hello, i'm designing a fft processor.Can any body please give me details of various architectures of fft processors.And topics on which i should concentrate more. with best regards, truely pavan This message was sent using the Comp.DSP web interface on www.DSPRelated.com

# FFT processor architecture

Started by ●August 20, 2005

Reply by ●August 20, 20052005-08-20

You should concentrate on the summation of areas that model the integration aspect of the Fourier Transform, and NOT on the summation of impulses of real range which are actually zero-integrable and therefore yield a zero result, contrary to the assertions by those who would be the experts and authors in the field of DSP. pabbu wrote:> hello, > i'm designing a fft processor.Can any body please give me details of > various architectures of fft processors.And topics on which i should > concentrate more. > with best regards, > truely > pavan > > > > This message was sent using the Comp.DSP web interface on > www.DSPRelated.com

Reply by ●August 20, 20052005-08-20

"Polymath" <aiyr.r.bean@lycos.co.uk> wrote in message news:1124544424.743620.206010@g43g2000cwa.googlegroups.com...> You should concentrate on the summation of areas that > model > the integration aspect of the Fourier Transform, and NOT > on the summation of impulses of real range which are > actually > zero-integrable and therefore yield a zero result, > contrary > to the assertions by those who would be the experts and > authors in the field of DSP. >Been hittin' a little hard on that Purple Haze, haven't you, Poly? If there was a Pulitzer prize for perfect gibberish, I think you'd have a lock on it.

Reply by ●August 20, 20052005-08-20

"Polymath" <aiyr.r.bean@lycos.co.uk> wrote in message news:1124544424.743620.206010@g43g2000cwa.googlegroups.com... Hi Polymath...does that mean you studied math at a Poly? Shytot

Reply by ●August 20, 20052005-08-20

Grab any good Discrete Time Signal Processing book, Oppenheim has a classic one, check out radix implementations. Depending on what you are trying to due, what your designs constraints are there are hundreds of ways to do it. There is the FFTW algorithm that is widely used, and plenty of variations, google search usually does wonders for this type of work. What is your platform you are using for your fft processor, what speeds do you need to process data at, etc?

