On the relationship between 1/f and α-stable processes
ICASSP(1998)
Abstract
1/fβ-type spectral behavior has received considerable attention in the past few years because it arises from a wide range of natural phenomena. By expressing a 1/fβ process as a fractional integral of white noise, we show that, if β<1, the process is stationary and follows an α-stable model, while if β>1, the process has stationary α-stable increments. We also provide closed form expressions for the relationship between β and α. The theoretical results are verified via real ultrasound data. Ultrasound breast data, or their increments, which appear to be 1/fβ, are shown to follow reasonably well the α-stable model
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Key words
1/f noise,ultrasound breast data,1/f process,statistical analysis,fractional integral,biomedical ultrasonics,α-stable process,ultrasound data,spectral analysis,closed form expressions,white noise,stationary process,1/fβ-type spectral behavior,α-stable model,ultrasound,frequency domain analysis,mathematical model,stable process,wavelet analysis
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