The Structure of Vector Radix Fast Fourier Transforms

IEEE Transactions on Acoustics, Speech, and Signal Processing

Volumn 37, Issue 9, 1989, Pages 1415-1424

  Wu, Hong Ren ^a   Paoloni, Frank John ^a  

^a UNIVERSITY OF WOLLONGONG   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER METATHEORY--COMPUTABILITY AND DECIDABILITY; COMPUTER PROGRAMMING--ALGORITHMS; SIGNAL PROCESSING--DIGITAL TECHNIQUES;

COMPUTATIONAL COMPLEXITY; LOGIC DIAGRAMS; MATRIX REPRESENTATION; VECTOR RADIX FFT ALGORITHMS;

MATHEMATICAL TRANSFORMATIONS;

EID: 0024738552     PISSN: 00963518     EISSN: None     Source Type: Journal    
DOI: 10.1109/29.31295     Document Type: Article

References (21)

1. J.W. Cooley and J.W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput., vol. 19, no. 90, pp. 296–301, 1965.
2. M.T. Heideman, D.H. Johnson, and C.S. Burrus, “Gauss and the history of the fast Fourier transform,” IEEE ASSP Mag., pp. 14–21, 1984.
3. E.O. Brigham, The Fast Fourier Transform. Englewood Cliffs, NJ: Prentice-Hall, 1974.
4. C.S. Burrus and T.W. Parks, Discrete Fourier Transform)'Fast Fourier Transform and Convolution Algorithms. New York: Wiley-In-terscience, 1985.
5. P. Duhamel, “Implementation of ‘split-radix’ FFT algorithms for complex, real, and real-symmetric data,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 285–295, Apr. 1986.
6. R.E. Blahut, Fast Algorithms for Digital Signal Processing. Reading, MA: Addison-Wesley, 1985.
7. G.E. Rivard, “Direct fast Fourier transform of Divariate functions,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-25, pp. 250–252, June 1977.
8. D.B. Harris, J.H. McClellan, D.S.K. Chan, and H.W. Schuessler, “Vector radix fast Fourier transform,” in 1977 IEEE Int. Conf. Accoust., Speech, Signal Processing Rec., May 1977, pp. 548–551.
9. R.M. Mersereau and T.C. Speake, “A unified treatment of Cooley-Tukey algorithms for the evaluation of the multidimensional DFT,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-29, pp. 1011–1018, Oct. 1981.
10. L. Auslander, E. Feig, and S. Winograd, “New algorithms for the multidimensional discrete Fourier transform,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-31, pp. 388–403, Apr. 1983.
11. D.E. Dudgeon and R.M. Mersereau, Multidimensional Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1984.
12. S.-C. Pei and J.-L. Wu, “Split vector radix 2-D fast Fourier transform,” IEEE Trans. Circuits Syst., vol. CAS-34, pp. 978–980, Aug. 1987.
13. R.W. Linderman, P.M. Chau, W.H. Ku, and P.P. Reusens, “CUSP: A 2-μm CMOS digital signal processor,” IEEE J. SolidState Circuits, vol. SC-20, pp. 761–769, June 1985.
14. J.D. O'Sullivan, D.R. Brown, K.T. Hua, and C.E. Jacka, “A VLSI chip for fast Fourier transforms,” in Dig. Papers, IREECON′87, 1987, p. 142.
15. I. Gertner and M. Shamash, “VLSI architectures for multidimensional Fourier transform processing,” IEEE Trans. Comput., vol. C-36, pp. 1265–1274, Nov. 1987.
16. H.W. Johnson and C.S. Burrus, “On the structure of efficient DFT algorithms,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-33, pp. 248–254, Feb. 1985.
17. A. Guessoum and M. Mersereau, “Fast algorithms for the multidimensional discrete Fourier transform,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 937–943, Aug. 1986.
18. M.A. Richard, “On the efficient implementation of the split-radix FFT,” in Proc. ICASSP-86, 1986, pp. 1801–1804.
19. H.R. Wu and F.J. Paoloni, “The structure of vector radix multidimensional fast Fourier transforms,” Dep. Elec. Comput. Eng., Univ. Wollongong, Tech. Rep. 1, 1986.
20. P.R. Halmos, Finite-Dimensional Vector Spaces. New York: Van Nostrand, 1958.
21. B. Arambepola, “Fast computation of multidimensional discrete Fourier transforms,” IEE Proc, vol. 127, Pt. F., no. 1, Feb. 1980.