@inproceedings{caf-fer-lop-car-10-aa-sqnr-c,
  author = {Caffarena, Gabriel and Fern{\'a}ndez-Herrero, {\'A}ngel and L{\'o}pez, Juan A. and Carreras, Carlos},
  title = {Fast Fixed-Point Optimization of {DSP} Algorithms},
  booktitle = {Forward-Looking Trends in IC and Systems Design: Proceedings of the 8th IFIP WG 10.5/IEEE International Conference on Very Large Scale Integration (VLSI-SoC)},
  location = {Madrid, ES},
  year = 2010,
  month = sep,
  pages = {182-205},
  doi = {10.1007/978-3-642-28566-0_8},
  note = {See also [caf-lop-fer-car-10-aa-nlsqnr-c].}
  comment = {Quantization noise estimator based on AA. SQNR is Signal-to-Quantization Noise Ratio.},
  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 fixed-point 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.}
}