Spline interpolation of the fast fourier transform of a biological rhythm: Determination of the spectral components

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Abstract
Biological rhythms are often studied by complementary explorations in the temporal and the frequency domains. This provides a means of investigating purely frequential features such as periods and phases, as well as those related to the shape of the curve. A comparison of the characteristics of the DFT (Discrete Fourier Transform) and the FFT (Fast Fourier Transform) shows that, whereas the latter is clearly advantageous in terms of calculation time, it does not allow for precise localization of the spectral lines. This drawback can be overcome by interpolating with Spline functions. The determination of Splines associated with an FFT is detailed for microcomputer application. The algorithm proposed here is then tested on a concrete example of measurement of biological rhythms of activity on an inbred mouse.

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