A novel digital implementation of a Gaussian noise generator

Abstract

A method is proposed and studied for digital generation of analog Gaussian noise. In the proposed system, the parallel output from a maximal-length shift register (MSR) forms a sequence of random numbers with equal probability, which are then transformed into a Gaussian distribution by a mapping table. The system is different in its principle of operation and performance from the well-established technique of summing a large number of consecutive random outputs of an MSR to generate a Gaussian noise by virtue of the central limit theorem. Furthermore, it can be made to generate any arbitrary probability distribution function by changing the mapping table. The generator can be realized readily both in hardware as a physical instrument and in a software package as a simulated instrument. While the probability distribution of the generated noise is governed by the mapping table, its random properties are dominated by the behavior of the MSR.<>