Reply by ●September 1, 20052005-09-01

On Sat, 20 Aug 2005 08:06:08 -0500, "pabbu" <pavan2000ind@rediffmail.com> wrote:> hello, > i'm designing a fft processor.Can any body please give me details of >various architectures of fft processors.And topics on which i should >concentrate more. > with best regards, > truely >pavanHi, Here ya' go. [-Rick-] ---------- References [1] M. T. Heideman, D. H. Johnson, and C. S. Burrus, "Gauss and the history of the FFT," IEEE Acoustics, Speech, and Signal Processing Magazine, vol. 1, pp. 14-21, October 1984. also in IEEE Press FFT Reprints, by P. Duhamel, 1995. [2] H. V. Sorensen, C. S. Burrus, and M. T. Heideman, Fast Fourier Transform Database. Boston: PWS Publishing, 1995. Update of Technical Report TR-8402. [3] L. R. Rabiner and C. M. Rader, eds., Digital Signal Processing, selected reprints. New York: IEEE Press, 1972. [4] DSP Committee, ed., Digital Signal Processing II, selected reprints. New York: IEEE Press, 1979. [5] DSP Committee, ed., Programs for Digital Signal Processing. New York: IEEE Press, 1979. [6] P. Duhamel, ed., Papers on the Fast Fourier Transform. New York: IEEE Press, to appear in 1995. [7] J. H. McClellan and C. M. Rader, Number Theory in Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, Inc., 1979. [8] H. J. Nussbaumer, Fast Fourier Transform and Convolution Algorithms. Heidelberg, Germany: Springer-Verlag, second ed., 1981, 1982. [9] R. E. Blahut, Fast Algorithms for Digital Signal Processing. Reading, MA: Addison-Wesley, Inc., 1984. [10] M. T. Heideman, Multiplicative Complexity, Convolution, and the DFT. Springer-Verlag, 1988. [11] R. Tolimieri, M. An, and C. Lu, Algorithms for Discrete Fourier Transform and Convolution. New York: Springer-Verlag, 1989. [12] D. G. Myers, Digital Signal Processing, Efficient Convolution and Fourier Transform Techniques. Sydney, Australia: Prentice-Hall, 1990. [13] R. E. Blahut, Algebraic Methods for Signal Processing and Communications Coding. New York: Springer-Verlag, 1992. [14] W. L. Briggs and V. E. Henson, The DFT: An Owner's Manual for the Discrete Fourier Transform. Philadelphia: SIAM, 1995. [15] W. W. Smith and J. M. Smith, Handbook of Real-Time Fast Fourier Transforms. New York: IEEE Press, 1995. [16] C. S. Burrus and T. W. Parks, DFT/FFT and Convolution Algorithms. New York: John Wiley & Sons, 1985. [17] J. S. Lim and A. V. Oppenheim, Advanced Topics in Signal Processing, ch. 4. Prentice-Hall, 1988. [18] J. W. Cooley, "How the FFT gained acceptance," IEEE Signal Processing Magazine, vol. 9, pp. 10-13, January 1992. Also presented at the ACM Conference on the History of Scientific and Numerical Computation, Princeton, NJ, May 1987 and published in: A History of Scientific Computing, edited by S. G. Nash, Addison-Wesley, 1990, pp. 133-140. [19] P. Duhamel and M. Vetterli, "Fast Fourier transforms: a tutorial review and a state of the art," Signal Processing, vol. 19, pp. 259-299, April 1990. [20] J. W. Cooley, "The structure of FFT algorithms," April 1990. Notes for a Tutorial at IEEE ICASSP-90. [21] S. Winograd, "On computing the discrete Fourier transform," Mathematics of Computation, vol. 32, pp. 175-199, January 1978. [22] S. Winograd, "On the multiplicative complexity of the discrete Fourier transform," Advances in Mathematics, vol. 32, pp. 83-117, May 1979. also in[7]. [23] S. Winograd, Arithmetic Complexity of Computation. SIAM CBMS-NSF Series, No. 33, Philadelphia: SIAM, 1980. [24] J. W. Cooley and J. W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Math. Computat., vol. 19, pp. 297-301, 1965. [25] R. Yavne, "An economical method for calculating the discrete Fourier transform," in Proceedings of the Fall Joint Computer Conference, pp. 115-125, 1968. [26] P. Duhamel and H. Hollmann, "Split radix FFT algorithm," Electronic Letters, vol. 20, pp. 14-16, January 5 1984. [27] P. Duhamel, "Implementation of `split-radix' FFT algorithms for complex, real, and real-symmetric data," IEEE Trans. on ASSP, vol. 34, pp. 285-295, April 1986. A shorter version appeared in the ICASSP-85 Proceedings, p. 20.6, March 1985. [28] J. B. Martens, "Recursive cyclotomic factorization - a new algorithm for calculating the discrete Fourier transform," IEEE Trans. on ASSP, vol. 32, pp. 750-762, August 1984. [29] M. Vetterli and H. J. Nussbaumer, "Simple FFT and DCT algorithms with reduced number of operations," Signal Processing, vol. 6, pp. 267-278, August 1984. [30] M. Vetterli and P. Duhamel, "Split-radix algorithms for length - pm DFT's," IEEE Trans. on ASSP, vol. 37, pp. 57-64, January 1989. Also, ICASSP-88 Proceedings, pp. 1415-1418, April 1988. [31] R. Stasinski, "The techniques of the generalized fast Fourier transform algorithm," IEEE Transactions on Signal Processing, vol. 39, pp. 1058-1069, May 1991. [32] H. V. Sorensen, M. T. Heideman, and C. S. Burrus, "On calculating the split-radix FFT," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 34, pp. 152-156, February 1986. [33] A. Saidi, "Decimation-in-time-frequency FFT algorithm," in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, (IEEE ICASSP-94, Adelaide, Australia), pp. III:453-456, April 19-22 1994. [34] M. T. Heideman and C. S. Burrus, "On the number of multiplications necessary to compute a length-2n DFT," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 34, pp. 91-95, February 1986. [35] J. K. Beard, "An