Pink noise

Pink noise, noise or fractal noise is a signal or process with a frequency spectrum such that the power spectral density (power per frequency interval) is inversely proportional to the frequency of the signal. In pink noise, each octave interval (halving or doubling in frequency) carries an equal amount of noise energy. Pink noise sounds like a waterfall. It is often used to tune loudspeaker systems in professional audio. Pink noise is one of the most commonly observed signals in biological systems. The name arises from the pink appearance of visible light with this power spectrum. This is in contrast with white noise which has equal intensity per frequency interval. Within the scientific literature, the term 1/f noise is sometimes used loosely to refer to any noise with a power spectral density of the form where f is frequency, and 0 < α < 2, with exponent α usually close to 1. One-dimensional signals with α = 1 are usually called pink noise. The following function describes a length one-dimensional pink noise signal (i.e. a Gaussian white noise signal with zero mean and sd that has been filtered), as a sum of sine waves with different frequencies, whose amplitudes fall off inversely with the square root of frequency (so that power, which is the square of amplitude, falls off inversely with frequency), and phases are random: are iid chi-distributed variables, and are uniform random. In a two-dimensional pink noise signal, the amplitude at any orientation falls off inversely with frequency. A pink noise square of length can be written as: General 1/f α-like noises occur widely in nature and are a source of considerable interest in many fields. Noises with α near 1 generally come from condensed-matter systems in quasi-equilibrium, as discussed below. Noises with a broad range of α generally correspond to a wide range of non-equilibrium driven dynamical systems. Pink noise sources include flicker noise in electronic devices.