Wavelet-based spectral analysis of 1/f processes

The authors attempt to show how and why a time-scale-based spectral estimation naturally suits the nature of 1/f processes, characterized by a power spectral density proportional to mod nu mod /sup - alpha /. They show that a time-scale approach allows an unbiased estimation of the spectral exponent alpha and interpret this result in terms of matched tilings of the time-frequency plane. They derive explicitly the probability density function of the estimated value of alpha . From this analysis, they find that there exists an optimum number of scales to use in a discrete wavelet scheme for obtaining a minimum variance estimator and that an improved procedure can be designed by making use of weighted least-squares in the estimation.<>