A better decomposition of speech obtained using modified Empirical Mode Decomposition

Abstract

The objective of this work is to obtain meaningful time domain components, or Intrinsic Mode Functions (IMFs), of the speech signal, using Empirical Mode Decomposition (EMD), with reduced mode mixing, and in a time-efficient manner. This work focuses on two aspects – firstly, extracting IMFs of the speech signal which can better reflect its higher frequency spectrum; and secondly, to get a better representation and distribution of the vocal tract resonances of the speech signal in its IMFs, compared to that obtained from standard EMD. To this effect, modifications are proposed to the EMD algorithm for processing speech signals, based on the critical nature of the interpolation points (IPs) used for cubic spline interpolation in EMD. The effect of using different sets of IPs, other than the extrema of the residue – as used in standard EMD – is analyzed. It is found that having more IPs is beneficial only upto a certain limit, after which the characteristic dyadic filterbank nature of EMD breaks down. For certain sets of IPs, these modified EMD processes perform better than EMD, giving better frequency separability between the IMFs, and an enhanced representation of the higher frequency content of the signal. A detailed study of the distribution of the formants, in the IMFs of the speech signal, is done using Linear Prediction (LP) analysis of the IMFs. It is found that the IMFs of the EMD variants have a far better distribution of the formants structure within them, with reduced overlapping amongst their filter spectrums, compared to that of standard EMD. Henceforth, when subjected to the task of formants estimation of voiced speech, using LP analysis, the IMFs of the modified EMD processes cumulatively exhibit a superior performance than that of standard EMD, or the speech signal itself, under both clean and noisy conditions.