The nonlinear Characteristic Output Spectrum (nCOS) function provides an explicit and analytically tractable representation of the relationship between a nonlinear system’s output spectrum and its key parametric characteristics—namely, excitation frequency, nonlinear coefficients, and input amplitude. This formulation significantly advances the theoretical understanding and practical implementation of nonlinear system analysis and design in the frequency domain. Given simulation or experimental output data, the nCOS function can be accurately constructed to capture contributions from arbitrarily high-order nonlinearities. Compared to conventional simulation-based or purely theoretical approaches, this method requires substantially fewer simulation trials and incurs lower computational overhead, thereby enhancing efficiency without compromising accuracy. Moreover, the nCOS framework facilitates the precise decomposition of the nonlinear output spectrum into its linear and nonlinear components, enabling detailed insight into the system’s dynamic behavior. These capabilities are particularly valuable for a wide range of engineering applications, including nonlinear system identification, signal processing, fault diagnosis, and performance optimization.