Stochastic modeling for floating-point to fixed-point conversion

The floating-point to fixed-point transformation process is error prone and time consuming as the distortion introduced by the limited data size is difficult to evaluate. In this paper a method to estimate the range of variables in LTI systems with respect to the corresponding overflow probability is presented. Furthermore, we will show that the quantization noise evaluation can be realized using the same approach. The variance and the probability density function of the error are computed. The results obtained for several typical applications are presented.