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Optimal Word-Length Allocation for the Fixed-Point Implementation of Linear Filters and Controllers

Abstract : This article presents a word-length optimization problem under accuracy constraints for the hardware implementation of linear signal processing systems with fixed-point arithmetic. For State-Space systems (describing a linear filter or a controller), a complete error analysis is exhibited, where the final output error bound depends on the word-lengths and the fixed-point formats chosen for each variable. The Most Significant Bit of each one can be determined in order to guarantee that no overflow occurs. Thus, it is possible to obtain a hardware implementation minimizing resource use. This leads to a convex nonlinear integer optimization problem where the resources to minimize and the accuracy constraints depend on the internal word-lengths. This problem can then be solved with appropriate heuristics. Finally, a global approach is proposed and illustrated by some examples.
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https://hal.sorbonne-universite.fr/hal-02393851
Contributor : Thibault Hilaire <>
Submitted on : Wednesday, December 4, 2019 - 3:19:29 PM
Last modification on : Tuesday, April 21, 2020 - 1:04:06 AM
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Thibault Hilaire, Hacène Ouzia, Benoit Lopez. Optimal Word-Length Allocation for the Fixed-Point Implementation of Linear Filters and Controllers. ARITH 2019 - IEEE 26th Symposium on Computer Arithmetic, Jun 2019, Kyoto, Japan. pp.175-182, ⟨10.1109/ARITH.2019.00040⟩. ⟨hal-02393851⟩

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