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Noise for continuous-time system simulation is relevant for many applications, whenever 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 form filters are often used as approximate state space implementations. In this article, we address the problem with a new method which relies 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 AdvancedNoise 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.