This chapter presents aperiodic resonance caused by a single excitation. In a nonlinear system, we use the aperiodic binary signal and the aperiodic M-ary signal as excitations, respectively. When the time scale of the signal matches well with the system parameters, aperiodic system resonance can be achieved by adjusting the system parameters. If they do not match well, it is necessary to achieve matching through scale transformation. This chapter introduces the theoretical framework of the general re-scaling method to achieve aperiodic system resonance under aperiodic excitation.