Journal ArticleDOI
Simplified Design of Constant Coefficient Multipliers
TLDR
The results show that the number of adders and subtracters decreases on average 25% for 19-bit coefficients compared with the canonic signed-digit representation.Abstract:
In many digital signal processing algorithms, e.g., linear transforms and digital filters, the multiplier coefficients are constant. Hence, it is possible to implement the multiplier using shifts, adders, and subtracters. In this work two approaches to realize constant coefficient multiplication with few adders and subtracters are presented. The first yields optimal results, i.e., a minimum number of adders and subtracters, but requires an exhaustive search. Compared with previous optimal approaches, redundancies in the exhaustive search cause the search time to be drastically decreased. The second is a heuristic approach based on signed-digit representation and subexpression sharing. The results for the heuristic are worse in only approximately 1% of all coefficients up to 19 bits. However, the optimal approach results in several different optimal realizations, from which it is possible to pick the best one based on other criteria. Relations between the number of adders, possible coefficients, and number of cascaded adders are presented, as well as exact equations for the number of required full and half adder cells. The results show that the number of adders and subtracters decreases on average 25% for 19-bit coefficients compared with the canonic signed-digit representation.read more
Citations
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50 Years of CORDIC: Algorithms, Architectures, and Applications
TL;DR: A brief overview of the key developments in the CORDIC algorithms and architectures along with their potential and upcoming applications is presented.
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Exact and Approximate Algorithms for the Optimization of Area and Delay in Multiple Constant Multiplications
TL;DR: This paper proposes an exact common subexpression elimination algorithm for the optimum sharing of partial terms in multiple constant multiplications (MCMs) and describes how this algorithm can be modified to target the minimum area solution under a user-specified delay constraint.
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Lower Bounds for Constant Multiplication Problems
TL;DR: Lower bounds for problems related to realizing multiplication by constants with shifts, adders, and subtracters are presented and have applications in proving the optimality of solutions obtained by heuristics.
Journal ArticleDOI
Search algorithms for the multiple constant multiplications problem: Exact and approximate
TL;DR: The main contribution of this article is the proposal of an exact depth-first search algorithm that, using lower and upper bound values of the search space for the MCM problem instance, finds the minimum solution consuming less computational resources than the previously proposed exact breadth- first search algorithm.
Journal ArticleDOI
Maximally Flat CIC Compensation Filter: Design and Multiplierless Implementation
TL;DR: This brief introduces a design and implementation of maximally flat cascaded integrator comb compensation filters, in particular, second- and fourth-order linear phase filters for narrow-band and wideband compensation.
References
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Book
Discrete-Time Signal Processing
TL;DR: In this paper, the authors provide a thorough treatment of the fundamental theorems and properties of discrete-time linear systems, filtering, sampling, and discrete time Fourier analysis.
Journal ArticleDOI
Subexpression sharing in filters using canonic signed digit multipliers
TL;DR: This paper examines methods for optimizing the design of CSD multipliers, and in particular the gains that can be made by sharing subexpressions, and it is shown that sharing the two most common sub expressions can be expected to lead to a 33% saving of the number of additions.
Journal ArticleDOI
Primitive operator digital filters
David Bull,D.H. Horrocks +1 more
TL;DR: Vertex rearrangement, retiming and edge elimination techniques are presented which facilitate the generation of a logical graph with an efficient allocation of pipeline registers.
Journal ArticleDOI
A new algorithm for elimination of common subexpressions
TL;DR: A new solution of the multiple constant multiplication problem based on the common subexpression elimination technique is presented and it is shown that the number of add/subtract operations can be reduced significantly this way.