An explanation of infrared catastrophe of 1/f power spectra

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.