The power spectrum of a stationary process is calculated using the Wiener - Khinchin theorem which gives the connection between the power spectrum and the correlation function of the observed process [1, 2]. In many experiments the spectrum exhibits 1/f^ß  spectral behavior, i.e. the spectral density is observed at low frequencies as S(ω)~ω^-ß where 0 < ß < 2. This power-law behavior seems unphysical since the total energy diverges, thus the noise cannot be described with the stationary Wiener - Khinchin theorem. We have found that the  1/f^ß noise possess nonstationarity, i.e. the spectrum is time-dependent [3-5]. The time dependence of the 1/f^ß spectrum resolves the so called "1/f paradox".

The nonstationary 1/f^ß noise is backed by only two noteworthy experimental evidences. The spectrum of intermittent quantum dots was measured showing that the 1/f^ß spectrum ages as the measurement time is increased, indicating a nonstationary behavior [6]. Furthermore this aging 1/f^ß behavior was measured in the interface fluctuations in the (1+1)-dimensional Kardar-Parisi-Zhang universality class [7]. However, in many other processes, the 1/f^ß noise does not exhibit experimental evidences of nonstationarity and the famous paradox apparently remains open.

The tension between the requirement of time-dependent 1/f^ß noise and the experimental evidences which support the stationarity is reduced in three levels: (i) we have shown that an unbounded process may present an appearance of time-independent 1/f^ß noise, while for bounded process the 1/f^ß noise ages [3-5], We note that for unbounded process there is no paradoxial behavior of 1/f noise anyway. (ii) in macroscopic measurements the spectrum appears stationary while in the single-particle measurements the aging 1/f^ß is recovered [8], and (iii) if the fixed waiting time is much longer than the measurement time the 1/f^ß spectrum does not depend on the measurement time [9].

[1] R.Kubo, M.Toda, and H. Hashitsume, Statistical Physics II- Nonequilibrium Statistical Mechanics, Springer (1995).

[2] M. B. Priestley, Spectral Analysis and Time Series, Academic Press, London (1981).

[3] N. Leibovich and E. Barkai, Aging Wiener-Khinchin Theorem, Phys. Rev. Lett. 115, 080602 (2015).

[4] A. Dechant and E. Lutz, Wiener-Khinchin theorem for nonstationary scale-invariant processes, Phys. Rev. Lett. 115, 080603 (2015).

[5] N. Leibovich, A. Dechant, E. Lutz and E. Barkai, Aging Wiener-Khinchin Theorem and Critical Exponents of 1/f^ß Noise, Phys. Rev. E, 94, 052130 (2016).

[6] S. Sadegh, E. Barkai and D. Krapf, Five critical exponents describing 1/f noise for intermittent quantum dots, New J. Phys. 16, 113054 (2014).

[7] K.A.Takeuchi, 1/f^ß power spectrum in the KardarParisi Zhang universality class, J. Phys. A: Math. Theor. 50, 264006 (2017).

[8] N. Leibovich and E. Barkai, Conditional 1/f^ß noise: From single molecules to macroscopic measurement, Phys. Rev. E. 96, 0321232 (2017).

[9] N. Leibovich and E. Barkai, 1/f^ß noise for scale-invariant processes: How long you wait matters, Eur. Phys. J. B 90, 229 (2017).