm signals," in Proc. IEEE-SP Int. Symp. Time-Freq. Time-Scale Anal., 1998, pp. 213-216.
34. T. Alieva and M. J. Bastiaans, "On fractional Fourier transform moments," IEEE Signal Processing Lett., vol. 7, pp. 320-323, Nov. 2000.
35. L. Stankovic, T. Alieva, and M. Bastiaans, "Wigner distribution weighted in the fractional Fourier domains," in Proc. ProRISC, Veldhoven, The Netherlands, Nov. 2001, pp. 635-640.
36. F. Zhang, Y. Q. Chen, and G. Bi, "Adaptive harmonic fractional Fourier transform," IEEE Signal Processing Lett., vol. 6, pp. 281-283, Nov. 1999.
37. A. K. Özdemir, L. Durak, and O. Arikan, "High resolution time-frequency analysis by fractional domain warping," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., May 2001.
38. A. J. E. M. Janssen, "On the locus and spread of pseudo-density functions in the time-frequency plane," Philips J. Res., vol. 37, pp. 79-110, 1982.