On Spectroscopy of Sampled Signals Using the Hilbert Transform

In the present contribution the influence of the sampling procedure on the Hilbert spectrum is analysed, where the masking of the real spectrum by the sampling frequency is shown. A benchmark problem, where the instantaneous amplitude and frequency are known as analytical functions depending on time is presented and discussed. An algorithm is proposed, which is designed to work with sampled signals and an application is discussed with emphasis to the spectral analysis, where the theoretical expectation is confronted with the modulated spectrum from the sampled data analysis and the results from an alternative approach.