Synthesis of low-peak-factor signals and binary sequences with low autocorrelation (Corresp.)

This correspondence considers the problem of how to adjust the phase angles of a periodic signal with a given power spectrum to minimize its peak-to-peak amplitude. This "peak-factor problem" arises in radar, sonar, and numerous other applications. However, in spite of the wide-spread interest it has evoked, the peak-factor problem has so far defied solution except in cases where the number of spectral components is small enough to permit an effectively exhaustive search of all phase angle combinations. In this correspondence, a formula for the phase angles is derived that yields generally low peak factors, often comparable to that of a sinusoidal signal of equal power. A formula is also derived for the case in which the phase angles are restricted to 0 and
\pi
. The latter formula is applicable to the problem of constructing binary sequences of arbitrary length with Iow autocorrelation coefficients for nonzero shifts.