Analysis of 1/f processes

Abstract

1/f processes can be very useful in modeling processes with long term correlation. We propose a simple yet efficient algorithm for analysis and synthesis of these processes. Unlike previous techniques, our analysis procedure generates uncorrelated decomposition coefficients for the 1/f process. This is done by taking into account, and then removing, the residual correlation between the wavelet components. The analysis procedure is the major contribution of this work. The proposed synthesis algorithm, which is a by-product of the proposed analysis algorithm, is competitive with other techniques. These procedures can be very useful in different fractal signal processing applications.