Abstract
A fast and accurate quantization noise estimator aiming at fixed-point implementations of Digital Signal Processing (DSP) algorithms is presented. The estimator enables significant reduction in the computation time required to perform complex word-length optimizations. The proposed estimator is based on the use of Affine Arithmetic (AA) and it is presented in two versions: (i) a general version suitable for differentiable nonlinear algorithms, and Linear Time-Invariant (LTI) algorithms with and without feedbacks; and (ii) an LTI optimized version. The process relies on the parameterization of the statistical properties of the noise at the output of fixed-point algorithms. Once the output noise is parameterized (i.e., related to the fixed-point formats of the algorithm signals), a fast estimation can be applied throughout the word-length optimization process using as a precision metric the Signal-to-Quantization Noise Ratio (SQNR). The estimator is tested using different LTI filters and transforms, as well as a subset of non-linear operations, such as vector operations, adaptive filters, and a channel equalizer. Fixed-point optimization times are boosted by three orders of magnitude while keeping the average estimation error down to 4%.
Highlights
The original infinite precision of an algorithm based on the use of real arithmetic must be reduced to the practical precision bounds imposed by digital computing systems
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 Time-Invariant (LTI) systems [6, 11] and to differentiable nonlinear systems [12,13,14,15]
Since Signal-to-Quantization Noise Ratio (SQNR) is a very popular error metric within Digital Signal Processing (DSP) systems, our work aims at fast SQNR estimation techniques for LTI and differentiable nonlinear systems
Summary
The original infinite precision of an algorithm based on the use of real arithmetic must be reduced to the practical precision bounds imposed by digital computing systems. WLO is a slow process due to the fact that the optimization is very complex (NP-hard [8]) and because of the necessity of a continuous assessment of the algorithm accuracy which may involve a high computational load This estimation is normally performed adopting a simulationbased approach [7, 9, 10] which leads to exceedingly long design times. 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 Time-Invariant (LTI) systems [6, 11] and to differentiable nonlinear systems [12,13,14,15].
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