Design by emulation has been widely used in the field of control systems. Design by emulation is a process where initially a continuous time controller is designed to achieve desired closed loop specifications. This continuous time controller is then mapped to a digital equivalent using a suitable mapping technique. Methods traditionally used for this mapping include forward rectangular rule, bilinear rule and zero-pole matching. We are presenting a new approach for mapping a continuous time controller to a discrete time controller. This approach, unlike any of the traditional mapping method, produces a discrete time transfer function with a magnitude response or phase response nearly the same as its analog prototype. To achieve this objective we are using the Magnitude Invariance Method (MIM) and Phase Invariance Method (PIM) that were recently developed in the field of signal processing. The frequency responses and the step responses of the closed loop systems obtained using this approach are systematically investigated to evaluate the effectiveness of these mapping techniques