The minimum number of samples that must be taken from a\udsinusoidal signal affected by white Gaussian noise, in order to find its\udfrequency with a predetermined maximum error, is derived. This analysis\udis of interest in evaluating the performance of velocity-measurement systems\udbased on the Doppler effect. Specifically, in laser Doppler anemometry\ud(LDA) it is usual to receive bursts with a poor signal-to-noise\udratio, yet high accuracy is required for the measurement. In recent years\udspecial attention has been paid to the problem of monitoring the temporal\udevolution of turbulent flows. In this kind of situation averaging or filtering\udthe data sequences cannot be allowed: in a rapidly changing environment\udeach one of the measurements should rather be performed\udwithin a maximum permissible error and the bursts strongly affected by\udnoise removed. The method for velocity extraction that will be considered\udhere is the spectral analysis through the squared discrete Fourier transform,\udor periodogram, of the received bursts. This paper has two parts. In\udthe first an approximate expression for the error committed in LDA is\udderived and discussed. In the second a mathematical formalism for the\udexact calculation of the error as a function of the signal-to-noise ratio is\udobtained, and some universal curves for the expected error are provided.\udThe results presented here appear to represent a fundamental limitation\udon the accuracy of LDA measurements, yet, to our knowledge, they have\udnot been reported in the literature so far.
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