On Fourier Series for Gaussian Noise

The often mistakenly omitted constant term in the Fourier-series representation of a stationary gaussian noise is shown to represent the range of frequencies from zero up to half the fundamental frequency of the series. The coefficients, including the constant term, are asymptotically statistically independent, but when the fundamental period of the series is not long enough, all of the sine and all of the cosine coefficients become statistically interdependent, and their variances differ from their well known asymptotic values. The Fourier-integral representation for gaussian noise is also investigated but is found to be comparatively awkward.