Stochastic resonance phenomenon driven by aperiodic echo signal is observed.

FrFT operator is used to equivalently analyze the stochastic resonance system in transform domain.

The analytical expression of the output SNR is derived.

Proposed system shows the generalized SR behaviors in the case of different internal parameters of chirp signal and the external parameters of moving target.

It has the potential applications in engineering systems for moving target detection and localization and biological systems for describing some animal behaviors.