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This paper is concerned with the Hankel operator and the Hankel norm of sampled-data systems. Even though these systems are intrinsically periodically time-varying, no studies have taken this important feature into account in the treatment of the Hankel operator/ norm. We characterize the Hankel operator/ norm of sampled-data systems adequately under the treatment with the $L_2$ norm for the past input and the $L_infty$ norm for the future output. Such treatment still captures the essential issue on the periodicity but contributes to neat arguments compared with the case when the $L_2$ norm is also considered on the future output.