An algorithm for synthesis of low-peak-factor periodic functions

Abstract

Peak factor (PF) is the ratio of the range to the rms value of a periodic function. A low PF is desirable in applications such as radar, sonar, communications techniques, and the design of test signals. The PF of a frequency-modulated (fm) periodic function is low because the peak-to-peak amplitude remains fixed and the rms value changes very little for all values of the modulation index. But in some applications an ‘‘fm-like’’ function is undesirable, and for many applications a low PF periodic function consisting of a specified number of equal-amplitude and harmonically related frequency components is sought. Here, results from an algorithm that uses phases of some spectral components of a frequency-modulated sinusoid to construct low PF functions with M harmonically related and equal-amplitude components are presented for the range 1≤M≤101. These functions are less fm-like than frequency-truncated fm functions. [Work performed in the ONR Scientific Officer Research Program.]