An explanation of infrared catastrophe of 1/f power spectra

2003/05/09 by W. Chen, Chen, W.
Mathematics · Physics and Astronomy · #26A33 #26Axx #60Gxx #74Dxx #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #math-ph #math.MP #math.PR #msc:26A33 #msc:26Axx #msc:60Gxx #msc:74Dxx

paper · pdf · doi:10.48550/arxiv.math-ph/0305019

Welcome any comments to [email protected]

arxiv created 2003/05/09 · arxiv updated 2009/11/30

Abstract

Chen [1] builds the intrinsic link between the 1/f power spectra and the acoustic frequency power law dissipation and, accordingly, presents two explanations of the so-called infrared catastrophe of the 1/f power spectra. This note is an immediate follow-up. The major progress is to connect the 1/f power spectra and the power law dissipation of an acoustic signal of finite duration, and then, we factor out the augmented function in the 1/f power spectra, predicted by Mandelbrot [2]. The resolution of the infrared catastrophe puzzle is an easy byproduct of this research. In the appendix, we give a brief comment on the exponent of the 1/f power spectra of intermittent turbulence.

Related

• 1/f spectral trend and frequency power law of lossy media
• 1/f Noise and the Infrared Catastrophe
• A general approach for analyzing baseline power spectral densities: Zwanzig-Mori projection operators and the generalized Langevin equation
• Scaling properties of signals as origin of 1/f noise
• Dynamic Synchronization and Resonance as a Universal Origin of 1/f Fluctuations -- Amplitude Modulation Across Music and Nature