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A method for decomposing anharmonic periodic signals and the corresponding computer program



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French patent application FR1050106 filed on January 8, 2010



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Exclusive or non-exclusive licenses.


Centre de recherches Paul Pascal (CRPP, UPR8641), Pessac, France



The invention provides a general way of analyzing any anharmomic periodic signal as they are produced by numerous physical systems, an algorithm for decomposing and coding them with a small number of universal quantities thus allowing their compact representation and easy synthesis and understanding.


Nonlinear or anharmonic periodic signals appear to live in a space which has a much smaller dimension than the space of their Fourier series. This information is exhibited by the analysis of the phase function and classified according to its dynamics. The method consists in decomposing the phase dynamics using newly introduced nonlinear trigonometric functions and producing a small number of measurements that capture the main features of the signal, namely, a measure of the anharmonicity and a morphological parameter or pairs of such parameters.


The method produces an extremely compact coding of anharmonic periodic signals, whatever their origin, thus allowing a universal understanding through highly relevant measurements, greatly facilitating the comparison of signals and providing a signature of the underlying physical processes that produce such signals.

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