Origin of Diverse 1/f Fluctuations―Amplitude Modulation and Demodulation

Abstract

The origin of diverse 1/f fluctuations is identified as a process of amplitude modulation and demodulation. Specifically, a large number of waves with systematically accumulating frequencies interfere with each other to generate beats that modulate signals in the low-frequency region. Synchronization, resonance, and infrared divergence are proposed as mechanisms for frequency accumulation. These modulated low-frequency signals emerge after various demodulation processes. To verify this explanation, we examine 1/f fluctuations observed in music, earthquakes, solar flares, and electric currents. The corresponding demodulation processes are, respectively, the data-squaring, fault rupture, magnetic reconnection, and the electric current as a square of the wave packet.