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In many real-time applications, sample values and time stamps are delivered in pairs, where sampling times are non-uniform. Frequency analysis using non-uniform data occurs in various real life problems and embedded systems, such as vibrational analysis in cars and control of packet network queue lengths. Our contribution is first to overview different ways to approximate the Fourier transform, and secondly to give analytical expressions for how non-uniform sampling affects these approximations. The results are expressed in terms of frequency windows describing how a single frequency in the continuous time signal is smeared out in the frequency domain, or, more precisely, in the expected value of the Fourier transform approximation.