http://iet.metastore.ingenta.com
1887

Microprocessor implementation of number theoretic transforms

Microprocessor implementation of number theoretic transforms

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IEE Journal on Electronic Circuits and Systems — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

Consideration is given to the suitability of microprocessor systems for the fast implementation of number theoretic transforms (n.t.t.s). Fast-multiply instructions available on some microprocessors, or the use of external multipliers, relax the basic constraints on the choice of a particular n.t.t. A search was made for suitable moduli which allow fast computation of n.t.t.s using Winograd's algorithm. The search was extended for other moduli which allow increased dynamic range when combined using the Chinese remainder theorem. Finally, a description is given of how modular arithmetic may efficiently be performed using microprocessors

References

    1. 1)
      • R.C. Agarwal , C.S. Burrus . Fast convolution using Fermat number transforms with applications to digital filtering. IEEE Trans. , 87 - 99
    2. 2)
      • R.C. Agarwal , S.C. Burrus . Number theoretic transforms to implement fast digital convolution. Proc. IEEE , 550 - 560
    3. 3)
      • R.C Agarwal , J.W. Cooley . New algorithms for digital convolution. IEEE Trans. , 392 - 410
    4. 4)
      • P. Melhuish . Fermat transform implementation by a minicomputer. Electron. Lett. , 109 - 111
    5. 5)
      • J.H. McClellan . Hardware realisation of a Fermat number transform. IEEE Trans. , 216 - 225
    6. 6)
      • C.M. Rader . Discrete convolution via Mersenne transforms. IEEE Trans. , 1269 - 1273
    7. 7)
      • S. Winograd . On computing the discrete Fourier transform. Prod. Nat. Acad. Sci. , 1005 - 1006
    8. 8)
      • H.F. Silverman . An introduction to programming the Winograd Fourier transform algorithm (WFTA). IEEE Trans. , 152 - 165
    9. 9)
      • H.F. Silverman . Corrections and an addendum to An introduction to the Winograd Fourier transform algorithm (WFTA). IEEE Trans.
    10. 10)
      • D. Bailey . Winograds algorithm applied to number theoretic transforms. Electron.Lett. , 548 - 549
    11. 11)
      • N. Sridhar Reddy , V. Umpathi Reddy . Implementation of Winograds algorithm in modular arithmetic for digital convolutions. Electron. Lett. , 228 - 229
    12. 12)
      • P.J. Nicholson . Algebraic theory of finite Fourier transforms. J. Comput. and Syst. Sci. , 524 - 547
    13. 13)
      • A.C. Davies , Y.T. Fung . Interfacing a hardware multiplier to a general purpose microprocessor. Microprocessors , 425 - 432
    14. 14)
      • C.H. Moore . FORTH: A new way to program a minicomputer. Astron. and Astrophys. , 497 - 511
    15. 15)
      • N. Sridhar Reddy , V. Umpathi Reddy . Complex convolutions using rectangular transforms. Electron. Lett. , 458 - 459
    16. 16)
      • M.C. Vanwormhoudt . Structural properties of complex residue rings applied to number theoretic Fourier transforms. IEEE Trans. , 99 - 104
    17. 17)
      • H.J. Nussbaumer . Complex convolutions via Fermat number transforms. IBM J. Res. & Dev. , 282 - 284
http://iet.metastore.ingenta.com/content/journals/10.1049/ij-ecs.1979.0004
Loading

Related content

content/journals/10.1049/ij-ecs.1979.0004
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address