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A numerical method to treat cylindrical cloaks with cyclic symmetry using the Method of Moments (MoM) has been developed and presented in [1]. This method uses the Array Scanning Method (ASM) in the azimuthal direction and Infinite Linear Array approach along the axis of the cylinder. In this paper the method has been extended to perform fast transient analysis of such cylindrical cloaks in order to study pulse transmission and scattering cross-section over a large bandwidth. The method is also very well suited for treating metamaterial cloaks which are known to be highly dispersive.