Crest factor minimization of multisine signals based on the Chebyshev norm approximation method: With application to wafer stage FRF identification

Multisine signals serve as a common choice for excitation signals in the identification of frequency response function (FRF). To minimize the influence of noise, it is essential to maximize the signal power while adhering to the amplitude constraints imposed by the signal generation and acquisition hardware. The power of multisine signals is determined by the amplitude of each sine signal, while the amplitude of multisine signals depends on the phase of each sine signal. By optimizing the phase of each sinusoidal signal, the crest factor (CF) is reduced, leading to a decrease in signal amplitude while maintaining a constant power level. This paper presents a Levenberg-Marquardt algorithm designed to improve CF minimization for multisine excitation signals with a predetermined power spectrum. The algorithm utilizes L p -based norms (a type of p-norm) of multisine signals as the optimization objective with increasing values of p . The method proposed is compared with existing approaches for reducing the CF of multisine signals. Statistical evaluation demonstrates that the proposed CF reduction technology achieves the higher performance in terms of efficiency and effectiveness. Furthermore, the quality of the FRF measurements for the excitation signal generated by the proposed method is significantly improved, as demonstrated by FRF experiments on the wafer stage. • L p norm optimizes multisine signals, approximating L ∞ as p → ∞ to handle non-smoothness. • L-M algorithm minimizes L p norm for improved crest factor reduction and convergence. • L-M shows superior cost-effectiveness (CF minimum/average/maximum, runtime) across randomized tests vs. benchmarks.