Toward tools and methodology for the fixed-point implementation OF linear filters

Hilaire, Thibault

doi:10.1109/dsp-spe.2011.5739263

Cited by 2 publications

(2 citation statements)

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“…This work will allow one to quantify this, although it will not be completely straightforward: these structures have many intermediate formats, whose sizes also have to be determined and minimized. A unifying filter representation called SIF [31] could be the key to generalize the approach of the present article.…”

Section: Discussionmentioning

confidence: 99%

Towards Hardware IIR Filters Computing Just Right: Direct Form I Case Study

Volkova

Istoan

Dinechin

et al. 2019

IEEE Trans. Comput.

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Linear Time Invariant (LTI) filters are often specified and simulated using high-precision software, before being implemented in low-precision fixed-point hardware. A problem is that the hardware does not behave exactly as the simulation due to quantization and rounding issues. This article advocates the construction of LTI architectures that behave as if the computation was performed with infinite accuracy, then converted to the low-precision output format with an error smaller than its least significant bit. This simple specification guarantees the numerical quality of the hardware, even for critical LTI systems. Besides, it is possible to derive the optimal values of all the internal data formats that ensure that the specification is met. This requires a detailed error analysis that captures not only the quantization and rounding errors, but also their infinite accumulation in recursive filters. This generic methodology is detailed for the case of low-precision LTI filters in the Direct Form I implemented in FPGA logic. It is demonstrated by a fully automated and open-source architecture generator tool, and validated on a range of Infinite Impulse Response filters.

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Section: Discussionmentioning

confidence: 99%

Towards Hardware IIR Filters Computing Just Right: Direct Form I Case Study

Volkova

Istoan

Dinechin

et al. 2019

IEEE Trans. Comput.

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“…This final code may be executed on a device (software implementation) or describing hardware operations to be performed (hardware implementation). This problem is a difficult one, that can be decomposed in several steps [4] as illustrated in Figure 1. First, one should consider the various equivalent realizations to implement the filter.…”

Section: Introductionmentioning

confidence: 99%

Reliable implementation of linear filters with fixed-point arithmetic

Hilaire

Lopez

2013

SiPS 2013 Proceedings

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This article deals with the implementation of linear filters or controllers with fixed-point arithmetic. The finite precision of the computations and the roundoff errors induced may have an important impact on the numerical behavior of the implemented system. Moreover, the fixed-point transformation is a time consuming and errorprone task, specially with the objective of minimizing the quantization impact. Based on a formalism able to describe every structure of linear filters/controllers, this paper proposes an automatic method to generate fixed-point version of the inputs-to-outputs algorithm and an analysis of the global error added on the output. An example illustrates the approach.

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Toward tools and methodology for the fixed-point implementation OF linear filters

Cited by 2 publications

References 24 publications

Towards Hardware IIR Filters Computing Just Right: Direct Form I Case Study

Towards Hardware IIR Filters Computing Just Right: Direct Form I Case Study

Reliable implementation of linear filters with fixed-point arithmetic

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