In this chapter, we introduce frequency-modulated signals in the excitation process to induce aperiodic stochastic resonance. We primarily focus on several types of signals: linear frequency-modulated signals, linear frequency-modulated signals with unknown parameters, ultra-high frequency linear frequency-modulated signals, and nonlinear frequency-modulated signals. To achieve aperiodic stochastic resonance with these characterized signals, we present a theoretical framework that incorporates piecewise or real-time re-scaling, fractional Fourier transformation, fractional signal-to-noise ratio, and a parametric asymmetric bistable system. Additionally, we explore the use of signal decomposition methods to address the associated challenges. Under the excitation of frequency-modulated signals, both aperiodic stochastic resonance and inverse periodic stochastic resonance may be observed.