While noise is by definition derived from a random signal, it can have different characteristic statistical properties corresponding to different mappings from a source of randomness to the concrete noise.
With different types named after different colors, and is common in different disciplines where noise is an important factor (like acoustics, electrical engineering, and physics). However, different fields may use the terminology with different degrees of specificity.
Many of these definitions assume a signal with components at all frequencies, with a power spectral density per unit of bandwidth proportional to 1/f b β and hence they are examples of power-law noise.
For instance, the spectral density of white noise is flat (b = 0), while flicker or pink noise has b = 1, and brown noise has b = 2.
