WAVELET-BASED REPRESENTATIONS FOR THE 1/F FAMILY OF FRACTAL PROCESSES

The 1/f family of fractal random processes model a truly extraordinary range of natural and man-made phenomena, many of which arise in a variety of signal processing scenarios. Yet despite their apparent importance, the lack of convenient representations for 1/f processes has, at least until recently, strongly limited their popularity. In this paper, we demonstrate that 1/f processes are, in a broad sense, optimally represented in terms of orthonormal wavelet bases. Specifically, via a useful frequency-domain characterization for 1/f processes, we develop the wavelet expansion's role as a Karhunen-Loeve-type expansion for 1/f processes. As an illustration of potential, we show that wavelet-based representations naturally lead to highly efficient solutions to some fundamental detection and estimation problems involving 1/f processes.