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The Scaling of Physical Quantities and Its Relation to the Power Spectrum of the Mellin Transform.
Physical sciences research papers,
AIR FORCE CAMBRIDGE RESEARCH LABS L G HANSCOM FIELD MASS
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Just as one uses the power spectrum of the Fourier transform of data given as a function of a one-dimensional variable to find periodicities in the translation of the variable, one may use the power spectrum of the Mellin transform to find periodicities in the magnification. The relation of the Fourier transform to the Mellin transform is discussed, and a theorem of the Wiener-Khinchine type is presented. The use of the Mellin transform, offers a new method of extracting meaningful features from data, particularly when the data is noisy.
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