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Periodic/aperiodic sequence with good correlation and stopband properties has received widespread attention and been widely applied in radar and communication systems. To meet the hardware requirement and maximize the transmitter efficiency, the unimodular or peak-to-average ratio (PAR) constraint is always required in sequence design. In this paper, we consider the problem of designing PAR-constrained periodic/aperiodic sequence with good properties. After establishing the corresponding criterions for both correlation and stopband properties, the unified PAR-constrained problem is formulated and then transformed into an unconstrained minimization problem via sequence synthesis. To solve the problem, an efficient gradient-based algorithm is proposed to minimize the objective function directly. As the main steps can be implemented by fast Fourier transform (FFT) operations and Hadamard product, the whole algorithm is computationally efficient. In addition, the proposed algorithm can be applied to design both the periodic and aperiodic sequences by choosing proper parameters. Numerical experiments show that the proposed algorithm has better performance than the state-of-the-art algorithms in terms of the sequence quality and the running time. [ABSTRACT FROM AUTHOR]