Starting from paraxial wave equation, analytical propagation expressions of hyperbolic secant pulsed beams with narrowband and broadband are derived. By the use of numerical calculations, pulsed beams obtained by means of complex amplitude envelope representation and complex analytical signal representation are compared. The condition to determine what representation should be chosen is also given. It is found that pulsed beam obtained by using complex amplitude envelope representation has singularity, which is anti-beam behavior and loses physical meaning. In the case of pulsed beams with broadband, singularity of complex amplitude envelope solution locates near axis, which causes that the solution failed to describe pulsed beam. But for the case of pulsed beam with narrowband, singularity locates far from axis, which can be neglected in the study of pulsed beam. It is concluded that both of the representations are applicable to study narrowband pulse, but for broadband pulse only rigorous complex analytical signal representation should be adopted.