A new discrete fractional fourier transform based on constrained eigendecomposition of dft matrix by largrange multiplier method

IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing

Volumn 46, Issue 9, 1999, Pages 1240-1245

  Pel, Soo Chang ^a   Tseng, Chien Cheng ^a   Yeh, Min Hung ^a  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

Discrete fourier transform; Discrete fractional fourier transform

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; LAGRANGE MULTIPLIERS; MATRIX ALGEBRA; OPTIMIZATION; SIGNAL PROCESSING; SIGNAL THEORY;

DISCRETE FOURIER TRANSFORM MATRIX; DISCRETE FRACTIONAL FOURIER TRANSFORM; EIGENDECOMPOSITION; HERMITE GAUSS FUNCTIONS;

FOURIER TRANSFORMS;

EID: 0033189498     PISSN: 10577130     EISSN: None     Source Type: Journal    
DOI: 10.1109/82.793715     Document Type: Article

References (15)

1. V. Namias, "The fractional order Fourier transform and its application to quantum mechanics," J. Inst. Math. Applicat, vol. 25, pp. 241-265, 1980.
2. H. M. Ozaktas and B. Barshan, "Convolution, filtering, and multiplexing in fractional Fourier domains and their relationship to chirp and wavelet transform," J. Opt. Soc. Amer. A, vol. 11, pp. 547-559, 1994.
3. A. W. Lohmann, "Image rotation, Wigner rotation, and the fractional Fourier domain," J. Opt. Soc. Amer. A, vol. 10, pp. 2181-2186, 1993.
4. D. Mendlovic, Z. Zalevsky, R. G. Dorsch, Y. Bitran, A. W. Lohmann, and H. Ozaktas, "New signal representation based on the fractional Fourier transform: Definitions," J. Opt. Soc. Amer. A, vol. 11, pp. 2424-2431, 1995.
5. D. Dragoman, "Fractional Wigner distribution function," J. Opt. Soc. Amer. A, vol. 13, pp. 474-78, 1996.
6. S. Y. Lee and H. H. Szu, "Fractional Fourier transforms, wavelet transform, and adaptive neural network," Opt. Eng., vol. 33, pp. 2326-2330, 1994.
7. R. G. Dorsch, A. W. Lohmann, Y. Bitran, and D. Mendlovic, "Chirp filtering in the fractional Fourier domain," Appl. Opt., vol. 33, pp. 7599-7602, 1994.
8. L. B. Almeida, "The fractional Fourier transform and time frequency representation," IEEE Trans. Signal Processing, vol. 42, pp. 3084-3091, Nov. 1994.
9. H. M. Ozaktas and O. Aytar, "Fractional Fourier domains," Signal Processing, vol. 46, pp. 119-124, 1995.
10. H. M. Ozaktas, N. Erkaya, and A. Kutay, "Effect of fractional Fourier transform on time-frequency distributions belonging to the Cohen class," IEEE Signal Processing Lett., vol. 3, pp. 40-41, Feb. 1996.
11. X. G. Xia, "On bandlimited signals with fractional Fourier transform," IEEE Signal Processing Lett., vol. 3, pp. 72-74, Mar. 1996.
12. M. A. Kutay, H. M. Ozaktas, L. Onural, and O. Arikan, "Optimal filtering in fractional Fourier domains," in Proc. ICASSP, 1995, pp. 937-940.
13. H. M. Ozaktas, O. Arikan, A. Kutay, and G. Bozdagi, "Digital computation of the fractional Fourier transform," IEEE Trans. Signal Processing, vol. 44, pp. 2141-2150, Sept. 1996.
14. B. Santhanam and J. H. McClellan, "The DRFT-A rotation in time frequency space," in Proc. ICASSP, 1995, pp. 921-924.
15. J. H. McClellan and T. W. Parks, "Eigenvalue and eigenvector decomposition of the discrete Fourier transform," IEEE Trans. Audio Electroacoust., vol. AE-20, pp. 66-74, Mar. 1972.