ABSTRACT
This work presents a novel perfect reconstruction filterbank decomposition (PRFBD) method for nonlinear and non-stationary time-series and image data representation and analysis. The Fourier decomposition method (FDM), an adaptive approach based on Fourier representation (FR), is shown to be a special case of the proposed PRFBD. In addition, adaptive Fourier–Gauss decomposition (FGD) based on FR and Gaussian filters, and adaptive Fourier–Butterworth decomposition (FBD) based on Butterworth filters are developed as the other special cases of the proposed PRFBD method. The proposed theory of PRFBD can decompose any signal (time-series, image, or other data) into a set of desired number of Fourier intrinsic band functions (FIBFs) that follow the amplitude-modulation and frequency-modulation (AM-FM) representations. A generic filterbank representation, where perfect reconstruction can be ensured for any given set of lowpass or highpass filters, is also presented. We performed an extensive analysis on both simulated and real-life data (COVID-19 pandemic, Earthquake and Gravitational waves) to demonstrate the efficacy of the proposed method. The resolution results in the time-frequency representation demonstrate that the proposed method is more promising than the state-of-the-art approaches.