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.

自适应傅里叶分解（AFD）在有理解析函数中使用自适应基础而不是固定基础，从而实现了快速的能量收敛速度。在每个分解级别，重要的步骤是从字典中确定新的基础元素，以使提取的能量最大化。然而，现有的基础搜索方法仅仅是效率很低的穷举搜索方法。本文基于四种典型的优化技术，提出了四种加速AFD算法的方法，包括无味卡尔曼滤波（UKF）方法，Nelder-Mead（NM）算法，遗传算法（GA）和粒子群优化（PSO）。算法。与现有的穷举搜索方法相比，在分解四个代表性信号和实际心电信号的模拟中，