Low Peak Derivative Sum of Sines

This paper proposes a method to generate multisines signals with reduced peak derivative. This is done by adjusting the phases in the Fourier domain with Genetic Algorithm such that in the time domain the maximum absolute signal's derivative is minimized. The performance evaluation is made by comparing the method to signals with the same spectrum but with phase adjusted randomly. It will be shown for an audio test signal case study of a multisines signal comprising 2500 sines that a reduction of 42% with respect to the mean maximum peak derivative and 31% with respect to the minimum maximum peak derivative over 1 million random trials. The proposed method is contrasted with a low crest factor signal method. It is found that there is a positive correlation between peak amplitude and peak derivative when signals are generated with random phases. Moreover, the signals obtained by minimizing either the peak amplitude of the peak derivative had also good performances with respect to the non-optimized criterion.