Analytical Fixed-Point Accuracy Evaluation in Linear Time-Invariant Systems

One of the most important stages of floating-point to fixed-point conversion, is the evaluation of the fixed-point specification accuracy. This evaluation is required to optimize the data word-length according to accuracy constraints. Classical methods for accuracy evaluation are based on fixed-point simulations but they lead to very long optimization times.A new method based on an analytical approach is presented for the case of linear-time-invariant (LTI) systems. The use of this method in data word-length minimization processes reduces significantly the optimization time compared to simulation based methods. Our approach allows the automatic determination of the signal-to-quantization-noise-ratio (SQNR) expression at the system output according to the fixed-point data format. This method is valid for recursive and non-recursive LTI systems and takes account of the quantization modes (truncation or rounding). The theoretical concepts and the different methodology stages are explained. Then, the ability to efficiently evaluate the fixed-point specification accuracy is demonstrated through examples.