Sum-of-product architectures computing just right

Dinechin, Florent de; Istoan, Matei; Massouri, Albdelbassat

doi:10.1109/asap.2014.6868629

Cited by 7 publications

(8 citation statements)

References 15 publications

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“…Such an SOPC will ensure ε r < 2 ext . Using (20), we obtain that the optimal value of ext that ensures this constraint is…”

Section: Putting It All Togethermentioning

confidence: 99%

“…In a previous work [20], all the x i shared the same format, as is the case for a FIR filter. In the context of an IIR filter, this is no longer true: in Figure 4, we have a single SOPC where the c i may be a i or b i , and the x i may be either some delayed u(k), or some delayed y(k).…”

Section: Problem Statementmentioning

confidence: 99%

“…Another difference with [20] is that the output MSB m r is input to the generator. An overestimation of m r could be computed out of the c i and the input formats, as in [20].…”

Section: Problem Statementmentioning

confidence: 99%

“…Another difference with [20] is that the output MSB m r is input to the generator. An overestimation of m r could be computed out of the c i and the input formats, as in [20]. However, the worst case peak gain of an IIR filter provides a finer value of m r , and in this case we want to provide this value to the SOPC generator.…”

Section: Problem Statementmentioning

confidence: 99%

See 3 more Smart Citations

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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“…Such an SOPC will ensure ε r < 2 ext . Using (20), we obtain that the optimal value of ext that ensures this constraint is…”

Section: Putting It All Togethermentioning

confidence: 99%

Section: Problem Statementmentioning

confidence: 99%

“…Another difference with [20] is that the output MSB m r is input to the generator. An overestimation of m r could be computed out of the c i and the input formats, as in [20].…”

Section: Problem Statementmentioning

confidence: 99%

Section: Problem Statementmentioning

confidence: 99%

See 2 more Smart Citations

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

Volkova

Istoan

Dinechin

et al. 2019

IEEE Trans. Comput.

Self Cite

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“…• specify and determine a mathematical representation of the filter (usually in terms of polynomials/rational functions); • quantize the values (i.e., coefficients) found at the previous step, using some imposed numerical representations (be it fixed-point or floating-point formats) [31]; • synthesize the obtained filter in hardware/software [20]. The Parks-McClellan exchange algorithm [40] solves the first step.…”

Section: Introductionmentioning

confidence: 99%

A Robust and Scalable Implementation of the Parks-McClellan Algorithm for Designing FIR Filters

Filip

2016

ACM Trans. Math. Softw.

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With a long history dating back to the beginning of the 1970s, the Parks-McClellan algorithm is probably the most well-known approach for designing finite impulse response filters. Despite being a standard routine in many signal processing packages, it is possible to find practical design specifications where existing codes fail to work. Our goal is twofold. We first examine and present solutions for the practical difficulties related to weighted minimax polynomial approximation problems on multi-interval domains (i.e., the general setting under which the Parks-McClellan algorithm operates). Using these ideas, we then describe a robust implementation of this algorithm. It routinely outperforms existing minimax filter design routines.

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Determining fixed-point formats for a digital filter implementation using the worst-case peak gain measure

Volkova¹,

Hilaire²,

Lauter³

2015

2015 49th Asilomar Conference on Signals, Systems and Computers

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International audienceIn this article, we focus on the Fixed-Point implementation of Linear Time Invariant (LTI) filters in state-space representation. For that purpose, we give an algorithm to determine the Fixed-Point Formats of all the involved variables (states and outputs). For the sake of generality, the algorithm works in the case of Multiple Inputs Multiple Outputs filters. The computational errors in the intermediate steps of the filter evaluation as well as their accumulation over time are fully taken into account. We handle several rounding modes (round to nearest and truncation) for two's-complement-based Fixed-Point Arithmetic. Our approach is fully rigorous in the way that the output Fixed-Point formats are shown to be free of overflows and we do not use any (non-exhaustive) filter simulation steps but proofs

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Sum-of-product architectures computing just right

Cited by 7 publications

References 15 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

A Robust and Scalable Implementation of the Parks-McClellan Algorithm for Designing FIR Filters

Determining fixed-point formats for a digital filter implementation using the worst-case peak gain measure

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