in-place, self-reordering FFT," in Proceedings of the ICASSP-78, (Tulsa), pp. 632- 633, April 1978. [36] H. W. Johnson and C. S. Burrus, "An in-place, in-order radix-2 FFT," in ICASSP-84 Proceedings, p. 28A.2, March 1984. [37] C. Temperton, "Self-sorting in-place fast Fourier transforms," SIAM Journal of Sci. Statist. Comput., vol. 12, no. 4, pp. 808-823, 1991. [38] C. S. Burrus, "Unscrambling for fast DFT algorithms," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 36, pp. 1086-1087, July 1988. [39] P. R"osel, "Timing of some bit reversal algorithms," Signal Processing, vol. 18, pp. 425-433, December 1989. [40] J. Jeong and W. J. Williams, "A fast recursive bit-reversal algorithm," in Proceedings of the ICASSP- 90, (Albuquerque, NM), pp. 1511-1514, April 1990. [41] D. M. W. Evans, "A second improved digit-reversal permutation algorithm for fast transforms," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 37, pp. 1288-1291, August 1989. [42] J. J. Rodriguez, "An improved FFT digit-reversal algorithm," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 37, pp. 1298-1300, August 1989. [43] J. S. Walker, "A new bit reversal algorithm," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 38, pp. 1472-1473, August 1990. [44] A. A. Yong, "A better FFT bit-reversal algorithm without tables," IEEE Transactions on Signal Processing, vol. 39, pp. 2365-2367, October 1991. [45] D. Sundararajan, M. O. Ahamad, and M. N. S. Swamy, "A fast FFT bit-reversal algorithm," IEEE Transactions on Circuits and Systems, II, vol. 41, pp. 701-703, October 1994. [46] J. M. Rius and R. De Porrata-Doria, "New FFT bit-reversal algorithm," IEEE Transactions on Signal Processing, vol. 43, pp. 991-994, April 1995. [47] L. R. Morris, Digital Signal Processing Software. Toronto, Canada: DSPSW, Inc., 1982, 1983. [48] R. Meyer and K. Schwarz, "FFT implementation on DSP-chips," Sept. 18 1990. preprint. [49] D. P. Kolba and T. W. Parks, "A prime factor FFT algorithm using high speed convolution," IEEE Trans. on ASSP, vol. 25, pp. 281-294, August 1977. also in[7]. [50] C. S. Burrus and P. W. Eschenbacher, "An in-place, in-order prime factor FFT algorithm," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 29, pp. 806-817, August 1981. Reprinted in it DSP Software, by L.R. Morris, 1983 and IEEE Press FFT Reprints, by P. Duhamel, 1995. [51] C. Temperton, "A self-sorting in-place prime factor real/half-complex FFT algorithm," Journal of Computational Physics, vol. 75, pp. 199-216, 1988. [52] C. Temperton, "Nesting strategies for prime factor FFT algorithms," Journal of Computational Physics, vol. 82, pp. 247-268, June 1989. [53] C. Temperton, "A generalized prime factor FFT algorithm for any n = 2p 3q5r," SIAM Journal of Sci. Stat. Comp., 1992. to appear. [54] R. Stasinski, "Prime factor DFT algorithms for new small-N DFT modules," IEE Proceedings, Part G, vol. 134, no. 3, pp. 117-126, 1987. [55] H. W. Johnson and C. S. Burrus, "The design of optimal DFT algorithms using dynamic programming," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 31, pp. 378-387, April 1983. [56] H. W. Johnson and C. S. Burrus, "On the structure of efficient DFT algorithms," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 33, pp. 248-254, February 1985. [57] H. W. Johnson and C. S. Burrus, "Large DFT modules: N = 11, 13, 17, 19, and 25," Tech. Rep. 8105, Department of Electrical Engineering, Rice University, Houston, TX 77251-1892, 1981. [58] C. Temperton, "A new set of minimum-add small-n rotated DFT modules," Journal of Computational Physics, vol. 75, pp. 190-198, 1988. [59] C. Lu, J. W. Cooley, and R. Tolimieri, "FFT algorithms for prime transform sizes and their implementations on VAX, IBM3090VF, and IBM RS/6000," IEEE Transactions on Signal Processing, vol. 41, pp. 638-648, February 1993. [60] S. Chu and C. S. Burrus, "A prime factor FFT algorithm using distributed arithmetic," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 30, pp. 217-227, April 1982. [61] K. T. Chen, "A new record: the largest known prime number," IEEE Spectrum, vol. 27, p. 47, February 1990. [62] H. V. Sorensen, D. L. Jones, C. S. Burrus, and M. T. Heideman, "On computing the discrete Hartley transform," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 33, pp. 1231-1238, October 1985. [63] R. N. Bracewell, The Hartley Transform. Oxford Press, 1986. [64] F. M. Wang and P. Yip, "Fast prime factor decomposition algorithms for a family of discrete trigonometric transforms," Circuits, Systems, and Signal Processing, vol. 8, no. 4, pp. 401-419, 1989. [65] K. R. Rao and P. Yip, Discrete Cosine Transform: Algorithms, Advantages, Applications. San Diego, CA: Academic Press, 1990. [66] H. V. Sorensen, D. L. Jones, M. T. Heideman, and C. S. Burrus, "Real valued fast Fourier transform algorithms," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 35, pp. 849-863, June 1987. also in IEEE Press FFT Reprints, by P. Duhamel, 1995. [67] P. Duhamel and M. Vetterli, "Improved Fourier and Hartley transfrom algorithms, application to cyclic convolution of real data," IEEE Trans. on ASSP, vol. 35, pp. 818-824, June 1987. [68] M. Popovic and D. Sevic, "A new look at the comparison of the fast Hartley and Fourier transforms," IEEE Transactions on Signal Processing, vol. 42, pp. 2178-2182, August 1994. [69] P. R. Uniyal, "Transforming