Split-radix algorithms for arbitrary order of polynomial time frequency transforms

IEEE Transactions on Signal Processing

Volumn 55, Issue 1, 2007, Pages 134-141

  Bi, Guoan ^a   Wei, Yongmei ^a,b  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^b Genista Corporation   (Singapore)

Author keywords

Fourier transform; Polynomial time frequency transform; Polynomial phase signals (PPSs); Split radix algorithm

Indexed keywords

COMPUTATIONAL COMPLEXITY; FAST FOURIER TRANSFORMS; MAXIMUM LIKELIHOOD ESTIMATION; POLYNOMIALS;

DATA SEQUENCE; POLYNOMIAL TIME FREQUENCY TRANSFORM; POLYNOMIAL-PHASE SIGNALS; SPLIT-RADIX ALGORITHM;

SIGNAL DETECTION;

EID: 33947393586     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2006.882079     Document Type: Article

References (22)

1. O. Besson, M. Ghogho, and A. Swami, "Parameter estimation for random amplitude chirp signals," IEEE Trans. Signal Process., vol. 47, no. 12, pp. 3208-3219, Dec. 1999.
2. M. Z. Ikram and G. T. Zhou, "Estimation of multicomponent polynomial phase signals of mixed orders," Signal Process., vol. 81, no. 11, pp. 2293-2308, 2001.
3. S. Peleg and B. Porat, "Estimation and classification of polynomial-phase signals," IEEE Trans. Inf. Theory, vol. 37, no. 2, pp. 422-430, 1991.
4. S. Barbarossa, "Detection and imaging of moving objects with synthetic aperture radar - Part 1: Optimal detection and parameter estimation theory," Proc. Inst. Elect. Eng. - F, vol. 139, no. 1, pp. 79-88. 1992.
5. M. Martone, " A multicarrier system based on the fractional fourier transform for time-frequency selective channels," IEEE Trans. Signal Process., vol. 49, no. 6, pp. 1011-1020, Jun. 2001.
6. M. Z. Ikram, A. Belouchrani, D. Gesbert, and K. Abed-Meraim, "Parametric estimation and suppression of non-stationary interference in ds-spread spectrum communications," in Proc. 32nd Asilomar Conf. Signals, Syst. Comput., 1998, pp. 1401-1405.
7. S. Barbarossa, A. Scaglione, and G. B. Giaanakis, "Product high-order ambiguity function for multicomponent polynomial-phase signal modeling," IEEE Trans. Signal Process., vol. 46, no. 3, pp. 691-708, Mar. 1998.
8. T. J. Abatzoglou, "Fast maximum likelihood joint estimation of frequency frequency rate," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., 1986, pp. 1409-1412.
9. P. O'shea, "Fast parameter estimation algorithms for linear fm signals of frequency and frequency rate," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., 1994, pp. 17-20.
10. M. Z. Ikram, K. Abed-Meraim, and Y. Hua, "Fast quadratic phase transform for estimating the parameters of multicomponent chirp signals," Digit. Signal Process., vol. 7, no. 2, pp. 127-135, 1997.
11. S. Peleg and B. Friedlander, "Multicomponent signal analysis using the polynomial-phase transform," IEEE Trans. Aerosp. Electron. Syst., vol. 32, no. 1, pp. 378-386, 1996.
12. X. G. Xia, "Discrete chirp-Fourier transform and its application to chirp rate estimation," IEEE Trans. Signal Process., vol. 48, no. 11, pp. 3122-3133, Nov. 2000.
13. B. Barkat and B. Boashash, "Instantaneous frequency estimation of polynomial FM signal using the peak of the PWVD: Statistical performance in the presence of additive Gaussian noise," IEEE Trans. Signal Process., vol. 47, no. 9, pp. 2480-2490, Sep. 1999.
14. G. Bi and Y. Wei, "Fast computation for third-order polynomial time frequency transforms," Electron. Lett., vol. 40, no. 5, pp. 349-351, 2005.
15. M. Soumekh, "Reconnaissance with ultra wideband UHF synthetic aperture radar," IEEE Signal Process. Mag., vol. 12, no. 4, pp. 21-40, 1995.
16. +(m)." IEEE Trans. Circuits Syst. II - Analog Digit. Signal Process., vol. 45, no. 6, pp. 685-690, 1998.
17. G. Bi, Gang, Li, and K. K. Ma et al., "On the computation of two-dimensional DCT," IEEE Trans. Signal Process., vol. 48, no. 4, pp. 1171-1183, Apr. 2000.
18. L. Cohen, Time-Frequency Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1995.
19. S. Barbarossa and V. Petrone, "Analysis of polynomial-phase signals by the integrated generalized ambiguity function," IEEE Trans. Signal Process., vol. 45, no. 2, pp. 316-327, Feb. 1997.
20. S. Peleg and B. Porat, "The Cramer-Rao lower bound for signals with constant amplitude and polynomial phase," IEEE Trans. Signal Process., vol. 39, no. 3, pp. 749-752, Mar. 1991.
21. B. Porat and B. Friedlander, "Asymptotic statistical analysis of the high-order ambiguity function for parameter estimation of polynomial-phase signals," IEEE Trans. Inf. Theory, vol. 42, no. 3, pp. 995-1001, 1996.
22. S. M. Kay, Fundamentals of Statistical Signal Processing-Detection Theory. Englewood Cliffs, NJ: Prentice-Hall, 1993.