  Recently, it is observed [Md. Nurujjaman et al, Phy. Rev. E \textbf{80},
015201 (R) (2009)] that in an excitable system, one can maintain noise induced
coherency in the coherence resonance by blocking the destructive effect of the
noise on the system at higher noise level. This phenomenon of constant
coherence resonance (CCR) cannot be explained by the existing way of simulation
of the model equations of an excitable system with added noise. In this paper,
we have proposed a general model which explains the noise induced resonance
phenomenon CCR as well as coherence resonance (CR) and stochastic resonance
(SR). The simulation has been carried out considering the basic mechanism of
noise induced resonance phenomena: noise only perturbs the system control
parameter to excite coherent oscillations, taking proper precautions so that
the destructive effect of noise does not affect the system. In this approach,
the CR has been obtained from the interference between the system output and
noise, and the SR has been obtained by adding noise and a subthreshold signal.
This also explains the observation of the frequency shift of coherent
oscillations in the CCR with noise level.
