On minimum peak-to-average power ratio spectral factorization

The design of a filter with a given autocorrelation function — or in other words, the factorization of an autocorrelation sequence — is a standard task in digital communications. This paper demonstrates that different spectral factors have a different impact on finite-support random sequences in terms of peak-to-average power ratio. It is shown that selecting the factor with minimum ℓ1-norm when implementing a digital filter is a penalty-free way to decrease a filtered signal's peakiness. Potential benefit and limitations in practical applications are explored.