Empirical Mode Decomposition

For analysing data and/or signals a multitude of methods were developed in the past. A large group of these methods is based on the Fourier-Transformation (e.g.: Short-Time-Fourier-Transformation, Wavelet-Transformation, ect.). But using Fourier for data analysing, there exists two requirements necessarily: the signal must be stationary and linear over the subjected time span.

Generally a physical signal does not fulfil these conditions. Therefore it exists a constraint for detecting frequency components, which are not present over the whole signal. Based on these problems a new method was developed by N. E. Huang at al. called Empirical Mode Decomposition (EMD).

This method decomposes the signal into amplitude- and frequency modulated functions which are called Intrinsic Mode Functions (IMF). These IMFs are detected by calculating the mean value, which is composed of two envelopes interpolating the local maxima and local minima. The first IMFs which have been found include the high frequency components. So there exists a hierarchy because this sifting process terminates, when a monotonic IMF (called “Residuum”) has been detected.

Empirical Mode Decomposition is a data dependent method which means, that it adapts to the input signal and it can not be determinated a priori like the Fourier–Transformation. In order to get the instantaneous frequencies from the IMFs, the phases of these IMFs must be derivated over time. This process results in the Hilbert – Huang - Spektrum (HHS), which represents the original input signal in its energy – frequency – time domain. Compared with other spectral analysis methods the advantage of EMD is, that there exists no leakage effect in the frequency domain.

The aim of this project is to adapt EMD for analysis and resynthesis of music signals. Therefore it is necessary to research this method about the interpolation process for calculating the envelopes, the influence of sampling frequency and the Hilbert – Transformation for deriving the HHS. Another problem needing improvement concerns the edge effect arising by the interpolation process for detecting the envelopes at the beginning and the end of the signal.