How to Shape Noise Spectra for Continuous System Simulation

Abstract

Noise for continuous-time system simulation is relevant for many applications, where time-domain results are required. Simulating such noise raises the need to consistently shape the frequency content of the signal. However, the methods for this task are not obvious and often state space implementations of form filters are approximated. In this paper, we address the problem with a new method relying on directly using the specified power spectral density for a convolution filter. For the example of railway track irregularities, we explain how to derive the required filters, implement them in the open-source Noise library, and verify the results. The new method produces correct results, is very simple to use, and enables new features for time simulation of physical systems.