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

被引:214
作者
WORNELL, GW
机构
[1] Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA
关键词
D O I
10.1109/5.241506
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
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.
引用
收藏
页码:1428 / 1450
页数:23
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