Fast fixed-point optimization of DSP algorithms

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.