Modelling the I.M.F’s produced by the E.M.D of musical audio for synthesis and manipulation

This paper describes a process with which to analyse musical sounds by first applying empirical mode decomposition to find a set of data dependant AM-FM basis functions. These basis functions are such that they facilitate Hilbert Spectrum calculation, which describes the signal in terms of its instantaneous amplitude and phase, and hence instantaneous frequency. The IF and IA are then modelled, which allows for representation of the IMFs analytically. This provides a greater insight into the content the basis functions, as EMD is only defined by its algorithm and has no mathematical proof, as yet. Secondly, this modelling allows for the interpretation of the Hilbert Spectrum for musical audio as well as providing a novel representation of the signal as a sum of AM-FM basis functions. This technique is validated by applying the modelling of the IMFs produced for a piano note. Manipulation of the model parameters of the IA and IF of IMFs can be exploited to change the signal content and project the modelled data beyond the given input samples. Details of this procedure are contained in this paper as is an example of this process being applied to synthesise multiple notes of differing pitch and duration from a very small segment of an instrument sound.