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The auto-correlation function and the frequency power spectral density due toa super-position of uncorrelated exponential pulses are considered. These areshown to be independent of the degree of pulse overlap and thereby theintermittency of the stochastic process. For constant pulse duration and aone-sided exponential pulse shape, the power spectral density has a Lorentzianshape which is flat for low frequencies and a power law at high frequencies.The algebraic tail is demonstrated to result from the discontinuity in thepulse function. For a strongly asymmetric two-sided exponential pulse shape,the frequency spectrum is a broken power law with two scaling regions. In thecase of a symmetric pulse shape, the power spectral density is the square of aLorentzian function. The steep algebraic tail at high frequencies in thesecases is demonstrated to follow from the discontinuity in the derivative of thepulse function. A random distribution of pulse durations is shown to result inapparently longer correlation times but has no influence on the asymptoticpower law tail of the frequency spectrum. The effect of additional random noiseis also discussed, leading to a flat spectrum for high frequencies. Theprobability density function for the fluctuations is shown to be independent ofthe distribution of pulse durations. The predictions of this model describe thevariety of auto-correlation functions and power spectral densities reportedfrom experimental measurements in the scrape-off layer of magnetically confinedplasmas.

Auto-correlation function and frequency spectrum due to a super-position of uncorrelated exponential pulses