A Comparative Review of Real and Complex Fourier-Related Transforms

Proceedings of the IEEE

Volumn 82, Issue 3, 1994, Pages 429-447

  Ersoy, Okan K ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; FOURIER TRANSFORMS; IMAGE PROCESSING; INTEGRAL EQUATIONS; LAPLACE TRANSFORMS; Z TRANSFORMS;

FOURIER SERIES;

SIGNAL PROCESSING;

EID: 0028393318     PISSN: 00189219     EISSN: 15582256     Source Type: Journal    
DOI: 10.1109/5.272147     Document Type: Article

References (24)

1. B. Davis, Integral Transforms and Their Applications. New York: Springer-Verlag, 1978.
2. R. N. Bracewell, The Hartley Transform. New York: Oxford Univ. Press, 1986.
3. O. K. Ersoy, Fourier-Related Transforms and Applications. Englewood Cliffs, NJ: Prentice Hall, in press.
4. R. V. Churchill and J. W. Brown, Fourier Series and Boundary Value Problems. New York: McGraw-Hill, 1978.
5. S. C. Lanczos, Discourse on Fourier Series. New York: Hafner Pub., 1966.
6. O. K. Ersoy, “Real discrete Fourier transform,” IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-33, no. 4, pp. 880–882, Aug. 1985.
7. O. K. Ersoy and C. H. Chen, “Transform coding of images with reduced complexity,” Comput. Vision, Graph. Image Process., vol. 42, pp. 19–41, Jan. 1988.
8. N.C. Hu and O. K. Ersoy, “Fast computation of real discrete Fourier transform for any number of data points,” IEEE Trans. Circuits Syst., vol. 38, no. 11, pp. 1280–1292, Nov. 1991.
9. O.K. Ersoy and A. Nouira, “Image coding with the discrete cosine-III transform,” IEEE J. Selected Areas Commun., vol. 10, no. 5, pp. 884–891, June 1992.
10. N. Ahmed, T. Natarajan, and K. R. Rao, “Discrete cosine transform,” IEEE Trans. Comput., vol. C-23, pp. 90–93, Jan. 1974.
11. O. K. Ersoy and N-C. Hu, “Fast algorithms for the real discrete Fourier transforms,” in IEEE ICASSP Conf. Proc. (New York, Apr. 1988), pp. 1902–1905.
12. A. K. Jain, “A sinusoidal family of unitary transforms,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-1, pp. 356–365, Oct. 1979.
13. D. F. Elliott and K. R. Rao, Fast Transforms. New York: Academic Press, 1982.
14. A Papoulis, Probability, Random Variables and Stochastic Processes. New York: McGraw-Hill, 1984.
15. J. Pearl, “On coding and filtering stationary signals by discrete Fourier transforms,” IEEE Trans. Informat. Theory, vol. IT-19, pp. 229–232, Mar. 1973.
16. H. J. Nussbaumer, Fast Fourier Transform and Convolution Algorithms. New York: Springer-Verlag, 1982.
17. L. R. Rabiner and R. W. Schafer, Digital Processing of Speech Signals. Englewood Cliffs, NJ: Prentice-Hall, 1979.
18. D. Gabor, “Theory of Communication,” Proc. Inst. Elec. Eng., vol. 93, pp. 429–457, 1946.
19. J. W. Cooley and J. W. Tukey, “An algorithm for the machine computation of complex Fourier series,” Math Comput., vol. 19, no. 90, pp. 297–301, 1965.
20. H. F. Weinberger, A First Course in Partial Differential Equations. Blaisdell Publishing Co., 1965.
21. A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1989.
22. N.C. Hu, “Fast and parallel algorithms for signal transforms and convolutions,” Ph.D. dissertation, Purdue Univ., W. Lafayette, IN, May 1989.
23. R. E. Crochiere and L. R. Rabiner, Multirate Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1983.
24. O. K. Ersoy, and C. H. Chen, “New approaches to real-time transform coding and reconstruction of signals and images,” in Annu. Allerton Conf. on Communications, Control and Computing (Univ. of Illinois at Urbana-Champagne, Oct. 1986), pp. 214–233.