Abstract
The adaptive Fourier decomposition (AFD) uses an adaptive basis instead of a fixed basis in the rational analytic function and thus achieves a fast energy convergence rate. At each decomposition level, an important step is to determine a new basis element from a dictionary to maximize the extracted energy. The existing basis searching method, however, is only the exhaustive searching method that is rather inefficient. This paper proposes four methods to accelerate the AFD algorithm based on four typical optimization techniques including the unscented Kalman filter (UKF) method, the Nelder-Mead (NM) algorithm, the genetic algorithm (GA), and the particle swarm optimization (PSO) algorithm. In the simulation of decomposing four representative signals and real ECG signals, compared with the existing exhaustive search method, the proposed schemes can achieve much higher computation speed with a fast energy convergence, that is, in particular, to make the AFD possible for real-time applications.
Highlights
1 Introduction The adaptive Fourier decomposition (AFD), introduced by Qian et al, is a type of positive frequency expansion algorithm based on a given basis search dictionary [1,2,3]
It offers fast energy decomposition via the adaptive basis, which is different from the conventional Fourier decomposition that is based on the Fourier basis
2.3 Evaluation indices In the following simulation studies, three indices are considered to evaluate the performances of different optimization algorithms: a b c d
Summary
The adaptive Fourier decomposition (AFD), introduced by Qian et al, is a type of positive frequency expansion algorithm based on a given basis search dictionary [1,2,3]. In order to apply these methods, the optimization problem in (5) is reformulated from a maximization problem with one complex-valued variable to a minimization problem with two real-valued variables The performances of these proposed methods in the sifting of the AFD are compared with the conventional exhaustive search method in the decomposition of four representative signals, including the heavisine signal, the doppler signal, the block signal, and the bump signal. These signals are chosen because they caricature spatially variable functions arising in imaging, spectroscopy, and other scientific signal processing [18].
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