Optimized Gradient-Based Method for Crest Factor Minimization of a Multisine Signal

Accurate system identification requires excitation signals that deliver sufficient broadband energy while maintaining controlled peak levels at the input. In this context, minimizing the crest factor (CR) of multisine signals is essential to improve frequency response function (FRF) estimation accuracy. This work proposes an optimized gradient-based algorithm that integrates the Newton–Raphson method with the Levenberg– Marquardt (LM) scheme, where closed-form gradient and Hessian expressions are derived to ensure stability and efficient convergence. A systematic procedure for selecting the LM damping coefficient is introduced, where multiple candidate values are tested during the initial iterations and the best one is retained, ensuring stable convergence and consistent performance across different multisine scenarios. The method is validated on five multisine configurations with varying harmonic counts, amplitude distributions, and frequency spacings, each repeated over 1000 realizations. Compared with Guillaume’s method, the proposed approach achieved consistent improvements, reducing the minimum CR from 1.3700 to 1.3502 (31 harmonics) and from 1.3512 to 1.3481 (100 harmonics), representing the lowest reported values in the literature. Across all cases, the improvement rate exceeded 70% of realizations, reaching 91.7% for exponential–flat spectra. Although the computation time increased by 1.2–3.5×, the method consistently delivered superior minimum and average CR values. These results establish new benchmark values for multisine excitation design, confirming the method’s effectiveness for accurate and efficient system identification.