Statistical properties of one-dimensional binary sequences with power-law power spectrum

By the Fourier filtering method, we generate one-dimensional binary sequences from coarse-grained continuous sequences with preset exponents α 0 . Using the spectrum analysis, we find that the corresponding binary sequences have pure 1 / f α power spectrum and spectrum exponents α ∈ [ 0.0 , 2.0 ] , where f is the frequency. We evaluate numerically the relation between α and α 0 . Using the autocorrelation function analysis, the detrended fluctuation analysis, the duration time analysis and the entropy analysis, we investigate extensively the statistical properties of such binary sequences. We find that the statistical properties are basically different for α < 1 and α > 1 , and binary sequences become more and more ordered as α increases.