An Efficient Method for Evaluating Complex Polynomials

Abstract : We propose an effi cient hardware-oriented method for evaluating complex polynomials. The method is based on solving iteratively a system of linear equations. The solutions are obtained digit-by-digit on simple and highly regular hardware. The operations performed are defined over the reals. We describe a complex-to-real transform, a complex polynomial evaluation algorithm, the convergence conditions, and a corresponding design and implementation. The la- tency and the area are estimated for the radix-2 case. The main features of the method are: the latency of about m cycles for an m-bit precision; the cycle time independent of the precision; a design consisting of identical modules; and digit-serial connections between the modules. The number of modules, each roughly corresponding to serial-parallel multiplier without a carry-propagate adder, is 2(n + 1) for evaluating an n-th degree complex polynomial. The method can also be used to compute all successive integer powers of the complex argument with the same latency and a similar implementation cost. The design allows straightforward tradeoffs between latency and cost: a factor k decrease in cost leads to a factor k increase in latency. A similar tradeoff between precision, latency and cost exists. The proposed method is attractive for programmable plat- forms because of its regular and repetitive structure of simple hardware operators.
Type de document :
Article dans une revue
Journal of Signal Processing Systems, Springer, 2010, 58 (1), pp.17-27. 〈10.1007/s11265-008-0265-8〉
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Contributeur : Jean-Michel Muller <>
Soumis le : mercredi 13 janvier 2010 - 15:56:00
Dernière modification le : samedi 21 avril 2018 - 01:27:10
Document(s) archivé(s) le : jeudi 17 juin 2010 - 22:43:44


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Milos Ercegovac, Jean-Michel Muller. An Efficient Method for Evaluating Complex Polynomials. Journal of Signal Processing Systems, Springer, 2010, 58 (1), pp.17-27. 〈10.1007/s11265-008-0265-8〉. 〈ensl-00446889〉



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