real-valued sequences: fast Fourier versus fast Hartley transform algorithms," IEEE Transactions on Signal Processing, vol. 42, pp. 3249-3254, November 1994. [70] G. Bruun, "Z-transform DFT filters and FFTs," IEEE Transactions on ASSP, vol. 26, pp. 56-63, February 1978. [71] R. Storn, "On the Bruun algorithm and its inverse," Frequenz, vol. 46, pp. 110-116, 1992. a German journal. [72] C. M. Rader and N. M. Brenner, "A new principle for fast Fourier transformation," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-24, pp. 264-266, June 1976. [73] K. M. Cho and G. C. Temes, "Real-factor FFT algorithms," in Proceedings of IEEE ICASSP-78, (Tulsa, OK), pp. 634-637, April 1978. [74] P. Duhamel, B. Piron, and J. M. Etcheto, "On computing the inverse DFT," IEEE Transactions on ASSP, vol. 36, pp. 285-286, February 1978. [75] R. Singleton, "An algorithm for computing the mixed radix fast Fourier transform," IEEE Transactions on Audio and Electroacoustics, vol. AU-17, pp. 93-103, June 1969. [76] J. A. Glassman, "A generalization of the fast Fourier transform," IEEE Transactions on Computers, vol. C-19, pp. 105-116, Feburary 1970. [77] W. E. Ferguson, Jr., "A simple derivation of Glassman general-n fast Fourier transform," Comput. and Math. with Appls., vol. 8, no. 6, pp. 401-411, 1982. Also, in Report AD-A083811, NTIS, Dec. 1979. [78] L. Rabiner, R. Schafer, and C. Rader, "The chirp z-transform algorithm," IEEE Transactions on Audio Electroacoustics, vol. AU-17, pp. 86-92, June 1969. [79] G. A. Sitton, "The QFT algorithm," unpublished paper, 1985. [80] H. Guo, G. A. Sitton, and C. S. Burrus, "The quick discrete Fourier transform," in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, (IEEE ICASSP-94, Adelaide, Australia), pp. III:445-448, April 19-22 1994. [81] H. Guo, G. A. Sitton, and C. S. Burrus, "The quick Fourier transform, an FFT based on symmetries," IEEE Transactions on Signal Processing, submitted Oct. 1994. [82] I. W. Selesnick and C. S. Burrus, "Automating the design of prime length FFT programs," in Proceedings of the IEEE International Symposium on Circuits and Systems, (ISCAS-92, San Diego, CA), pp. 133-136, May 1992. [83] I. W. Selesnick and C. S. Burrus, "Multidimensional mapping techniques for convolution," in Proceedings of the IEEE International Conference on Signal Processing, (IEEE ICASSP-93, Minneapolis), pp. III-288-291, April 1993. [84] I. W. Selesnick and C. S. Burrus, "Automatic generation of prime length FFT programs," IEEE Transactions on Signal Processing, to appear. 1995. [85] I. W. Selesnick and C. S. Burrus, "Extending Winograd's small convolution algorithm to longer lengths," in Proceedings of the IEEE International Symposium on Circuits and Systems, (IEEE ISCAS- 94, London), pp. 2.449-452, June 30 1994. [86] W. K. Hocking, "Performing Fourier transforms on extremely long data streams," Computers in Physics, vol. 3, pp. 59-65, January 1989. [87] R. Stasinski, "Extending sizes of effective convolution algorithms," Electronics Letters, vol. 26, no. 19, pp. 1602-1604, 1990. [88] R. C. Agarwal and J. W. Cooley, "New algorithms for digital convolution," IEEE Trans. on ASSP, vol. 25, pp. 392-410, October 1977. [89] I. Pitas and C. S. Burrus, "Time and error analysis of digital convolution by rectangular transforms," Signal Processing, vol. 5, pp. 153-162, March 1983. [90] R. Meyer, R. Reng, and K. Schwarz, "Convolution algorithms on DSP processors," in Proceedings of the ICASSP-91, (Toronto, Canada), pp. 2193-2196, May 1991. [91] R. C. Agarwal and C. S. Burrus, "Number theoretic transforms to implement fast digital convolution," Proceedings of the IEEE, vol. 63, pp. 550-560, April 1975. also in IEEE Press DSP Reprints II, 1979. [92] H. V. Sorensen and C. S. Burrus, "Efficient computation of the short-time FFT," in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, (New York), pp. 1894- 1897, April 1988. [93] H. V. Sorensen, C. S. Burrus, and D. L. Jones, "A new efficient algorithm for computing a few DFT points," in Proceedings of the IEEE International Symposium on Circuits and Systems, (Espoo, Finland), pp. 1915-1918, June 1988. [94] C. Roche, "A split-radix partial input/output fast Fourier transform algorithm," IEEE Transactions on Signal Processing, vol. 40, pp. 1273-1276, May 1992. [95] H. V. Sorensen and C. S. Burrus, "Efficient computation of the DFT with only a subset of input or output points," IEEE Transactions on Signal Processing, vol. 41, pp. 1184-1200, March 1993. [96] R. Meyer and K. Schwarz, "FFT implementation on DSP-chips _ theory and practice," in Proceedings of the ICASSP-90, (Albuquerque, NM), pp. 1503-1506, April 1990. [97] H. V. Sorensen, C. A. Katz, and C. S. Burrus, "Efficient FFT algorithms for DSP processors using tensor product decomposition," in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, (Albuquerque, NM), pp. 1507-1510, April 1990. [98] J. Johnson, R. W. Johnson, D. Rodriguez, and R. Tolimieri, "A methodology for designing, modifying, and implementing Fourier transform algorithms on various architectures," Circuits, Systems and Signal Processing, vol. 9, no. 4, pp. 449-500, 1990. [99] C. Van Loan, Matrix Frameworks for the Fast Fourier Transform. Philadelphia, PA: SIAM, 1992. [100] R. Tolimieri, M. An, and C. Lu, Mathematics of Multidimensional Fourier Transform Algorithms. New York: Springer-Verlag, 1993.

