Fast and accurate computation of the round-off noise of linear time-invariant systems

López, Juan Antonio Martínez; Caffarena, Gabriel; Carreras, Carlos; Nieto–Taladriz, Octavio

doi:10.1049/iet-cds:20070198

Cited by 35 publications

(51 citation statements)

References 14 publications

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“…Its main feature is that it automatically cancels the linear dependencies of the included uncertainties along the computation path, thus avoiding the oversizing produced by Interval Arithmetic (IA) approaches [15]. Regarding fixed-point optimization, it has been applied to both scaling computation [16,17,10], and word-length selection [5,16,10,18]. Also, a modification, called Quantized Affine Arithmetic (QAA), has been applied to the computation of limit cycles [19] and dynamic range analysis of quantized LTI algorithms [17].…”

Section: Affine Arithmeticmentioning

confidence: 99%

“…The deviation from the original behavior of an algorithm with feedback loops caused by quantized signals can be modeled by adding an affine formn i [k] to each signal i at each simulation time instant k (i.e. loop iteration index) [5]. These affine forms can properly model the quantization noise of each signal if the error term is assigned a uniform distribution:…”

Section: Affine Arithmetic Applied To Error Propagation Analysismentioning

confidence: 99%

“…and it is formed by a collection of affine forms at each time step n. This expression of the error can be used to estimate the error peak-value, using the traditional interpretation of AA [20,10], and, also, to obtain the PDF of the error [5,20]. However, in the next subsection we focus on obtaining the value of the power of the error considering the actual PDF of each error term (i.e.…”

Section: Affine Arithmetic Applied To Error Propagation Analysismentioning

confidence: 99%

“…This proves that the accuracy of the presented estimation is very high for LTI systems. Nonetheless, the method presented here is not intended for LTI systems, since there are already more efficient ways to compute their output noise [2,5,21]. The accuracy for non-linear algorithms is presented in the next section.…”

Section: Accuracy For Lti Systemsmentioning

confidence: 99%

“…However, in the last few years there have been attempts to provide fast estimation methods based on analytical techniques. These approaches can be applied to Linear TimeInvariant (LTI) systems [5,2,6] and to differentiable non-linear systems [7][8][9][10]. As for the noise metric used, they are based on the peak value [10] and on the computation of SQNR [2,7,5,9,8].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Fast Fixed-Point Optimization of DSP Algorithms

Caffarena

Carreras

López

et al. 2012

VLSI-SoC: Forward-Looking Trends in IC and Systems Design

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Abstract. In this chapter, the fast fixed-point optimization of Digital Signal Processing (DSP) algorithms is addressed. A fast quantization noise estimator is presented. The estimator enables a significant reduction in the computation time required to perform complex fixed-point optimizations, while providing a high accuracy. Also, a methodology to perform fixed-point optimization is developed.Affine Arithmetic (AA) is used to provide a fast Signal-to-Quantization Noise-Ratio (SQNR) estimation that can be used during the fixed-point optimization stage. The fast estimator covers differentiable non-linear algorithms with and without feedbacks. The estimation is based on the parameterization of the statistical properties of the noise at the output of fixed-point algorithms. This parameterization allows relating the fixedpoint formats of the signals to the output noise distribution by means of fast matrix operations. Thus, a fast estimation is achieved and the computation time of the fixed-point optimization process is significantly reduced.The proposed estimator and the fixed-point optimization methodology are tested using a subset of non-linear algorithms, such as vector operations, IIR filter for mean power computation, adaptive filters -for both linear and non-linear system identification -and a channel equalizer. The computation time of fixed-point optimization is boosted by three orders of magnitude while keeping the average estimation error down to 6% in most cases.

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Section: Affine Arithmeticmentioning

confidence: 99%

Section: Affine Arithmetic Applied To Error Propagation Analysismentioning

confidence: 99%

Section: Affine Arithmetic Applied To Error Propagation Analysismentioning

confidence: 99%

Section: Accuracy For Lti Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Fast Fixed-Point Optimization of DSP Algorithms

Caffarena

Carreras

López

et al. 2012

VLSI-SoC: Forward-Looking Trends in IC and Systems Design

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Set‐Membership Filtering Based Model Predictive Control for Trajectory Tracking of Automated Guided Vehicles

Liang,

Hu,

Zhang

et al. 2024

Adaptive Control & Signal

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This article considers the trajectory tracking problem of automated guided vehicles with unknown‐but‐bounded noises and proposes a set‐membership filtering (SMF) based model predictive control strategy. A 2‐DOF vehicle model is first established with considering the unknown‐but‐bounded process and measurement noises. Then, a trajectory tracking control scheme is proposed which consists of two parts, that is, a set‐membership observer and a model predictive controller. The proposed set‐membership observer is able to deal with the unknown‐but‐bounded noises and obtain the state estimation ellipsoid for the considered automated guided vehicle. Further, the designed model predictive controller utilizes the estimated ellipsoid to compute the control sequence. Finally, simulation results demonstrate the effectiveness and superiority of the proposed method.

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Development of numerical linear algebra algorithms in dynamic fixed‐point format: a case study of Lanczos tridiagonalization

Pradhan

Kabi

Mohanty

et al. 2015

Circuit Theory & Apps

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SUMMARYProper range and precision analysis play an important role in the development of fixed-point algorithms for embedded system applications. Numerical linear algebra algorithms used to find singular value decomposition of symmetric matrices are suitable for signal and image-processing applications. These algorithms have not been attempted much in fixed-point arithmetic. The reason is wide dynamic range of data and vulnerability of the algorithms to round-off errors. For any real-time application, the range of the input matrix may change frequently. This poses difficulty for constant and variable fixed-point formats to decide on integer wordlengths during float-to-fixed conversion process because these formats involve determination of integer wordlengths before the compilation of the program. Thus, these formats may not guarantee to avoid overflow for all ranges of input matrices. To circumvent this problem, a novel dynamic fixed-point format has been proposed to compute integer wordlengths adaptively during runtime. Lanczos algorithm with partial orthogonalization, which is a tridiagonalization step in computation of singular value decomposition of symmetric matrices, has been taken up as a case study. The fixed-point Lanczos algorithm is tested for matrices with different dimensions and condition numbers along with image covariance matrix. The accuracy of fixed-point Lanczos algorithm in three different formats has been compared on the basis of signal-toquantization-noise-ratio, number of accurate fractional bits, orthogonality and factorization errors. Results show that dynamic fixed-point format either outperforms or performs on par with constant and variable formats. Determination of fractional wordlengths requires minimization of hardware cost subject to accuracy constraint. In this context, we propose an analytical framework for deriving mean-square-error or quantization noise power among Lanczos vectors, which can serve as an accuracy constraint for wordlength optimization. Error is found to propagate through different arithmetic operations and finally accumulate in the last Lanczos vector. It is observed that variable and dynamic fixed-point formats produce vectors with lesser round-off error than constant format. All the three fixed-point formats of Lanczos algorithm have been synthesized on Virtex 7 field-programmable gate array using Vivado high-level synthesis design tool. A comparative study of resource usage and power consumption is carried out.

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Fast and accurate computation of the round-off noise of linear time-invariant systems

Cited by 35 publications

References 14 publications

Fast Fixed-Point Optimization of DSP Algorithms

Fast Fixed-Point Optimization of DSP Algorithms

Set‐Membership Filtering Based Model Predictive Control for Trajectory Tracking of Automated Guided Vehicles

Development of numerical linear algebra algorithms in dynamic fixed‐point format: a case study of Lanczos tridiagonalization

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