Statistics of Narrowband White Noise Derived from Clipped Broadband White Noise
COASTAL SYSTEMS STATION PANAMA CITY FL
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Broadband white Gaussian noise is modelled as a series of sine and cosine functions of discrete frequencies up to a maximum frequency. The series coefficients are Gaussian with uniform variance across the frequency band. For a given sample, the Nyquist-spaced values are generated for a full period of the lowest frequency sinusoid and a peak factor is imposed, clipping the values. The resulting signal is discrete-Fourier transformed via the fast Fourier transform, hard filtered at a prescribed bandwidth, and then inverse transformed to give a set of values for the narrow band signal sample, and these values are used to update a histogram. When a sufficient number of signal samples are generated, the resulting distribution is fitted to a Gaussian distribution by a least-squares technique. It is found that the resulting distributions are noticeably non-Gaussian down to a bandwidth ratio of 14, below which the distribution appears to be Gaussian with a reduced variance depending on the peak factor. For a bandwidth ratio of 140, it is found that peak factors as low as 1.7 or even 1.5 have little effect on the narrowband distribution.