Reply by ●September 2, 20052005-09-02

Rick Lyons wrote:> Hi, > > Here ya' go. > > [-Rick-] > ---------- > > References[100 references snipped] There is just something special with the short, succinct and informal style of posting here at comp.dsp... ;) How much time did you spend on organizing that list? Rune

Reply by ●September 2, 20052005-09-02

Rune Allnor wrote:> Rick Lyons wrote: > >>Hi, >> >> Here ya' go. >> >>[-Rick-] >>---------- >> >>References > > > [100 references snipped] > > There is just something special with the short, succinct and > informal style of posting here at comp.dsp... ;) > > How much time did you spend on organizing that list? > > Rune >Found it. http://www.jjj.de/fft/fftnote.txt

Reply by ●September 5, 20052005-09-05

"Rune Allnor" <allnor@tele.ntnu.no> wrote in message news:1125654544.637284.322910@g49g2000cwa.googlegroups.com...> > Rick Lyons wrote: >> Hi, >> >> Here ya' go. >> >> [-Rick-] >> ---------- >> >> References > > [100 references snipped] > > There is just something special with the short, succinct and > informal style of posting here at comp.dsp... ;) > > How much time did you spend on organizing that list?He probably already had it in a bibliography from one of his other writings or from an article he had on hand. But if not, kudus to Mr. Lyons!

Reply by ●September 15, 20052005-09-15

On 2 Sep 2005 02:49:04 -0700, "Rune Allnor" <allnor@tele.ntnu.no> wrote:> >Rick Lyons wrote: >> Hi, >> >> Here ya' go. >> >> [-Rick-] >> ---------- >> >> References > >[100 references snipped] > >There is just something special with the short, succinct and >informal style of posting here at comp.dsp... ;) > >How much time did you spend on organizing that list? > >RuneHi Rune, Mark Borderging tells the story. Years ago I found that bibliography (by Charles Burrus, Rice University) on the Internet. But in recent years that original website doesn't exist anymore. I didn't know about the website that Mark found. I realize now that I should have made it very clear from where I obtained that bibliography. Please forgive me. See Ya', [-Rick-]