An improved crest factor minimization algorithm to synthesize multisines with arbitrary spectrum

Abstract

Multisine signal with a low crest factor (CF) can bring a high signal-to-noise ratio for fast frequency response function (FRF) estimation. Synthesis of a low CF multisine with the given amplitude spectrum depends on optimum selection of the initial phases of its cosinusoidal components. The solutions investigated can be generally divided into two branches: (1) the analytical method based on direct formula calculation; and (2) the numerical method based on iterative computations. The analytical method works well only for an equidistant and flat amplitude spectrum, while the numerical method can generally output better results, even for a sparse or non-flat spectrum, but the number of iterations might be huge. This paper presents an improved CF minimization algorithm to synthesize multisine signals based on the combination of the previous Schroeder analytical method and the Van der Ouderaa (VDO) iteration procedure. The improved algorithm adopts the Schroder phases as the iterative initial phases, and employs a logarithmic clip function of the iterative index i in the VDO iteration procedure. Comprehensive experiments of multisine synthesis on three types of cosinusoidal amplitude spectra are performed, and the resulting CFs remain the lowest level in all cases compared with the earlier methods. The proposed algorithm provides a fast and efficient solution to synthesize multisine with the lowest CF for an arbitrary user-prescribed spectrum.