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 alpha(0). Using the spectrum analysis, we find that the corresponding binary sequences have pure 1/f(alpha) power spectrum and spectrum exponents alpha is an element of [0.0, 2.0], where f is the frequency. We evaluate numerically the relation between alpha and alpha(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 alpha < 1 and alpha > 1, and binary sequences become more and more ordered as alpha increases. (C) 2011 Elsevier B.V. All rights reserved.