Intrinsic mode chirp decomposition of non‐stationary signals

Abstract

We propose the discrete linear chirp transform (DLCT) for decomposing a non-stationary signal into intrinsic mode chirp functions. The decomposition of a signal into a finite number of intrinsic mode functions (IMFs) was introduced by the empirical mode decomposition (EMD). It exploits the local time-scale signal characteristics of the signal and provides spectral estimates obtained via the Hilbert transform. Although efficient, the EMD does not provide an analytic representation of the IMFs and is susceptible to noise and to closeness or overlap of the frequency of the IMFs. Using linear chirps as IMFs, the DLCT, a joint frequency instantaneous frequency procedure, provides a parsimonious local orthogonal representation of non-stationary signals. Moreover, the DLCT allows a parametric estimation of the instantaneous frequency of the signal that is robust to noise and to closeness or overlap in the instantaneous frequency of the modes. More importantly, the DLCT can be used to represent and process signals that are sparse in a joint time-frequency sense. The performance of the DLCT and the EMD are illustrated and compared when used to estimate the instantaneous frequency of individual signal components, to obtain signal decompositions at different frequency bands and to process frequency modulated signals with time-varying amplitude.