Crest-factor minimization using nonlinear Chebyshev approximation methods

Low crest-factor of excitation and response signals is desirable in transfer function measurements, since this allows the maximization of the signal-to-noise ratios (SNRs) for given allowable amplitude ranges of the signals. The authors present a new crest-factor minimization algorithm for periodic signals with prescribed power spectrum. The algorithm is based on approximation of the nondifferentiable Chebyshev (minimax) norm by l_p-norms with increasing values of p, and the calculations are accelerated by using FFTs. Several signals related by linear systems can also be compressed simultaneously. The resulting crest-factors are significantly better than those provided by earlier methods. It is shown that the peak value of a signal can be further decreased by allowing some extra energy at additional frequencies