Abstract
This work presents a novel perfect reconstruction filter bank
decomposition (PRFBD) for nonlinear and nonstationary time series and
image data representation and analysis. The Fourier decomposition method
(FDM), an adaptive approach wholly based on the Fourier representation,
is shown to be a special case of the proposed PRFBD. The adaptive
Fourier–Gauss decomposition (FGD) proposed in this work is a variation
of the FDM, which is based on the FR and Gaussian filtering. Similarly,
we also consider Butterworth filtering to develop adaptive
Fourier–Butterworth decomposition (FBD). The proposed theory can
decompose any signal (time series, image, or other data) into a set of
the desired number of Fourier intrinsic band functions (FIBFs), which
follow the amplitude-modulation and frequency-modulation (AM-FM)
representations. A generic filterbank representation is also provided,
where perfect reconstruction can be ensured for any given set of lowpass
or highpass filters. We have performed an extensive analysis of 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.