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Electrocardiogram (ECG) biometric recognition as a personal identification method is receiving more and more attention because it can support live verification results. Compared with other biometric-based methods, it can provide higher security performance. The difficulty of the problem lies in how to stably extract ECG signal features and achieve real-time verification. In this study, a new type of sparse representation learning framework called statistical <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula>-best adaptive Fourier decomposition (SAFD) originated by Qian is adopted in ECG biometric identification. Adaptive Fourier decomposition (AFD) is a recently developed combination of transform-based signal decomposition and sparse representation method, which can adaptively select the atoms from a redundant dictionary through orthogonal processing. The advantage of the AFD-type methods is that each atom in the dictionary has a precise mathematical formula with good analytic properties. This characteristic is significantly distinguished it from other existing sparse representations, where the atoms learned are usually matrix data and cannot be described mathematically. The proposed SAFD extends the existing <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula>-best AFD from processing single signal to multi-signals and implements the <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula>-best AFD in the stochastic Hardy space. Therefore, the small number of learned atoms by SAFD is sufficient to capture internal structure and robustness of the signal and generate a discriminative representation that reflects the time-frequency characteristics of signals. It is very suitable for non-stationary signals like ECG. The proof of convergence of the algorithm is presented. Extensive experiments are conducted on five public databases collected in different realistic conditions, and an average identification accuracy of 98.0% is achieved. In addition, less than 1 ms for one matching process makes it possible to be implemented in real time. Experimental results demonstrate that the proposed method can achieve superior performance compared to other state-of-the-art ECG biometric identification methods.