I have used white noise filtration method for the generation of road profile from the PSD spectrum using MATLAB. A band limited white noise or white Gaussian noise (wgn) is given as input to the first order filter and output is the required road profile. The PSD of road profile is inversely proportional to the square of frequency. I have calculated kurtosis value (k) and obtained PSD spectrum and probability density (PDF) curve for the input and output signal.
It is observed that the input (wgn) has k=3 +/- 0.05 and perfectly normal PDF and flat or constant PSD. The output (road profile) has k=3 +/- 0.8 and PSD is matching with the required one but the PDF is deviating from normal near the central part from flatness to peakdness..
The derivative of the output signal has same k and PDF as that of input signal and has flat PSD.
The above observations suggest that the only white noise is perfectly Gaussian and if it is true then it is contradictory with the theory of linear random vibrations as, If input has normal PDF then output also have normal PDF.
I have also used the method of summation of cosines with randomly distributed phase angles and obtained the same conclusions as that of white noise filtration method.
You may have encountered a modelling problem due to the discrete approximation of a continuous process.
Hello,
I am not sure of what you did exactly, but it sounds weird. I tried a Monte Carlo simulation (50000 runs in the figures) of a Simulink band-limited white noise filtered by the transfer function a/(s+a). I compared the experimentally computed first four moments (blue curves in the figures) with the theoretical moments obtained by solving the moment equations (obtained from the stochastic equation fed with a Gaussian white noise). The agreement is very good, so this tends to confirm that both the BLWN and its filtered version are indeed Gaussian.
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