On the concept of Intrinsic Wavelet Functions

This paper presents the concept of Intrinsic Wavelet Functions (IWFs) for efficient analysis of signals with transitory behavior. An approach is proposed for the decomposition of a given signal, consisting of localized waves, into IWFs that can best capture these small waves. To this end, first, we present a method to design a 2-channel signal-matched wavelet system based on least squares criterion. Next, IWFs are designed using this matched wavelet system. The proposed work differs from empirical mode decomposition (EMD) in one fundamental way. While EMD decomposes small segments of a given signal into oscillatory intrinsic mode functions (IMFs) similar to the concept of Short-Time Fourier transform, we extract localized small waves, namely, IWFs based on the concept of wavelets from a given signal. Simulation results demonstrate that this theory is aptly suited to analyze signals consisting of localized waves.